Streptococcus pneumoniae is a human pathogen that is a major cause of infant mortality. Identifying the pneumococcal serotype is an important step in monitoring the impact of vaccines used to protect against disease. Genomic microarrays provide an effective method for molecular serotyping. Previously we developed an empirical Bayesian model for the classification of serotypes from a molecular serotyping array. With only few samples available, a model driven approach was the only option. In the meanwhile, several thousand samples have been made available to us, providing an opportunity to investigate serotype classification by machine learning methods, which could complement the Bayesian model.We compare the performance of the original Bayesian model with two machine learning algorithms: Gradient Boosting Machines and Random Forests. We present our results as an example of a generic strategy whereby a preliminary probabilistic model is complemented or replaced by a machine learning classifier once enough data are available. Despite the availability of thousands of serotyping arrays, a problem encountered when applying machine learning methods is the lack of training data containing mixtures of serotypes; due to the large number of possible combinations. Most of the available training data comprises samples with only a single serotype. To overcome the lack of training data we implemented an iterative analysis, creating artificial training data of serotype mixtures by combining raw data from single serotype arrays.With the enhanced training set the machine learning algorithms out perform the original Bayesian model. However, for serotypes currently lacking sufficient training data the best performing implementation was a combination of the results of the Bayesian Model and the Gradient Boosting Machine. As well as being an effective method for classifying biological data, machine learning can also be used as an efficient method for revealing subtle biological insights, which we illustrate with an example. Streptococcus pneumoniae [Streptococcus pneumoniae is an important human pathogen and a major cause of infant mortality. There are over ninety known serotypes of the bacterium and there is a requirement to monitor the population dynamics of the different S. pneumoniae serotypes worldwide. A custom molecular serotyping array [We investigate different approaches to analysing the raw data from a custom genomic microarray that has been designed for molecular serotyping eumoniae , 2. Streng array  was deveGenomic microarrays are a method for detecting the presence or absence of multiple genes within a sample simultaneously, through specific binding to an array of high-density probes. A microarray constructed with probes for genes specific to different strains of an organism can detect the presence of a particular strain of the organism in a clinical sample according to which of the probes have an elevated signal.μGS SP-CPS molecular serotyping microarray [S. pneumoniae capsular polysaccharide synthesis (cps) genes. Each serotype is known to contain a small subset of these cps genes, ranging from 1 to 22 genes. However, there is considerable overlap between the subsets with no serotype having a set of genes unique to itself. In fact a few serotypes have identical, or near identical, subsets of cps genes, so in order to distinguish these serotypes the array contains further discriminative probes. An analysis method to produce a call as to which serotypes are present in a sample has to process these two types of probe and also allow for cross-hybridisation to probes and cope with the inevitable experimental noise. An empirical Bayesian model was an obvious choice of method, given this need to integrate data types with prior knowledge.The custom B croarray  containsThe model we developed  has provStreptococcus pneumoniae serotyping method is the ability to detect multiple serotypes in a sample. The main difficulty of applying machine learning to this particular problem is insufficient samples available containing all possible combinations of mixtures of serotypes. We overcame this limitation by implementing an two-step iterative approach which involves the construction of artificial training data.There are now a considerable number of training samples available that contain single serotypes. However, an important requirement for any The two machine learning methods investigated here are Random Forests (RF) and Gradient Boosting Machines (GBM). Random Forests is an ensemble learning method that uses decision trees to classify the data. To mitigate the tendency to overfit, many decision trees are fitted to the data and the mode of the predicted classes taken. Gradient Boosting Machines (GBMs) is also an ensemble learning method and in the current application, also uses decision trees. Unlike Random Forests, GBMs use boosting, that is, the ensemble of trees are fit in sequence and at each step the tree is fitted not to the data but to the residual error from the fit of the ensemble so far.The purpose of the study was to evaluate the analysis of the molecular serotyping microarray by machine learning methods, firstly as a classifier but also as a biological research tool. A further purpose of this study is to propose some generic strategies for the application of machine learning methods, for example, how to combine a statistical model with a machine learning classifier, or how to compensate for the lack of training data due to a combinatorial explosion of classification options.cps genes. On average there are 10 probes per gene. These probes are the primary source of information on the serotypes in the sample. Figure cps genes and the CPS probes on the array.Probes, referred to here as CPS probes, for 441 capsular polysaccharide synthesis cps genes alone.Probes, referred to here as STID probes, designed to identify serotypes that are too closely related to be resolved by the entire genome of Streptococcus pneumoniae from two sequenced strains of the bacterium, 6824 probes in total and referred to here as the genome probes. In the context of the current study these probes are used only to provide a reference level with which to normalise the arrays for the machine learning algorithms and in the derivation of priors for the Bayesian model.Probes on the microarray for the The custom genomic microarray  containsp-values from the t-tests for the top 75 genes.Figure S. pneumoniae contains a small subset of the 441 cps genes. The number of cps genes present in a serotype varies from 1 to 22, with an average of 13. There is considerable overlap in the gene complements of serotypes, with no serotype having a unique set of cps genes. In Fig. cps genes of the serotype found in the sample being tested by this microarray are marked in black. It can be seen that some cps genes that do not occur in this serotype also have elevated intensities. This is due to cross-hybridization of probes. This occurs when it has not been possible to design probes entirely specific to a particular gene, so probes for one gene bind to some extent to the DNA from a different gene.Each serotype of Streptococcus pneumoniae. Figure cps genes found in the three serotypes are shown in the figure for clarity. It can be seen that some of the cps genes are found in more than one of the serotypes contained in this sample, and one gene is found in all three.It is not uncommon for naso-pharyngeal samples to contain more than one serotype of cps genes, so cannot be distinguished by these probes alone. In order to differentiate between these closely related serotypes, the microarray contains extra probes, here referred to as STIDs. STID probes for a pair of serotypes come in pairs, with one probe for one serotype and a paired probe for the corresponding region of the genome of the second serotype. To test which of the two serotypes is present the difference in the fluorescent intensities of the paired probes is used. On average there will be around 65 pairs of STID probes for a pair of serotypes.Whilst the CPS probes are the primary measurements on the array for determining serotype content, eighteen sets of closely related serotypes have identical, or nearly identical, sets of Streptococcus pneumoniae sample can be contaminated by DNA from the host and from other commensal or pathogenic organisms. This could also bind to some extent to a probe, affecting the probe’s measured intensity.The arrays also suffer inevitably from different types of experimental noise. The fluorescent intensity signals can be affected by a variety of random factors which are difficult to control: from variation in the DNA extraction to variation in the binding of the DNA to its oligonucleotide probe due to divergent sequence. As mentioned above a probe’s intensity may be affected by cross-hybridisation; binding to DNA from a different gene. However in addition, the The dataset used in this work is an amalgamation of data from 60 different studies comprising more than four thousand samples. Every sample has initially been analysed by an empirical Bayesian Model and the result checked for errors by a single expert.A sample may contain between 1 and 5 serotypes. Figure http://sysbio.mrc-bsu.cam.ac.uk/papers_supplementary.In the dataset of single serotype arrays the frequency of occurrence of serotypes is very variable, there are many examples of some serotypes, whilst very few of some others. The histogram in Fig. Xcps) and the median of the genome probes (Xgen). All values x on the array were then normalised by xnorm=(x−Xcps)/(Xgen−Xcps). The normalised values were then logged. Initially the machine learning algorithms were applied to these CPS probe values directly, but the large number of probes resulted in relatively slow processing times. Therefore the CPS probe values were summarised to give one value for each of the 441 cps genes. Different summary methods were experimented with - mean, median, t-statistic and p-values. The p-values were found to work consistently well so these were adopted as the cps summary measure throughout the study. For each cps gene the p-values were calculated by testing whether the mean of the gene’s CPS probes was greater than the mean of all other CPS probes. The STID probes for a pair of serotypes are paired so the relevant measure is the difference in value between each probe pair. For each STID differentiated pair of serotypes there are approximately 65 such difference values, which were summarised by the p-value from testing whether their mean was significantly greater than zero. The R statistical environment [For the Bayesian model no pre-processing was applied, since each array is analysed on its own without reference to other arrays. For the machine learning algorithms the arrays were first normalised. To normalise an array two reference levels were calculated; the median of the CPS probes on the array  of these K serotypes.Form all 2cps genes’ probe values.Calculate the proportions of the constituent serotypes in the test array data from the medians of the serotypes’ M artificial mixture arrays by combining randomly selected single serotype arrays, corresponding to the constituent serotypes, in the calculated proportions (setting M to 200 was sufficient in practice). The artificial mixture arrays were constructed by combining the single serotype arrays at the probe level. That is, in the artificial array a probe value is the weighted mean of the corresponding probe values in the single serotype arrays, weighted by the proportions calculated in point 3. The probe values are then summarised as cps gene p -values as described in the ‘Construct For each of these combinations: M artificial arrays for the Kc combinations to create a new training data set.Concatenate the Train a new classifier on these artificial mixture arrays.Re-test the unknown array with the new classifier and choose the most probable class, giving the predicted serotype combination for the array.In the two-step method we train the machine learning algorithm on a set of single serotype arrays . Then, to test an unknown array, the first step is to use the classifier that has been generated by the training to predict the single serotypes on the unknown array. Then in the second step: K most probable predicted serotypes (point 1 above) the list of predicted serotypes is edited for serotypes which are separated by STIDs; for pairs of serotypes that are separated by STIDs the serotype that has the lowest predicted probability is removed from the list.Before choosing the top K, the number of most probable predicted serotypes (point 1 above), was chosen dynamically. Firstly the cps gene p-values where Bonferroni adjusted. Then for each serotype in the list of predicted serotypes, the percentage of that serotype’s cps genes that have adjusted p-values less than 0.05 was calculated. The serotypes with more that 50% of their cps genes significantly present were chosen for the second step. In practice K was rarely more than one more than the actual number of serotypes on the array. A limit of K<=6 was set to prevent excessive processing times occurring.In practice cps genes that are significantly present. For each array and each method the serotypes in the call from that method are examined in turn. The Bonferroni adjusted p-values of the cps genes are used to assess whether each gene is present or not. If a gene’s p-value is below a significance level of 0.05 the gene is deemed to be present. If a serotype has less than a pre-determined percentage of it unique cps genes present then the serotype is removed from the call. Note that only the cps genes that are unique to a serotype are considered. In a call containing several serotypes, in general some cps genes will be common to two or more serotypes, whilst some will be unique to each individual serotype; Fig. cps genes that are significantly present which is calculated.The Machine learning algorithms in particular were found to be overly sensitive so a final filtering step can be used to remove False Positives from an algorithm’s call. The filtering step is based on the percentage of a serotype’s cps genes that were significantly present. If all the serotypes in the call had more than a predetermined percentage threshold of cps genes present, then that sample was placed in the high confidence group of samples.This form of filtering was also used for a second role, that is, to divide the classified arrays into two categories with different confidence of prediction. For a sample and classification method, we inspected the serotype calls. For each serotype in the call we recorded the percentage of the serotype’s unique The results for each method were compared to curated results to give error rates for each method, applied to each of the datasets. The error rates used were the percentage of arrays in the dataset which contained at least one False Positive serotype call or False Negative call or both. Credible intervals for the error rates were calculated using the 0.025 and 0.95 quantiles of the beta distribution. The curated results were based on the Bayesian Model results, which were used as a guide by the expert who inspected the arrays. Therefore there is the danger that the comparison will be biased in favour of the Bayesian Model over the Machine learning algorithms. We were however interested in ascertaining whether the Machine learning algorithms perform better than the Bayesian model so any bias will be acting to reduce rather than enhance the outcome we were looking for.p-value vectors we turned to two representative and popular Machine learning methods. The implementations of Random Forests and Gradient Boosting Machines contained in the machine learning platform H2O [For the purpose of predicting sets of serotypes from form H2O  were useform H2O  interfacform H2O .The algorithms’ parameters were optimised using a grid search. Performance of different parameter combinations was assessed from the sum of two error rates. One was the error rate from the confusion matrix generated by the single serotype training data, that is, the performance of the algorithm as a single class classifier. Secondly the resulting classifier was applied to the mixture arrays. For each mixture array the list of the top six most probable predicted serotypes was examined to see if it contained all of the serotypes actually occurring in the sample. If all the actual serotypes were contained in the top six the test array was passed as not being an error, but if this was not the case the array was recorded as an error. The grid search minimised these two error rates combined. The parameter values used are shown in Table For the Random Forest as a single serotype classifier the parameters needed to be changed from the default settings. In particular, balancing the classes was important for reducing the error rate. Perfect single serotype classification was not achieved but the error rate was around 0.1%. Again this did not vary whether applied to a cross-validation subset or to the whole dataset. Further adjustment of parameters was carried out to minimise the second error rate. The optimum parameter adjustments were the same if the classifier was trained on the whole dataset or on one of the cross-validation subsets.Kc x 200 arrays, where Kc could be as high as 63. The time taken for these was minimised using the parSapply routine from the R package doParallel [http://sysbio.mrc-bsu.cam.ac.uk/papers_supplementary.The main speed constraint in the code is the fact that multiple t-tests are required. Four hundred forty one tests are needed for each of the Parallel , to distParallel , was usesingle serotype arrays to be used for training a classifier for the rare serotypes. For each of the single serotype arrays, we recorded the CPS probe values for the cps genes known to occur in that serotype, and the CPS probe values for all other cps genes on the array. We concatenated these two sets of probe values for all the arrays to produce two distributions - a distribution of probes for genes present  and a distribution of probes for genes absent (the null distribution). To create an artificial array for a particular serotype we took the known cps gene profile for the serotype in question and sampled from the alternative distribution to generate CPS probe values for those genes, and sampled from the null distribution to generate CPS probe values for all other genes. In this way we created 200 single serotype arrays for each serotype. In order to be able to validate the performance we explored the idea using the D.36 dataset. We used this artificial single serotype dataset to train a classifier and predict the D.36 arrays using the two-step process described above and compared the results with those obtained using a classifier trained on the actual D.36 single serotype arrays.The data currently available contains no examples of 18 particularly rare serotypes and few (less than 20) examples of 37 other serotypes. We investigated the possibility of generating entirely artificial The error rates for the three methods, the Bayesian Model, GBM and Random Forest, are shown in Table For the D.73 dataset, which includes serotypes with little training data, the three methods give roughly the same results for mixture arrays. The Bayesian Model, unaffected by lack of training data, has the same error rate as for D.36, but the machine learning error rates are increased greatly, reflecting insufficient training data for many serotypes in the dataset. For single serotype arrays, again the Bayesian Model has a similar error rate to D.36 but the two machine learning methods error rates are much worse. This suggests that at least 20 training examples are needed for successful machine learning of serotyping data.cps genes that are significantly  present. For each sample and for each method, the serotypes in the method’s call are examined to see what percentage of their cps genes are significantly present. If fewer cps genes are significantly present than a set percentage threshold then this serotype is removed from the method’s call.However, as described in the “Figure single serotype arrays to be used for training a classifier for the rare serotypes. In order to be able to validate the approach we used the D.36 dataset. For simplicity we removed all arrays containing serotypes with STIDS. This left 28 serotypes and 3486 single serotype arrays and 339 mixture arrays. The results are shown in Table We investigated the possibility of generating entirely artificial The GBM gives a lower error rate than the Bayesian Model, however a paucity of training data for some serotypes in the D.73 dataset does increase the GBM error rate. In addition 18 known serotypes which could be encountered in clinical samples currently lack any training data at all. An attempt to create artificial training data was unsuccessful, so until sufficient actual training data is available for all serotypes the Bayesian model will have to be used to analyse the arrays. The Bayesian model is unaffected by lack of training data, giving similar error rates for both the D.73 and the D.36 dataset.We investigated whether the GBM could be used to divide samples into two categories; a group of samples which we have high confidence in the class assignments (group C) and a second group of samples whose class assignments are less confident (group NC). There will clearly be a trade off, lowering the expected error rate that would be acceptable in group C, will increase the number of samples allocated to group NC.We investigated two different methods for dividing the dataset into the two groups. Firstly, for each sample, if the serotype calls from the Bayesian model and from the GBM were identical then the sample was placed in group C, that is, the high confidence group. If the serotype calls differed then the sample was placed in group NC. For the D.36 dataset we found group C contained 84% of the dataset with an error rate of just 0.37%. For the D.73 dataset group C contained 72% of the dataset with an error rate of 0.69%. These results may be biased since they include the Bayesian model results and, as explained in the “cps genes significantly present. For each sample and each classification method separately, we inspected the serotype calls. For each serotype in the call we recorded the percentage of the serotype’s unique cps genes that were significantly present . If all the serotypes in the call had more than a predetermined percentage threshold of cps genes present, then that sample was placed in group C, the high confidence group. If any of the serotypes had less than this percentage of genes present then the sample was placed in group NC. Percentage thresholds from 65 to 100% were tested. The percentage of samples placed in group C and the error rate in the group were recorded. The results for the GBM on the dataset D.36 are shown in Fig. The second method for creating two groups used a threshold on the percentage of a serotype’s The results for the D.73 dataset are also shown in Fig. cps genes lower than a predetermined threshold were moved from group C to group NC. The results for the D.36 dataset are shown in Fig. Finally we investigated combining the two different methods to define the two groups. We first divided the dataset based on the agreement between the Bayesian model and the GBM. We then examined the samples in group C using the second method for defining groups. Samples that had any called serotypes with a percentage of cps genes) in classifying each serotype. The H2O [Training on the single serotype arrays gives the relative importance of the variables  and 193 arrays containing serotype 6B (black dots). It can be seen that gene 81.02 is significantly present in both 6A and 6B arrays, with all p-values less than 0.05 . However the gene’s probes have a noticeably lower median intensity and higher standard deviation in most 6B arrays compared to the values in 6A arrays, suggesting that there is some sequence divergence in gene 81.02 between serotypes 6A and 6B. This is an example of how machine learning algorithms easily pick up on subtle differences that humans may miss.Investigating gene 81.02 in more detail. Figure A machine learning approach using a Gradient Boosting Machine can give a better error rate classifying serotyping data than even a carefully crafted Bayesian model. A lack of training examples containing mixtures of serotypes can be overcome with an iterative two-step approach that creates artificial mixture arrays from single serotype arrays. Sufficient single serotype training data is important, but even with relatively few training examples machine learning still gives a better performance than the Bayesian model provided an extra filtering step is included to remove False Positives. Of the two machine learning algorithms tested the GBM performed better than Random Forests.cps gene profiles of the serotypes. The strength of the machine learning approach is that there may be features in the data important for accurate classification which are currently unknown but which machine learning can identify automatically. And with sufficient training examples machine learning can cope with biological and experimental variability in features important for classification. The errors that do occur in the results from the GBM algorithm may be due to biological variability occurring in the erroneous samples, variability that the algorithm has not been sufficiently trained to detect.The Bayesian model relies on known prior information such as the Because training data is not available for all serotypes, in practice the Bayesian model will still need to be used to analyse the arrays, but we have shown that combining the results with those from the GBM can be used to assign arrays to a high confidence group with a very low error rate. The added advantage of a machine learning approach is that as further data becomes available the classifier can be updated with a view to increasing the prediction accuracy and increasing the proportion of arrays assigned to the high confidence group.cps gene profile of a new serotype can be added straight away to the information supplied to the Bayesian model, whereas the GBM will require training examples of the new serotype first.The bacterium is constantly evolving so it is likely that in the future the machine learning algorithm will encounter further serotypes which it will not have been trained to recognise. So probably an approach using the Bayesian model in combination with a GBM may never be entirely redundant. The advantage of the Bayesian model is that the cps genes.When no training data is available we found the Bayesian model is better than a machine learning approach that uses artificial single serotype training arrays. Lacking probe data for genes unique to the missing 18 serotypes meant that probe specific distributions were not possible. The approach also ignored cross-hybridisation effects. In future work we will investigate whether it is possible to construct better artificial training data using the information from a BLAST search of all the array probes against the sequences of the serotypes’ The study illustrates the strength of a machine learning approach for classifying genomic data with multiple variables. The algorithm learns which variables are important for classification, unlike in a modelling approach where the user has to make this choice. It also demonstrates that when suitable training data is lacking steps can be taken to create artificial training data. The general conclusion of the study however is that in practical classification problems the best approach may not be choosing between either a Bayesian modelling or a machine learning solution but using a combination of the two methods. The study also illustrates how the relative variable importance from a machine learning classification can be used as an efficient research tool to investigate differences in the objects to be classified, in this case the differences in the genomic compositions of the serotypes.


Microarray technology is important to simultaneously express multiple genes over a number of time points. Multiple classifier models, such as sparse representation (SR)-based method, have been developed to classify microarray gene expression data. These methods allocate the gene data points to different clusters. In this paper, we propose a novel collaborative representation (CR)-based classification with regularized least square to classify gene data. First, the CR codes a testing sample as a sparse linear combination of all training samples and then classifies the testing sample by evaluating which class leads to the minimum representation error. This CR-based classification approach is remarkably less complex than traditional classification methods but leads to very competitive classification results. In addition, compressive sensing approach is adopted to project the high-dimensional gene expression dataset to a lower-dimensional space which nearly contains the whole information. This compression without loss is beneficial to reduce the computational load. Experiments to detect subtypes of diseases, such as leukemia and autism spectrum disorders, are performed by analyzing the gene expression. The results show that the proposed CR-based algorithm exhibits significantly higher stability and accuracy than the traditional classifiers, such as support vector machine algorithm. The development of microarray technology facilitates the collection of information containing expression values of multiple genes under different experimental conditions. This technology also promotes and affects the progress in biological and biomedical research –3. Thereα by sparse representation over a dictionary Φ, while α is a sparse vector. Assuming that l0-norm indicates the number of non-zeros in α, the sparsity of α can be represented by l0-norm. Thus, α can be evaluated with the criteria of l0-norm minimization. However, the solution of l0-norm minimization is NP-hard, which is very time-consuming. Consequently, l1-norm minimization is considered as the alternative to l0-norm minimization because of its closest convex function of the former. The former minimization process is widely equipped with in sparse coding as follows: minα‖α‖1 s.t. ‖y − Φα‖2 ≤ ε, where ε is a small constant. Although the computational complexity of l1-norm minimization is much lower than that of l0-norm minimization, the applications of l1-norm minimization is still limited by the high complexity in real-time scenarios. Therefore, various algorithms have been presented to accelerate l1-norm minimization.Sparse representation is well-known as a powerful tool in various applications and has been highly developed for signal processing and machine learning . Sparse N signal x, that is, K-sparse in some basis can be recovered exactly in the polynomial from just M = O(K log(N/K)) linear measurements of the signal. Using the CS approach, high-dimensional feature data can be simply projected to a space with much lower dimension with a random sensing matrix. The low-dimensional data retain enough information and can recover the original high-dimensional features. In this paper, we employ a measurement matrix which is assumed to be very sparse to efficiently compress the feature from the gene expression dataset. CS facilitates the extraction of the feature data to a low-dimensional one in the compressed domain.Another issue is that the dimension of the feature space may be too high for classification algorithm. Numerous algorithms may become invalid or infeasible when lots of feature data in a dimension have to be processed –21. A sul1-norm minimization, this paper proposes a collaborative representation (CR)-based classification (CRC) to subtype gene expression datasets. CR collaboratively uses whole training samples from all classes to constitute the query sample y. CRC with regularized least square can achieve competitive classification results with considerably less complexity. Our works are beneficial in augmenting the study of sparsity-based genome-wide data pattern classification. We used benchmark cancer, autism spectrum disorder (ASD), and brain data sets, in the experiments. To measure the effectiveness of the CRC algorithm, accuracy in terms of prediction or error rate in classifying a selected gene subset is evaluated.To improve the sparse representation with computationally expensive X, the subset is naturally discriminative.In this study, the classification problem can be depicted as follows: The microarray gene data sets, which serve as sample to train, are classified for the diagnosis and prognosis of various types of diseases. To apply sparse representation model, the coding vector of y should be sparse. Moreover, coding should be performed collaboratively over the whole dataset instead of each subset. By identifying the sparsest representation of y over Classification of gene expression datasets using algorithms has been well studied for the robust diagnosis and prognosis of various diseases to achieve high prediction accuracy . The prix is required with many atoms from Φ, leading to a complex computation. Then, the orthogonality of Φ is relaxed to allow less atoms to represent x. That is, more atoms is required to be involved in Φ to allow more choices to represent x. The dictionary Φ with redundant atoms is referred to as an over-complete matrix, leading to a sparser representation of signal x. Such sparse representation has been utilized in image restoration, in which great success has been achieved.According to the theory of sparse representation, a complete dictionary of atoms, denoted by K classes of targets are assumed. Let ith class, X =  and the column of Xi is a sample belonging to class i. The existence of a microarray gene data Xα + w, where w is a vector indicating the residual, α =  and αi denotes the coding vector corresponding to class i. If y belongs to the ith class, w is a zero vector, then y = Xiαi holds. Only the coefficients in αi are significant when most entries in αj, j ≠ i are nearly zeros. That is, vector α is sparse, and its non-zero entries are used to encode the identity of sample y. α is to be reconstructed.A total number of Xi to be over-complete. However, the sample size of the gene expression data is very small compared to its high dimensionality, leading to the under-complete matrix Xi. Consequently, the representation error would be unacceptable, even when y belongs to class i. This characteristic leads to a failure decision made by the classifier. One obvious solution is to use more samples of class i to represent y. However, collecting huge number of samples is expensive. Nevertheless, differences among genes are very small such that the diverse classes of gene expression data share similarities. Thus, the testing gene y can be coded collaboratively by the dictionary of all samples X =  under the l1-norm sparsity constraint.Microarray gene expression datasets, such as breast cancer dataset, usually suffer from high dimensionality. In traditional SRC, enough training samples for each class is required for dictionary α can be determined by solving the following optimization problem:l0-optimization is an NP hard problem. Optimizations of l0-optimization and l1-optimization have recently been proved to be equivalent when α is sparse enough. In general, the sparse representation problem can be expressed as follows:l2-norm instead of that of l1-norm, Thus. the problem becomes as follows:X is over-complete, X, which can be expressed as follows:new can be classfied by evaluating the reconstruction representation errors:i. When the number of classes is too large, a stable solution of the least square X. The corresponding l2-minimization with regularized least square is as follows:P = (XTX + λI)−1XT, this formula shows that P is independent of y. Hence, P is only required to be computed once and can be shared in classifying different samples. The reduction in the complexity of CRC is not achieved at the expense of performance. Similar to SRC, i. However, the l2-norm When y is collaboratively represented with all classes containing all samples, y can be classified individually by SRC by checking class by class . The spaGene expression datasets may have very high dimensionality. High-dimensional gene expression datasets always result in high computational load and degradation of model performance of classification algorithm , 19, 21.y is a linear combination of entries in the microarray gene expression data vector x. A number of N gene expression data is assumed in every sample, but that at most K samples are collected, with K ≪ N. In random projection, a sensing matrix R with rows having unit length projects data from the high-dimensional feature M ≪ N. Each projection v is essentially identical to a compressive measurement during CS encoding. Therefore, using the CS principle, the number of data to be classified can be remarkably lower than the number of the original microarray gene data. With fewer data, the classification algorithm can also be more efficient. We refer to this reduction of microarray dimensionality as a CS dimensionality reduction.A common method of dimensionality reduction in high-dimensional classification is choosing some data from a dataset in an order and dropping the other data. This approach would inevitably result in the loss of some information. Many probes in traditional microarrays are inactive during detection. That is, the microarray gene expression data can be sparse. Only a few significant entries of gene expression data matrix may be of interest. This phenomenon suggests the fast transformation of a microarray along with the CS measurement process, where each measurement R can offer a stable embedding that approximately retains the important information in any K-sparse signal when K-sparse signals. Note that every signal pair shares the same K basis. That is, for any two K-sparse vectors x1 and x2 sharing the same K basis,N is large. The matrix which satisfies the RIP condition can be directly obtained using the Johnson-Lindenstrauss lemma. In this paper, we use a very sparse random measurement matrix with entries defined as follows:ρ = 1 or 3 satisfies the Johnson-Lindenstrauss lemma  and the test dataset ynew.Output: The classification result of s.X and y is reduced using the sensing matrix R in D and ynew are written as X and y, respectively.1: The dimensionality of X are normalized with l2-norm criteria.2: The columns of new is coded over X by P = (XTX + λI)−1XT3: y4: The regularized residuals new is determinated as Identity(ynew) = arg miniri5: The identity of yTo evaluate the classification performance, we performed experiments on two benchmark datasets and compared the proposed model with state-of-the-art models. The simulations were conducted on a system with i7-4790 CPU with 3.60 GHz processor and 8 GB RAM. The algorithms were evaluated based on accuracy to determine the rating prediction accuracy as follows:The performance of the classifiers is quantified by LOO cross-validation (LOOCV) and 10-fold cross validation (10-fold-CV). In the LOOCV scheme, each sample in the dataset was predicted by building a model from the remaining samples and recording the accuracy of each model. In 10-fold-CV, the dataset was randomly divided into 10 equally sized subsets. Nine of these subsets were used in the model construction, while the remaining subset was used for prediction.log2(RPKM+1) transformation operation was imposed on these data. The dataset had 524 samples with a developmental time point range from 8 weeks post-conception to 40 years of age from 26 brain structures. To our knowledge, this brain dataset is currently the most comprehensive transcriptome of the human developing brain. In the training dataset, the expression values for the temporospatial time points acted as features.In this study, we use gene data for leukemia and ASD to evaluate the performance of CRC. The leukemia data set was downloaded from an open resource on the website of Gene Pattern in Broad Institute. The original training data set consisted of 38 bone marrow samples (27 ALL and 11 AML), while the testing data set consisted of 35 bone marrow samples (21 ALL and 14 AML) –32. Usinhttp://www.biolab.si/supp/bi-cancer/projections/index.html   and breadex.html , and havM is sufficient to achieve good results for gene data classification. The average LOOCV accuracy under the incremental dimension reduced by CS is shown in Figs The computational load can be reduced, and overfitting can be avoided by reducing the dimensionality for a dataset. CS is used to project the high-dimensional data to a lower-dimensional space. The much lower bound for l1-minimization methods. We fixed the reduced dimensionality. In one LOOCV loop, the average running speeds of CRC and SRC are listed in We also compared the running time of CRC and SRC with fast X is overdetermined. SRC directly uses pseudoinverse to solve the l1 minimization problem. When more samples are used for training, SRC has to use the other fast l1 minimization methods, such as l_1_ls and homotopy. In such case, CRC is 7 times faster than SRC.The improved speed of CRC is obvious in the ASD database. However, in leukemia, DLBCL, and breast cancer datasets, the matrix Several state-of-art classifier models, including SRC, KNN , supportTables This paper presented a new classifier model for classifying microarray gene expression. The proposed classifier uniquely incorporates CS dimensionality reduction CS to guide data classification. This work has two important contributions. First, an effective CRC approach was implemented. This method exhibited very high performance and valuable insight into the different types of cancer data sets. CRC did not require the optimization of parameters to facilitate classification. This method can be used for different types of gene expression data with multiple classes without any modifications. Second, CS method was adopted to reduce the dimensionality of data. The sensing matrix is a very sparse random matrix with entries as 0 and S1 File(ZIP)Click here for additional data file.


PARP1 from TCGA data. Our approach is the first to test for epistasis between triplets of genes to identify biomarkers of synthetic lethality-based therapy. SurvLRT proved successful in identifying the known gene TP53BP1 as the biomarker of success of the therapy targeting PARP in BRCA1 deficient tumors. Search for other biomarkers for the same interaction revealed a region whose deletion was a more significant biomarker than deletion of TP53BP1. With the ability to detect not only pairwise but twelve different types of triple epistasis, applicability of SurvLRT goes beyond cancer therapy, to the level of characterization of shapes of fitness landscapes.Cancer aggressiveness and its effect on patient survival depends on mutations in the tumor genome. Epistatic interactions between the mutated genes may guide the choice of anticancer therapy and set predictive factors of its success. Inhibitors targeting synthetic lethal partners of genes mutated in tumors are already utilized for efficient and specific treatment in the clinic. The space of possible epistatic interactions, however, is overwhelming, and computational methods are needed to limit the experimental effort of validating the interactions for therapy and characterizing their biomarkers. Here, we introduce SurvLRT, a statistical likelihood ratio test for identifying epistatic gene pairs and triplets from cancer patient genomic and survival data. Compared to established approaches, SurvLRT performed favorable in predicting known, experimentally verified synthetic lethal partners of  Genomic alterations in tumors affect the fitness of tumor cells, controlling how well they replicate and survive compared to other cells. The landscape of tumor fitness is shaped by epistasis. Epistasis occurs when the contribution of gene alterations to the total fitness is non-linear. The type of epistatic genetic interactions with great potential for cancer therapy is synthetic lethality. Inhibitors targeting synthetic lethal partners of genes mutated in tumors can selectively kill tumor and not normal cells. Therapy based on synthetic lethality is, however, context dependent, and it is crucial to identify its biomarkers. Unfortunately, the space of possible interactions and their biomarkers is overwhelming for experimental validation. Computational pre-selection methods are required to limit the experimental effort. Here, we introduce a statistical approach called SurvLRT, for the identification of epistatic gene pairs and triplets based on patient genomic and survival data. First, we show that using SurvLRT, we can deliver synthetic lethal interactions of pairs of genes that are specific to cancer. Second, we demonstrate the applicability of SurvLRT to identify biomarkers for synthetic lethality, such as mutational status of other genes that can alleviate the synthetic effect. Fitness is a measure of replicative and survival success of an individual, relative to competitors in the same population. In this work, we consider the fitness of cells in tumors of cancer patients. Tumors of different patients, also those diagnosed with the same cancer type, display large genomic heterogeneity. Such diverse genotypes of tumor cells result in different tumor fitness, and consequently, different disease aggressiveness and patient survival.Epistasis is an interaction between genes, and in general refers to departure from independence of effects that their genomic alterations have on a phenotype of interest . BatesonBRCA1 and PARP1. BRCA1 mutations disturb error-free homologous recombinational (HR) repair of double strand breaks and the cells become acute sensitive to the lack of single strand DNA break repair, performed by the PARP protein. Thus, in BRCA1 deficient cells, treatment with a PARP inhibitor is expected to result in high genomic instability and cell death. Indeed, breast and ovarian cancers that harbor BRCA1 mutations can be treated with drugs targeting PARP1, such as Olaparib , the larger the exponent Δg, the lower the Gg(t) becomes. This is in agreement with the assumption that with increased tumor fitness, the disease becomes more aggressive, and patient survival decreases accordingly, as compared to the reference survival. Importantly, accumulation of mutations of independent (not interacting) genes, should correspond to raising the initial survival function G(t) to consecutive exponents. For example, for a pair of such not interacting genes, we expect that 01 ⋅ Δ10 = Δ00 ⋅ Δ11. In general, the condition for an epistatic interaction of any type  or negative (δ < 0). The likelihood ratio equalsF has a density, the maximum likelihood estimators are given by the formula4. If both do, we choose the one for which the value of the log likelihood is greater (Appendix).The model presented above allows us to develop a surprisingly simple method, which we call SurvLRT, for evaluating epistasis directly from cancer patient data. Indeed, suppose that In the case when the data contains only uncensored cases, by the Wilks’ theorem, we can safely assume that, asymptotically,sumption . This alG(t) using Kaplan Meier estimate of the survival function for a cohort of 582105 patients that died of other reasons than cancer, collected by the Surveillance, Epidemiology, and End Results Program [The data for 9899 patients of 32 cancer types generated by the Cancer Genome Atlas (TCGA)  was down Program  . Here, we investigated whether the parameters obtained using s, assuming they share the same genotype. To this end, we generated s observations of survival times T at random from the distribution G(t)Δ, where Δ = 1. Next, the censoring times Y were sampled from a truncated (up to 40 years) exponential distribution, Y ∼ Exp(c), where the parameter c was set so that the mean percentage of censored observations was either 33% or 66%. In the case when Y < T, the last time of follow up for that patient was fixed to Y, and the patient was flagged as censored. Otherwise, the patient was flagged as dead, and the time to death was fixed to T.To evaluate the performance of SurvLRT in a controlled setting, we simulated survival data and fitness values for all types of epistasis among triplets of genes. We first assessed the accuracy of parameter estimation  for diffT itself, but from the distribution of T conditioned on the event T < Y. Keeping the censored cases maintains the power of the test, and allows accurate parameter estimation  = log(Δ1) + log(Δ2) + δ, where δ was the value of the tested effect size. For each gene in the triple, we sampled k, the number of patients which had this gene mutated, according to the mutation frequencies observed in the real cancer patient cohort. Next, we chose k patients at random to have this gene mutated, fixing their value for this gene to 1, and for all remaining patients to 0. As a result, we obtained patient genotypes for the simulated triple. For each patient with genotype gi, we sampled survival time T from the distribution Y ∼ Exp(c), with c fixed to obtain the wished percentages of censored patients (33% or 66%). As above, the resulting observation for the patient was taken as the min, and the patient was flagged as censored if Y < T, and as dead otherwise. The simulation was repeated first assuming the total number of patients was 2942  is estimated from patient data (G(t) from survival times sampled from the exponential distribution, keeping its mean equal to mean survival in the patient data. Both the error of parameter estimates and the power of the tests do not depend on which of the alternative forms of the survival function G(t) we used, with the only exeption that the spread of the outliers was larger, when the survival times were sampled from the exponential distribution  when targeting the partner gene with two or more different siRNAs sensitized to KU0058948, the PARP1 inhibitor utilized in both studies. Otherwise, the gene pairs were flagged as noninteracting. Since the siRNA experiments were conducted on breast cancer cell lines, we applied SurvLRT to the breast cancer cohort  and negative conditional epistasis . The conditional epistasis type b turned out to be positive, but with a high adjusted p-value of 0.87. Both tests for the epistasis types a and b were clearly free of cancer type bias Click here for additional data file.S2 FigG(t) estimated from survival times sampled from a truncated exponential distribution . The results obtained with this alternative choice of the reference survival function are similar to those presented in A Box plots showing 25th, 50th and 75th percentiles , and 1.5 interquartile ranges  of log true to estimated fitness ratios (y-axis) as a function of sample sizes (x-axis), in the case when 33% and 66% of patients are censored and removed from the samples  and when 33% and 66% are censored and kept (third and fourth column). Gray lines at 0 mark the level where the estimated equal the true parameter values. B Box plots of SurvLRT p-values as a function of epistatic effect size, for two different patient cohort sizes (rows). Gray lines mark the p-value 0.05. Columns as in A.Figure panels are as in (PDF)Click here for additional data file.S3 Figy-axis) versus the proportions expected given no cancer type bias, when the cancer types are distributed uniformly across the genotypes (x-axis). The line is where the points should arrange if the observed and expected proportions were equal. The colums correspond to the tests for triple epistasis type a and b, respectively, The two rows correspond to the tests where the triple epistasis was tested for the interaction between BRCA1, PARP1 (in both rows), conditional on the alteration status of either the newly identified biomarker region (top row) or the known biomarker TP53BP1 (bottom row).Each plot corresponds to one SurvLRT test. Points: proportions of the number of patients with each cancer type and carrying each of genotypes in the considered test to the total number of patients, as observed in the data ((PDF)Click here for additional data file.S1 TableCensoring status , days to last follow up, and gene names (columns) altered in samples from TCGA pan cancer patient cohort (rows). Entries for genes with value 1 stand for alteration and 0 for no alteration compared to normal sample. This data is a result of preprocessing of the full downloaded dataset. From the full dataset, gene colums were removed if they contained 2000 or more NA values. Rows with 100 or more NA, or with missing value in the ‘status’, as well as NA or negative value in the ‘last follow up’ columns, were also removed. After that, the remaining missing values were filled with 0s.(CSV)Click here for additional data file.S2 TableColumns and entries as in (CSV)Click here for additional data file.S3 TableGene pairs , whose synthetic lethal interaction was previously investigated using siRNA screens on cancer cell lines. Column flag denotes whether the pair is synthetic lethal  or not (0).(CSV)Click here for additional data file.S4 TableThe table contains the column months recording the number of survival months, and column p recording the Kaplan-Meier estimate of the survival function (the probablity of surviving more than the corresponding number of months).(CSV)Click here for additional data file.S5 Table(CSV)Click here for additional data file.S1 Appendix(PDF)Click here for additional data file.


Microarray technology allows monitoring of gene expression profiling at the genome level. This is useful in order to search for genes involved in a disease. The performances of the methods used to select interesting genes are most often judged after other analyzes , which are also subject to error. A good evaluation of gene selection methods is possible with data whose characteristics are known, that is to say, synthetic data. We propose a model to simulate microarray data with similar characteristics to the data commonly produced by current platforms. The parameters used in this model are described to allow the user to generate data with varying characteristics. In order to show the flexibility of the proposed model, a commented example is given and illustrated. An R package is available for immediate use. Two fluorescent dyes  are used for labeling of the samples for hybridization. Then, after washing, scanning and quantification of images corresponding to the red and green fluorescence of the array, numerical values, or intensities are associated with each probe (gene). These values are normalized to correct for undesirable technical variations [Microarray is now a mature technology in the field of molecular biology for monitoring of gene expression profiling at the genome level. Using two-color microarray technology, the biological activities of two samples are compared on an array on which thousands of specific deoxyribonucleic (DNA) sequences are printed or synthesized riations ,2. Usingriations . For a gIn a screening study, the goal is to select genes with differential expression from data whose characteristics are unknown. To study the performance of gene selection methods, we often use synthetic data, which can also serve in developing new methods. To properly play their role, synthetic data must resemble as closely as possible the real data they represent. This is achieved by simulating the physical phenomena through a model. The parameters of this model are approximations of the physical laws that govern the observed phenomenon, and a good knowledge of the physical laws is therefore required to obtain a good model. A complex model that takes into account several components of a phenomenon may become less flexible and may be difficult to modify in order to include new factors. In contrast, a simple model can be effective and easy to modify to take into account an unexpected situation.a priori. For some of the above methods, there is no distinction between the number of weakly expressed genes and those strongly expressed.One way to generate synthetic data is to use real microarray values as seeds ,5,6,7. Iethod in ,9, where used in ,9 allowsversus knock-out ones, treated samples versus non-treated ones, etc. For these situations, we use the generic terms of control versus test samples. Two condition biological data can be obtained using either one-color or two-color microarray technology leading to The model proposed in  providesThis paper is organized as follows. In the next section, we present the model used and describe its parameter settings. In There are usually more genes with low intensities than genes with high intensities. One possible explanation for this observation is a non-response of all genes to given biological conditions.The Under similar biological conditions, the expression level of a gene varies around an average value. Exceptionally different values will be due to technical problems.The total number of DE genes depends on the biological conditions used. The number of over-regulated and under-regulated genes may be different.The variability observed for weakly expressed genes is larger than that observed for highly expressed genes. This is mitigated with today’s scanners and tools. However, genes which are not really expressed still have non-zero values, and strongly expressed genes (saturated) receive a single value corresponding to the maximum level of quantification.We propose here a model that does not require knowledge of the physical laws governing gene expression to produce data with similar characteristics to the data commonly produced by current platforms. The user provides a subset of parameters that control the behavior of the data generated. We assume the following characteristics for microarray data:In the model described below, the expression levels are n genes, i, , which vary between a lower bound (lb) and an upper bound (ub). The scaled values represent average expression levels for the n genes (issue 3). Optionally, real data can be used as seed at this step. We assume that intensities for each gene are uniformly distributed around its average level. The range of variation of values from this distribution is assumed to be dependent on the gene average level and is expressed as a percentage through a parameter, i (issue 5). This leads to vector i, an integer is randomly drawn from the set To generate data using model  that satThis is the number of probes (genes) on the arrays. It is on the order of thousands, and the default setting is These parameters are the number of control and test samples, respectively. Typically, the minimum number of samples per condition should be three to allow the use of statistical tests. The maximum value of these parameters rarely exceeds 100 ; the default setting is seven for both.ratio = 0 (default setting), This parameter option generates Algorithm 1: Steps of the micorarray data generation model.n values from a beta distribution using Generate lb and ub: Transform values of For each value of (a)i is differentially expressed (a sample Set i is up-regulated (a sample Generate If probe Generate ElseSet: If gene (b)Set: ElseThen, the first (a)If the noise standard deviation parameter is positive Do not use noise: ElseNow, we have a noise-free data matrix (a)The first column of If ratios are required(b)ElseDepending on user settings, To obtain more small values than high ones, we use a beta density distribution. Based on many histogram plots using various shape parameter values, we propose to set parameter lb and ub from intervals These parameters specify the n probes in the data set should be DE.This parameter controls the number of differentially expressed genes the user would like to have in the data set. Its values are taken from the interval sym = 0.5 (default setting). If the value of this parameter is less (greater) than This parameter results in nearly the same number of up- and down-regulated probes when α, controls the width of the uniform distribution and is expressed as a percentage of the average level. We assume that the values of each probe are uniformly distributed around an average value. An exponential distribution is used, t-test analysis. The statistic of the shift value is For a gene, the fold change is a shift of average expression levels between test and control samples. Assuming that (control and test) sample values of a given gene are uniformly distributed around an average level, the shift comes from a superposition of additional values to the test samples, see pde.This parameter represents a normal distribution standard deviation for additive noise. The default value is This parameter is used for computer random number initialization. It will allow one to generate the same data at different times. The default value is 50.rseed. For each simulation, we performed a Student t-test and selected genes with a p-value less than p-value threshold, To evaluate the performance of the proposed model, we performed simulations, in which we studied the influence of different parameter settings. Their default values are: pde, respectively. In comparison with the expected number of DE genes, the recovery powers of the Student t-test are pde. The median numbers of the false DE genes are 49, 49, pde, respectively.We used four different values  and the proportion of under- and over-regulated genes (sym) is at the discretion of the user. The parameter, rseed, allows one to produce the same data at different times using the same computer. This parameter is also useful for generating test data for different analysis algorithms. Settings, The choice of some setting parameters for the proposed model is easy and can be dictated by the experimental design. This applies to etc., for demonstration and/or teaching purposes.An interesting microarray study was reported in . In thatmadsim.R (MicroArray Data Simulation Model), which is deposed as a package on the Comprehensible R Archive Network (CRAN) server for download [xdata) and the indexes of DE genes (xid). Real data can be used as seed for each gene. An example of such data is available in the data folder of the package. Further explanations are available from the package’s help function.For immediate use of the proposed model, we provide an R code function download . The outWe proposed in this paper a simulation model of microarray data. This model is very flexible and allows one to generate data with similar characteristics to the data commonly produced by current platforms. We showed a commented example of its possible use. We considered the case of data from two biological conditions. This model can be extended to multiple biological conditions in different ways: (a) modify to take into account additional biological conditions and several levels for the parameters,


Hierarchical classification (HC) stratifies and classifies data from broad classes into more specific classes. Unlike commonly used data classification strategies, this enables the probabilistic prediction of unknown classes at different levels, minimizing the burden of incomplete databases. Despite these advantages, its translational application in biomedical sciences has been limited. We describe and demonstrate the implementation of a HC approach for “omics-driven” classification of 15 bacterial species at various taxonomic levels achieving 90–100% accuracy, and 9 cancer types into morphological types and 35 subtypes with 99% and 76% accuracy, respectively. Unknown bacterial species were probabilistically assigned with 100% accuracy to their respective genus or family using mass spectra (n = 284). Cancer types were predicted by mRNA data (n = 1960) for most subtypes with 95–100% accuracy. This has high relevance in clinical practice where complete datasets are difficult to compile with the continuous evolution of diseases and emergence of new strains, yet prediction of unknown classes, such as bacterial species, at upper hierarchy levels may be sufficient to initiate antimicrobial therapy. The algorithms presented here can be directly translated into clinical-use with any quantitative data, and have broad application potential, from unlabeled sample identification, to hierarchical feature selection, and discovery of new taxonomic variants. In the real world, these sets often have complex and diverse data structures covering non-linear relationships and often missing data points. In the case of microbiome research, there is a considerable need to integrate metagenomic information and other systems parameters such as metabolism. In most cases, the primary requirement is to predict multiple classifications and outcomes based on multivariate data and modeling such as the use of hierarchical classification (HC) strategies. Although HC methods have been used extensively in research applications such as text classification4, and limitedly in genomics5 and genome sequencing6, the translation into clinical science and practice remains limited. Here we present a generalized HC implementation in the biomedical context, demonstrate its performance on biomedical datasets, and discuss its immediate translational advantages and uses.The relentless drives towards precision medicine necessitate an ever-increasing reliance on integrating of complex and large-scale multi-omics and clinical datasets derived from multiple sources7, or organisms such as bacterial species9. Such approaches may be referred to as ‘flat classification’ and while this provides classification accuracy results which seem highly promising, there are key limitations which are often overlooked: (i) class discrimination at one level may diminish with increasing numbers of classes, resulting in lower classification accuracy for large datasets; (ii) since all classes in the model are considered to be either ‘training’ or ‘prediction’, the classification accuracy for a particular class can be influenced by other taxonomically ‘distant’ classes; and (iii) incomplete databases offer little or no predictive capacity for new (previously unknown) classes. In the microbiology field, for example, the continuous discovery of new species and the emergence of new bacterial strains means that a ‘complete’ database is impossible to compile. The same is true, though to a lesser extent, for undifferentiated cancers, where identification of cancer type is not possible in certain instances, limiting targeted therapeutic intervention.Current commonly used bioinformatics methods for classification of biomedical datasets are based on ‘training’ a single classification method  to discriminate between different classes e.g. patient outcomes or healthy and cancerous tissue2 and may in turn result in improved classification accuracy since classes unrelated taxonomically to a given class of interest are not considered in the classification of the latter. The advantage of HC is further amplified in circumstances where the quality of data for some classes may not be comparable to others. While in ‘flat classification’ the inferior data quality of some classes may potentially affect all others, in hierarchical classification, taxonomically-distinct classes are less susceptible to this phenomenon.To mitigate these limitations, here we propose a hierarchical ‘top-down’ classification algorithm, where classes are taxonomically classified and predicted. Unlike ‘flat classification’, a hierarchical approach enables the training of a number of models, one for each classification problem, considering hierarchical relationships. This approach subdivides classification into smaller and simpler classification problemsOne of the most significant advantages of adopting a HC approach that has not been realized or utilized before, particularly from a clinical application point of view, is that it provides the ability to predict a class at different classification tiers. While the specific class for classes not contained within the existing database may not be retrieved, this enables the prediction of upper tier classes. This information may still be highly clinically relevant as in many cases it would be adequate to determine appropriate treatment. For example, in the case of treatment of bacterial infections, where the specific species is not always identifiable.15, however prediction is difficult to achieve with the use of conventional classification methods which are frequently incapable of correctly assigning upper level taxonomy for species not encountered before in the dataset.Based on their cell wall structure, bacteria are classified as either Gram-positive or Gram-negative and, similar to other living organisms, taxonomically hierarchically classified down to the species level, thus prediction of upper hierarchy class is often sufficient for the appropriate antibiotic regimen to be prescribed. The identification of bacteria using mass spectra has been reported and reviewed several timesHere we apply and validate a HC and prediction approach to large-scale clinically relevant spectroscopic and genomic datasets; we demonstrate accurate prediction of bacterial species and cancer subtypes using mass spectral and gene expression profile data, respectively. A broad range of potential translational applications beyond those used to validate the algorithm are also outlined.Clostridium difficile, Pseudomonas aeruginosa and Klebsiella oxytoca were correctly classified with 100% accuracy. Staphylococcus spp. and Streptococcus spp. were misclassified into same-genus species.To validate and assess the performance of the proposed HC algorithm, we first applied it to mass spectral profiles acquired from 15 bacterial species Fig. , determiEnterobacteriaceae family  were misclassified into same-family species. Enterobacter spp. were misclassified between each other as well as into Klebsiella spp., and vice-versa Klebsiella pneumoniae was misclassified into Enterobacter spp. Serratia marcescens was misclassified into Enterobacter aerogenes and Proteus mirabilis was misclassified into Klebsiella pneumoniae. 5–11% of Enterobacter cloacae, Escherichia coli, Klebsiella pneumoniae and Serratia marcescens were not classified. Score plots for a selection of models are presented in Supplementary Fig. Species belonging to the We assessed the approach further by applying it to a large publicly-available cancer gene expression dataset. We defined a two-level hierarchy: (i) morphological cancer type (level 1); and (ii) molecular cancer sub-type (level 2), derived from previous literature Fig. . Nine caAverage percentage accuracies were consistent across multiple cross-validation repetitions. Overall classification of the 35 cancer subtypes (level 2) was achieved with a mean accuracy of 76 ± 2%, with individual subtype classifications ranging widely from 35–97%. Lowest classification was recorded for a LAML subtype , 19 out of 35 were classified with over 80% accuracy, 10 were classified with 60–80% accuracy, and 6 subtypes were classified with less than 60% accuracy. With the high classification accuracies at the first level, misclassification of cancer subtypes mostly occurred between subtypes of the same cancer. Subtype misclassifications are shown semi-quantitatively in Fig. Staphylococcus spp. and Streptococcus spp.  was achieved for 13 out of 15 species with 100% accuracy. For the cancer dataset, except for one LGG subtype and one KIRP subtype, all cancer subtypes were predicted into the correct cancer type with 95–100% accuracy Fig. . A list 12, using ‘flat’ classification approaches. Difficulties with accurately distinguishing Enterobacteriaceae from other species have been frequently reported in the literature, irrespective of the bacterial identification method used, owing to the high degree of biological similarity within this family. Next-generation sequencing and other emerging technologies are likely to enable refinement of bacterial taxonomic classification in the near future16. Nevertheless, here we are not proposing a new data acquisition method solely for improved results, but rather an alternative to the ‘flat’ classification methods that are conventionally used. With respect to performance of classification accuracy for the datasets presented herein, HC demonstrated equivalent results compared with ‘flat’ classification methods. Nonetheless, the described computational strategy can reduce classification complexity by hierarchically re-arranging data into more manageable multi-group classification problems – a strategy that is useful for hierarchical prediction which is not possible with conventional classification approaches (discussed below). Additionally, beyond what is available in the current literature9, here we have provided an automated solution for the selection of the ‘best’-performing statistical technique – both in terms of accuracy and computational efficiency.We have demonstrated the effective use of a HC approach for the classification of biomolecular datasets, and extended this principle to enable robust class prediction which has potential translational utility. The application of this methodology to bacterial speciation achieves overall classification accuracies that are comparable to previously published classification methodologies that have employed mass spectrometric profiling, such as MALDI-TOF and REIMS17. Using the proposed methodology upper hierarchy level information can be derived for rapid and more precise antibiotic treatment of unknown strains.Beyond HC, we demonstrate a major advantage of the proposed application that has not been exploited before – ‘hierarchical prediction’; in other words, the ability to assign upper-level taxonomic identity for classes that are not available in a given (incomplete) database. In ‘flat’ classification approaches the ‘parent-offspring’ nodal relationship is not retained between classification levels, hence hierarchical prediction is not possible with these methods. ‘Unknown’ bacterial species were identified here at the genus and family level with 100% accuracy. This approach could have significant implications in clinical microbiology where broad and narrow-spectrum antibiotics are often not species-specific, and where every hour of delay before initiating the correct antibiotic regimen can increase risk of sepsis associated mortality by 7.6%18. While this is of interest for the purpose of taxonomic reclassification, it has limited immediate clinical translational utility, pending further validatory studies. Even then, the hierarchical classification approach proposed here can easily be applied to the updated taxonomic tree.In contrast to HC, hierarchical clustering is an unsupervised technique used for grouping and differentiation of data according to overall similarities/differences; this can generate novel hierarchical taxonomiesApplying the same approach to a larger sample cohort of cancer genomic data, we found a stable 99% classification accuracy of cancer types and subsequently 74–78% accuracy at sub-type level. This enabled the probabilistic prediction of most cancer subtypes with 95–100% accuracy. With an unknown cancer subtype sample, the proposed approach thus enables the prediction of the cancer type, and subsequently suggests a subtype for it. This is especially useful for cancer types originating from the same organ of origin (e.g. KIRC and KIRP), where without any immune-histological knowledge, the model would predict the cancer type with a high degree of accuracy. Nonetheless, the pre-defined two-level cancer hierarchy used here was devised to generalize the hierarchical classification and prediction concept; showing that classes with reasonable discriminatory differences can often be identified with high accuracy, especially at upper levels. Lower prediction (and classification) accuracies are obtained in the presence of upper level misclassifications. This is a recognized limitation of a hierarchical approach where the classification error is propagated downstream.While in the present study the HC approach was applied to bacterial mass spectrometric and cancer RNA sequencing data, the developed algorithm is not data-specific and is highly versatile. Somatic mutations, 16S rRNA, microarray gene expression, microRNA profiles and any other quantitative data can be handled. The application possibilities are diverse: (i) an unlabeled laboratory sample can be identified with various degrees of accuracy ; (ii) group/taxon-specific feature selection can be retrieved, where variability or commonalities in the expression of a feature can be traced down a hierarchical tree; (iii) discovery of new species/variants/cancer subtypes if classification into existing well-classified groups is poor; and (iv) assessment of data stratification performance; where the effect of different stratification approaches on classification accuracy can be determined – to name a few.Here we presented a general workflow for the generation of robust cross-validated models for the classification and prediction of classes at different hierarchy levels by simplifying the classification task and optimizing the statistical models used at each node. Optimizing overall performance by deriving a single global learning model for all classes is a potential alternative approach, though exploring this lies beyond the scope of the current study. While the use of a single global learning strategy sounds attractive, this may impose added complexity and introduce scalability issues.The work presented herein has sought to demonstrate the translational utility of HC-based approaches in situations where ‘incomplete’ datasets are being evaluated, a situation that is frequently encountered in biomedical data analytics. Currently, only a tiny fraction of useable healthcare related data is actually put to translational use. This situation is unlikely to be rectified until more effective translational bioinformatics solutions are introduced capable of extracting actionable insights from the vast amounts of available data. The HC approach described here represents one such solution.Clostridium difficile and aerobic conditions for all other species) were acquired by rapid evaporative ionization mass spectrometry (REIMS) using an Exactive instrument 9. Spectral preprocessing was performed using an in-house MATLAB workflow. Spectral data were converted from RAW to mzXML format and imported at 0.001 Da resolution within the mass range of 150–2000 m/z. Noise was removed by an optimum threshold adaptively calculated using a histogram-based method19. Five mass spectra per sample were selected by total ion intensity (TIC) after optimum thresholding, and peak detection was performed by a 3rd order derivative of a Savitzy-Golay polynomial filter20. Peak-matching was performed following determination of a common m/z feature vector estimated using a kernel density estimation approach21, where a peak with the highest peak counts was considered as a common m/z value for all the spectra. A mean mass spectrum for each bacterial species sample was derived and subsequently median-fold change normalization was applied to adjust for relative ion intensities between spectra. We have previously demonstrated the robustness of this data processing strategy22.Mass spectral profiles for 15 different clinically-isolated bacterial species  log variance stabilizing transformation was performed on the normalized spectrahttp://www.nmpdr.org/), and List of Prokaryotic Names with Standing in Nomenclature (http://www.bacterio.net/) online data repositories.Hierarchy structure was defined by the taxonomy of bacterial species, where: Gram staining type, class, order, family, genus and species were considered. Taxonomic information was automatically retrieved from the National Microbial Pathogen Data Resource (https://tcga-data.nci.nih.gov/tcga/). Data preprocessing and filtering was performed using an in-house RNA sequencing workflow. This involved median fold change normalization followed by variance stabilizing log-2 transformation. Dubiously annotated genes were removed as well as normal tissue samples. To avoid biases, in circumstances where multiple samples were available for the same patient, a single sample was selected at random.For the cancer genomic data, raw RNA sequencing data (RNASeqV2) for 9 cancer types (breast adenocarcinoma (BRCA), glioblastoma multiforme (GBM), kidney renal clear cell carcinoma (KIRC), kidney renal papillary carcinoma (KIRP), acute myeloid leukemia (LAML), lower grade glioma (LGG), lung adenocarcinoma (LUAD), prostate adenocarcinoma (PRAD), and bladder urothelial carcinoma (BLCA)), profiled using Illumina HiSeq, were compiled from The Cancer Genome Atlas data repository  cancer type; and subsequently (ii) cancer sub-type. Subtype assignment was based on previous literature with published gene expression unsupervised cluster assignment of mutual samples used here36 is implemented using 4 different methods: (i) alternative partial least squares regression (SIMPLS)37, (ii) recursive linear discriminant analysis using maximum margin criterion (MMC-LDA)38, (iii) support vector machine (SVM) using LIBSVM version 3.20 (https://www.csie.ntu.edu.tw/~cjlin/libsvm/), and (iv) linear discriminant analysis using the Fisherfaces approach (PCA-LDA)39. Table The developed algorithm is based on training a discrimination model for each node of a hierarchical tree, stratifying the data at each parent node. Starting from the upper-most node, a selective dimensionality reduction method approachData are initially split into 5-fold cross-validated main test and training sets, and in turn the training set is then split into nested 5-fold cross-validated test and training sets  has only 1 species (level 6), and the genus is related to other genera through the family (level 4), a model is built between the ‘offspring’ nodes of these related species and the single species. Samples of this single class/species which are not classified into the same species are considered as ‘non-classified’.40. In addition to nested cross-validation, classifications are repeated to obtain an average classification accuracy for each node, at each level, assessing model discriminatory performance and stability. The choice of the above linear models is determined by their scalability to high-throughput datasets and the transparency of derived discriminatory molecular signatures.Probabilistic classification is performed throughout by logistic regression, where samples are assigned to the class with the highest probability. In a multi-class classification problem, classifiers are applied in a one-against-all mannerGraphic visualization is provided while the algorithm is operating to indicate workflow progress, as well as accuracies during the training phase. When complete, a set of confusion matrices are generated to summarize average classification accuracy for each node, at each taxonomic level. The quantitative accuracies given by the confusion matrices are listed in Supplementary Tables Based on the HC approach, a class prediction algorithm was developed and tested using a leave-class out cross-validation strategy where each class/down-stream-node from the lower-most hierarchical level was excluded completely from the training phase, one at a time. The most efficient cross-validated method map was again determined, now based on the new cross-validated data ‘subset’. The left-out class is then applied to the method map and predicted. Starting from the root node at the upper-most hierarchical level, each sample of the left-out class is assigned to a down-stream class based on probability estimates. A probability difference between the highest probability class and the second is set as a threshold, below which samples are considered as ‘non-classified’. Percentage prediction accuracy is determined for each species after repeated predictions to assess predictive robustness.Flowcharts illustrating the classification workflow and leave-one-out class prediction algorithms are presented in Supplementary Figure https://bitbucket.org/iAnalytica/hierarchical-classification-publication/overview.The source code for the developed algorithms and data are available at:  Supplementary Information