The increasing capacity of today’s technology represents great advances in diagnosing diseases using standard procedures supported by computer science. Deep learning techniques are able to extract the characteristics of temporal signals to study their patterns and diagnose diseases such as essential tremor. However, these techniques require a large amount of data to train the neural network and achieve good results, and the more data the network has, the more accurate the final model implemented. In this work we propose the use of a data augmentation technique to improve the accuracy of a Long short-term memory system in the diagnosis of essential tremor. For this purpose, the multivariate Empirical Mode Decomposition method will be used to decompose the original temporal signals collected from control subjects and patients with essential tremor. The time series obtained from the decomposition, covering different frequency ranges, will be randomly shuffled and combined to generate new artificial samples for each group. Then, both the generated artificial samples and part of the real samples will be used to train the LSTM network, and the remaining original samples will be used to test the model. The experimental results demonstrate the capability of the proposed method, which is compared to a set of 10 different data augmentation methods, and in all cases outperforms all other methods. In the best case, the proposed method increases the accuracy of the classifier from 83.20% to almost 93% when artificial samples are generated, which is a promising result when only small databases are available. ET is a worldwide disease which is more common than Parkinson’s disease (PD), approximately twenty times more according to2. The prevalence of this motor disorder is estimated to be between 0.3 and 4.0% in the Western world. It affects men and women in more or less equal proportions, with no gender differences being found. Its incidence is approximately 23.7 per 100,000 individuals per year and a large majority of cases, between 50 and 70%, are genetic in origin2.Essential tremor (ET) is a disorder of the nervous system that causes involuntary and rhythmic movements. The tremor is at a frequency between 4 and 12 Hz and only occurs when the muscle is strained. The amplitude of the tremor is not constant throughout the course of the disease,since it varies as the patient ages. Although it can arise in any part of the body, this tremor appears most frequently in the hands, and especially when the subject performs simple everyday tasks, such as eating, drinking or tying their shoelaces. Usually, it is not a serious condition, but can become so if it is severe and can be mistaken for Parkinson’s disease3. Despite the usefulness of these biomarkers, the expense and technology requirements make it unfeasible to use these tests for all patients with motor conditions. It is in this context that intelligent non-invasive diagnostic techniques can be very useful tools for the early diagnosis of neurodegenerative disorders. Among these techniques, handwriting analysis using Artificial Intelligence (AI) is a powerful option. Non-technical staff in the patient’s environment could use this technique without interfering with the patient’s daily life, as handwriting analysis is not considered stressful by most patients. In addition, this technique has a very low cost and its requirements in terms of infrastructure or medical equipment are very modest, providing information easily, quickly and cheaply. Currently, the Archimedes spiral is the gold standard test in clinical diagnosis4.In order to palliate and manage the symptoms, it is extremely important to be able to make a clinical diagnosis at the earliest manifestations of the disease. Early diagnostic techniques and the development or acquisition of usable clinical markers have advanced significantly in recent years, although these tests can be very expensive, such as the use of Single Photon Emission Computed Tomography (SPECT), and therefore not widely available in routine clinical practice7, have focused on the automatic analysis of handwritten data to determine the patterns that allow an accurate diagnosis of this disease. In this work we will study the use of a deep neural network based on LSTM9 to perform this diagnosis, so that the neural network itself will extract the main patterns from the data.Different studies, such asOn the other hand, it is common for a Deep Learning system to use hundreds or thousands of samples to train the system, given that the number of parameters of the model is very high. In our case, we only have a total of 51 samples. With small datasets, overfitting is a problem to be taken into account. Overfitting occurs when the system becomes too specialised with training data and is unable to successfully classify new test data, thus losing the ability to generalise. To reduce or avoid this problem, the input dataset should be larger.10, but in this work we will use a method based on a decomposition–recombination technique to generate artificial samples that has been tested on one-dimensional data (time series) but, to our knowledge, has never been used before in this scenario, dealing with 2D data . We will compare our proposed method with a set of 10 methods commonly used in time series data augmentation. As will be seen in the experiments, our method clearly outperforms all others, proving to be a very good candidate for this problem.Data augmentation (DA) refers to the process of synthesising new data from existing data. Applying various transformations to the available data to synthesise new data is one approach to deal with the issue of insufficient dataOne of the challenges of this project is having only a small number of subjects (samples) for training an LSTM model. To reduce this problem, a data augmentation method will be used, which will extend the number of samples used by more than 500%, increasing the variability of the input data, and thus reducing over-fitting.12, the frequency decomposition of all samples in the dataset is performed. This frequency decomposition generates the so-called Intrinsic Mode Functions (IMFs). Finally, using only the IMFs of the subjects selected for training, the new random samples are generated.The different steps to generate artificial random samples for training the model are explained below. First, the working scenario is presented and the samples are divided in two groups: ET  and CT (control subjects). Then, using the multivariate Empirical Mode Decomposition (mEMD)2 and has been used in previous works7 to analyze and classify samples (drawings) from ET patients and controls. As stated in7, this study was carried out in accordance with the recommendations of the Ethics Committee of the Donostia University Hospital , which approved the protocol. All subjects gave written informed consent in accordance with the Declaration of Helsinki.The analysis and diagnosis of the patients will be carried out using the dataset named BIODARW. This data was firstly presented in4 with both hands, using a digitizing tablet to acquire the samples.The participants in the study performed, among other exercises, the test of drawing the Archimedes’ Spiral7, we will use the same subset, BIODARWO, which consists of 51 samples: 24 samples for the ET group and 27 samples for the control group. Please, refer to7 for more details on the dataset.In order to compare our results with the previous mentioned worksX CoordinateY CoordinateTime StampStatus  (1 when the pen touches the paper)AzimuthAngular AltitudePressureWe will only work with the X and Y coordinates, as it was done in7 for two main reasons: (1) any digital tablet can obtain these parameters, but maybe not the others ; (2) X and Y coordinates carry enough information to diagnose essential tremor, as demonstrated in7.The data available in this database was obtained from a Wacom 4 digitizing tablet at a sampling frequency of 100 Hz. Each sample of data is stored in a matrix in which each column contains: 11. Each IMF represents a non-linear oscillation of the original signal, which can be reconstructed by summing all the IMFs of the signal and its residual (the IMF corresponding to the linear trend). All the IMFs have to fulfill the following two conditions: The number of maximums has to be the same as the number of zero crossings, or at least they have to differ by only one.For any sample, the mean value between the envelope of the local maxima and that of the local minima must be zero.The algorithm of this decomposition method consists in rewriting a real-valued signal x(t) as:r(t) is the residue signal.EMD is based on a method that allows decomposing the different time signals into a finite number of the so called Intrinsic Mode Functions (IMFs)Define s(t).Identify all the local maximum and minimum of Interpolate between the maximum (minimum) to obtain the upper envelope (lower envelope).m(t) by taking the mean of both envelopes.Obtain the local mean m(t) to the signal s(t): Obtain an IMF candidate by subtracting the local mean h(t) does not comply with the two conditions to become an IMF then go to step 2 with If Extract the n-th IMF as follows: h(t) satisfy the IMF conditions, then: If x(t) and the decomposition ends.If Otherwise, set In order to simultaneously decompose X and Y coordinates for each sample and for all the subjects, the multivariate EMD (mEMD)12 algorithm was used. In this way, the maximum and minimum envelope will be the same for all subjects and coordinates, and the number of IMFs will be the same for all of them. The decision to use mEMD instead of EMD was made to overcome the problem of having a different number of IMFs depending on the subject, due to the intrinsic data-driven characteristics of the EMD algorithm. This effect induced a desynchronisation of the weights, which caused the artificial samples to work improperly, clearly deteriorating the accuracy of the classification system.The iterative process to obtain them is described below: The decomposition process is presented in Fig. 13, and then used in14 as a data augmentation technique to train a deep learning classifier, also on EEG data.The method to create artificial samples is based on previous works in which this method was first presented and used on EEG data for decreasing the calibration step in a BCI applicationTo our knowledge, this is the first time this method has been used with handwritten data to create artificial drawings of Archimedes’ spirals.Define the number of artificial samples to be generated, per each group of subjects (ET and CT).Randomly select the IMFs to be used to create each artificial subject. This has to be done separately for each group.Generate the new samples by summing the selected IMFs, obtaining the new samples, as shown in Fig. Once the IMFs for each subject and coordinate (X and Y) have been obtained, and the group of training subjects has been selected, artificial samples can be generated. The strategy consists of: N subjects, and Fig. Table 15 and the code, provided by the authors, can be download here: https://github.com/uchidalab/time_series_augmentation. We refer the reader to15 and references therein for more details on these methods.To compare our data augmentation method with other methods, we briefly describe here a set of 10 methods that will also be used with the handwriting data. These methods can be grouped in: (1) magnitude domain transformation methods; (2) time domain transformations methods; (3) frequency domain mixing methods, and (4) generative models methods. All these algorithms are described and analysed inThe Magnitude domain transformation methods were: Jittering, Magnitude warping, Rotation and Scaling. For Jittering, Gaussian noise is added to the time series. For the Magnitude warping, the magnitudes of the time series are multiplied by a warping amount determined by a cubic spline line with four knots at random locations and magnitudes. For Rotation, because we have univariate time series, flipping is used, in which 50% of the patterns of the training set are inverted at random for each data augmentation set. Scaling method multiplies training set time series with random scalars from a Gaussian distribution. In this way, the time series are scaled by a single multiplier for all time steps.The Time domain transformations methods were: Permutation, Window slicing, Time warping and Window warping. In the Permutation method, two to five equal sized segments were permuted. Window slicing crops the time series to 90% of the original length. The starting point of the window slice is chosen at random and interpolation is used to keep the original length of the time series. Time warping uses a warping path defined by a smooth cubic spline-based curve with four knots of random magnitudes. Window Warping selects a random window, that is 10% of the original time series length and warps the time dimension by 0.5 times or 2 times.The Frequency domain mixing method was SuboPtimAl Warped time series geNEratoR (SPAWNER), which is a pattern mixing data augmentation method that suboptimally averages two intra-class randomly selected patterns. In addition, noise is also added to further transform the data.16. cGANs are similar to GANs but they use the label of the samples as a parameter during the training process, to generate data that belong to specific categories. In that case we used directly the Matlab implementation of cGAN.Finally, the Generative model method was a Conditional Generative Adversarial Network (cGAN)An LSTM network is a type of recurrent neural network (RNN) capable of learning long-term dependencies between time steps in a sequence of data. When a traditional RNN is trained by backpropagation, the long-term gradients that are backpropagated can vanish due to the computations involved in the process. The contrary effect can also happens, and in some situations the long-term gradients can explode. Therefore, traditional RNN are not useful when long-term dependencies are involved.t consists of the hidden state, the vector t is also the output of the LSTM layer for this time step. The cell state contains the information learned in the previous time steps. At each time step, the layer adds information to the cell state or removes it. The layer controls these updates through the following gates: (1) the entry gate, tanh represent the sigmoid and hyperbolic tangent activation functions, respectively.LSTM networks overcome the vanishing gradient problem and work very well for data sequences. Internally, as represented in Fig. ate; and  the exitt, i.e., when we have the raw sequence from the beginning of its processing, as is the case here, we can combine two LSTM structures, each of them processing the sequence in different directions, one the forward direction and the other one in the backward direction. In this case the layer is called biLSTM and it combines the information in both directions9. One of the most important parameters of this type of network is the number of hidden nodes. To make an LSTM networks deeper, extra LSTM layers can be added. To prevent overfitting, dropout layers are included after LSTM layers17.When the information of sequence Layer 1: Input sequence layer where the sequence is represented by two features (the X and Y coordinates) of the points that define the spiral going from one end to the other.Layer 2: biLSTM with a total on 52 hidden units.Layer 3: Dropout layer of 20%.Layer 4: biLSTM with a total on 40 hidden units.Layer 5: Dropout layer of 20%.Layer 6: biLSTM with a total on 25 hidden units.Layer 7: Dropout layer of 20%.Layer 8: biLSTM with a total on 20 hidden units.Layer 9: Dropout layer of 20%.Layer 10: biLSTM with a total on 15 hidden units.Layer 11: Dropout layer of 20%.Layer 12: Fully Connected Layer, that will act as a convergence layer on which the number of output classes to be obtained is identified, i.e. it matches the number of groups identified at the input Layer 13: Softmax Layer. This layer, using the input from the previous layer, assigns probabilities to the different classes obtained from the previous layer.Layer 14: Classification Layer, which provides the final output of the model, according to the output of the previous layer, identifying whether the input data  is from a control subject or an essential tremor subject.The final classifier based on the LSTM model is represented in Fig. In our case we built the model using 14 layers, operating in classification mode. The layers are the following:To evaluate the results, the accuracy (ACC), the sensitivity or true positive rate (SEN) and the specificity or true negative rate (SPE) will be used, calculated as follows:In the first experiment, 7 subjects from each group were randomly selected, and the model was trained using these subjects with different number of artificial samples: 0, 5, 50 and 100 artificial samples per group. This experiment allowed to quantify the effect of the artificial samples, and to identify which subjects from the test dataset were wrongly classified.In the second experiment, several training runs were performed with 10 repetitions for each, using the same parameters for the LSTM model but with a random selection of subjects. Therefore, the experiment allowed us to analyse the results in terms of accuracy, sensitivity and specificity, calculating the mean and standard deviation for each case.To validate the use of the proposed strategy as a DA method to create artificial samples for a better diagnosis of patients with ET, two experiments have been proposed:Control subjects: 1, 4, 6, 10, 13, 16 and 21ET subjects: 1, 3, 7, 13, 16, 18 and 22The model was trained with these subjects plus the artificial data generated by combining IMFs from them. Therefore, the changes in the accuracy of the results were determined by the number of artificial samples generated in each case. Results for the true negative rate (CT subjects) and true positive rate (ET subjects) are depicted in Fig. This experiment was carried out with 0, 5, 50 and 100 artificial samples generated for each group, using the same original input samples for training. The subjects for the training step were:Numerical results for the accuracy, sensitivity and specificity are presented in Table Since the results obtained when training a model fluctuate if it is executed several times and for different input data, in this case we repeated 10 times the same experiment, with a random selection of subjects used for the training step, and with 0, 5, 50, 100 or 250 artificial samples of each group. Moreover, the number of real subjects in the training step was explored considering 10%, 30% or 50% of the original subjects for training. In each case, the artificial samples were generated using the IMFs of the selected original subjects.Figure To validate the proposed method, we performed a set of experiments using the 10 different DA methods presented in “Two experiments have been proposed to test the effectiveness of the use of artificial samples using the proposed method based on a decomposition–recombination strategy, and in both cases the results with artificial samples have clearly outperformed the results obtained without artificial samples.In the first experiment Table  the bestIn the second experiment, we calculated the mean value of 10 experiments in different scenarios, in terms of the percentage of subjects used for training, and the number of artificial samples generated for each group.Table 18.The sensitivity is also improved in these cases, from 68.18%  to 93.64% for the best case, and from 81.33%  to 88% in the second-best case. Finally, the specificity slightly decreases from 95%  to 91.43% in the best case, and increases from 78.95%  to 87.37% in the second-best case. All these results are summarized in Fig. When comparing the proposed method with the other DA methods, we found that our method outperforms all methods in terms of accuracy and sensitivity, and only for specificity did one of the methods perform better. It’s interesting to note that our method based on mEMD increased the accuracy by about 10.5% , while the best other case (Rotation) only increased it by 5.5% . The other methods that obtained an accuracy over 80% where: Jittering, Magnitud warping and Permutation, all of them with a mean accuaracy of 82.08%; Scaling, with a 80.83%; and SPAWNER with a 80.42%. Without artificial samples, the mean accuracy was of 77.50%. The rest of the methods obtained a mean accuracy below that value, being cGAN the worst case. Note that the accuracy obtained by mEMD is in line with the result obtained in the first experiment, as reported in the last row of Table We observed that only the DA methods based on amplitude manipulations improved the results. The fact that Window warping, Window slice and Time warping did not provide results superior to the NONE case is probably due to the type of manipulation performed on the signal. In all three cases, the temporal relationship between the samples is affected, so the tremor (or lack of tremor) is also affected. Finally, the fact that cGAN is not useful is probably due to the lack of real samples. GANs are deep learning models that need huge amounts of data to train the generator, but in this application , the database is small. Therefore, if there is not enough data available, the artificially generated data is not useful, decreasing the performance of the classifier.Focusing on the proposed method, the best case, obtained when using 50% of the original samples for training plus 100 artificial samples, represents an interesting improvement compared to the case without artificial samples, but it is interesting to note that when using only 30% of the original samples for training and adding 50 or more artificial samples per group, the accuracy obtained is better than when using 50% of the original data without artificial samples. This is relevant because it indicates that mEMD-based artificial sample generation is useful when we have small datasets, where only a few samples are available to build the model. In this example, 15 original samples were used for training, to which the artificial samples generated per group were added. The new artificial samples contributed positively to the training of the LSTM model, improving its accuracy and controlling the over-fitting of the system.19 and calculated the difference in absolute value of the two indices. Graphical results are presented in Fig. To emphasise the fact that the proposed method is useful to increase accuracy but also to balance and improve sensitivity and specificity, we calculated Cohen’s Kappa and Matthews Correlation Coefficient (MCC). We used the same methodology presented in19, this indicates a high capacity to detect positive and negative cases with a minimum error. Furthermore, as detailed in19, the case where both indices show a very similar positive result correspond to a well-balanced experiment. Comparing the best case with the same configuration without the use of artificial samples, an improvement of about 20% is observed in both the MCC and the Kappa index.The results for the best case  are highlighted in Fig. It is also important to mention that continuously increasing the percentage of artificial samples do not improve the results, as a saturation effect appears. This is evidenced by the results obtained when using 250 artificial samples in all the experiments, which are similar to the ones obtained with only 50 artificial samples see Fig. .5 using 84 linear and non-linear features extracted from all the available variables generated by the digitizer tablet; and similar to the value obtained in6 using 77 linear and non-linear features. However, our method is below the 97.96% reported in7, which obtained this result after selecting the best 5 features over a set of 35 pre-computed linear and non-linear features (in time and frequency domains) and combining two different strategies . However, this is a complex system based on the pre-calculation of a large set of features, in contrast to the proposed system using LSTM, where no features are calculated beforehand.If we compare the best result obtained with the strategy proposed in this paper with those already published in other papers, we can see that the method proposed here is powerful since only using the X and Y coordinates achieves 92.40% accuracy, which is better than the 91% obtained inFinally, in terms of the computational time needed by the system, all DA methods required much less time compared to the time used to train the LSTM model. In a desktop Intel(R) Core(TM) i7-7700K CPU @ 4.20 GHz with 16.0 GB of RAM, the training of the LSTM network took about 75 min, while the DA methods took only a few seconds to generate the artificial samples. The only two methods that took slightly longer were the mEMD method, which took about 5 min for the decomposition of the time series, and the SPAWNER method, which took about 10 min. Therefore, if we are interested in reducing the overall computational time, efforts should be made to reduce the time needed for training the model.This study presents a deep learning LSTM network for the diagnosis of essential tremor from the X and Y coordinates of the Archimedes spiral. Since deep neural networks need a large amount of data to converge, a data augmentation strategy based on a decomposition–recombination strategy using mEMD was implemented. The artificial samples avoided overfitting in the training stage of the LSTM network and increased the classification results in the test stage. Moreover, since the acquisition of the original data required specific equipment, the study was carried out using only the X and Y coordinate points, with the idea that it can be easily replicated by acquiring the data using any digitising tablet.The results obtained with the proposed method show a significant improvement of about 10% compared to the case without artificial samples. The other DA methods only showed an improvement of half or less than that achieved by our decomposition–recombination method, and even worsened the result in 4 cases. Furthermore, the proposed method has proven to be useful when only 30% of the available samples were used for training, which is an interesting result when dealing with small datasets.These results have been produced by generating 600–800% more artificial samples than the existing number of original samples. In the case of increasing the number of artificial samples above these percentages, the results obtained are still better than when using only real samples, but at the same time do not improve on or worsen the results achieved when fewer artificial samples are used. This effect could be explained by the fact that excessive reuse of the original data to create more artificial samples causes a saturation effect when training the model.20, could be explored. Taking into account that the decomposition–recombination strategy works well, other types of decomposition methods could also be investigated. For example, the DCT transform was used in18 to decompose iEEG signals in frequency bands and new artificial data was created by recombining frequency bands from different subjects, which could also be used with handwritten signals. Another aspect that could be further investigated would be to add attention layers in the LSTM network, which could improve the performance of the model. In that sense, Transformers21 could be a good choice for use in this application. Finally, we would like to stress that the use of this approach could benefit the advancement of low-cost, non-invasive methods that are easily adaptable to patients and hospitals, as they can be useful and helpful in real-world situations from a social and economic point of view.In future works, faster methods for decomposing the samples with mEMD, such as serial-EMD


Preeclampsia remains a high cause of incidence and death for mothers and fetuses in developing nations. Preeclampsia has numerous clinical and biochemical markers that have been tested, but they have failed to provide a conclusive diagnosis in the different phases of the disease's progression. Herein, our team intended to determine potential diagnostic biomarkers for preeclampsia and analyzed associations with immune cells. Two microarray data from mankind's preeclampsia and control specimens were acquired from GSE75010 and GSE44711 datasets. Differentially expressed genes (DEGs) were identified between77 normal samples and 80 preeclampsia samples. Candidate biomarkers were discovered using the least absolute shrinkage and selection operator (LASSO) and the support vector machine recursive feature elimination (SVM-RFE) analysis. The expressions and diagnostic values of genes in preeclampsia were further demonstrated in the GSE44711 dataset (8 control samples and 8 preeclampsia samples). The correlation of critical genes with the proportion of immune cells was analyzed. We identified 20 DEGs in preeclampsia. Diseases enriched by DEGs were mainly related to preeclampsia, gestational diabetes, ovarian disease, female reproductive system disease, and endocrine system disease. COL17A1, FLT1, FSTL3, and SERPINA3 were identified as diagnostic genes of preeclampsia and validated in the GSE44711 datasets. Immune cell infiltration assays suggested that COL17A1, FLT1, FSTL3, and SERPINA3 were related to several immune cells. Overall, we identified four critical diagnostic genes in preeclampsia. Furthermore, more well-designed research studies with larger cohorts were warranted to confirm the value of the four genes for the diagnosis and outcome of preeclampsia patients. Two percent to eight percent of all pregnant females have the complication of preeclampsia, which occurs when high blood pressure and proteinuria develop suddenly and without warning during pregnancy . It has Generally, in the absence of a definitive cause, preeclampsia is thought to be the result of a complex interplay between a number of maternal genes, environment factors , and/or a deregulated immunoresponse on behalf of the mother in response to the paternal component of the fetal genotype , 8. SeveMore and more interest has been aroused in terms of determining gene expression profiles on the foundation of gene chips and high-throughput sequencing for diagnoses and risk forecasts of substantial multifactor disorders, like preeclampsia –16. HereFirstly, our team acquired a set of preeclampsia chip data, GSE75010 and GSE44711, from the GEO datasets. GSE75010 datasets included 77 preeclampsia samples and 80 normal samples. GSE44711 included 8 preeclampsia samples and 8 normal samples. The data were processed via the following: (1) the multiple probes were mapped to the same gene, (2) the null probes were removed, (3) the probes were first mapped to the gene, and (4) the acquired dataset was log2-transformed quantile-normalized signal strength.P value of 0.05 or less.Package limma in R was used to study data on gene expression differences between preeclampsia samples and normal samples, using thresholds of ∣log2 fold change (FC) | >0.8 and a modified P < 0.05 had significance in statistics. The “ggplot2” and “GOplot” packages in R were used to create the visual GO enrichment maps generated by the annotation analysis. Using R's “clusterProfiler” and “DOSE” packages, we ran enrichment analyses for disease ontology (DO) terms on DEGs [Then, GO enrichment and KEGG pathway enrichment analyses were completed to find the major biological attributes of DEGs. Adjusted  on DEGs .Preeclampsia diagnostic markers were classified using the least absolute shrinkage and selection operator (LASSO) method and support vector machine (SVM) arithmetic. glmnet's LASSO package was used, with the response type set to binomial and alpha set to 1. In addition, as a surveillant machine learning approach to support vectors, the support vector machine recursive feature elimination (SVM-RFE) identified the optimal variates via the deletion of the SVM-produced eigenvectors . For theUsing mRNA expression data from 77 normal samples and 80 preeclampsia samples, we created a ROC curve to investigate the predictive usefulness of the suggested biomarkers. Preeclampsia and control samples were separated using ROC assays, which were further validated in the GSE44711 datasets which included 8 control samples and 8 preeclampsia samples.http://cibersortx.stanford.edu) was utilized to identify the relative proportions of 22 invading immunocyte types. Every specimen's immunological scores were calculated using the ESTIMATE algorithm.In each preeclampsia sample, CIBERSORT , soluble FMS-like tyrosine kinase-1 (sFlt-1), placental growth factor (PlGF), and vascular endothelial growth factor (VEGF) –21. VascAs a machine learning approach on the foundation of SVM, SVM-RFE is applied to observe the optimal variates via the deletion of SVM-produced feature vectors . When thThe precise pathogenesis of preeclampsia remains elusive; nevertheless, endothelial aberrant function, improper angiogenetic activity, insufficient trophoblast invasive ability, and spiral uterine artery remodeling have been determined as pivotal contributing factors , 29. TheThis study also has some shortcomings. Firstly, our team acquired data merely from the GEO datasets, and the sample size was not quite large. More research studies with bigger sample sizes ought to complete to verify the discoveries herein. Secondly, although 4 critical genes were identified as potential biomarkers for preeclampsia immunotyping, no in vivo or in vitro studies were carried out, so this should be a focus in future work.Our study identified COL17A1, FLT1, FSTL3, and SERPINA3 as novel diagnostic biomarkers for preeclampsia patients. In addition, their associations with immune cell infiltration may promote the development of immunotherapy in patients with preeclampsia.


Current advances in omics technologies are paving the diagnosis of rare diseases proposing a complementary assay to identify the responsible gene. The use of transcriptomic data to identify aberrant gene expression (AGE) has demonstrated to yield potential pathogenic events. However, popular approaches for AGE identification are limited by the use of statistical tests that imply the choice of arbitrary cut-off for significance assessment and the availability of several replicates not always possible in clinical contexts.Hence, we developed ABerrant Expression Identification empLoying machine LEarning from sequencing data (ABEILLE) a variational autoencoder (VAE)-based method for the identification of AGEs from the analysis of RNA-seq data without the need for replicates or a control group. ABEILLE combines the use of a VAE, able to model any data without specific assumptions on their distribution, and a decision tree to classify genes as AGE or non-AGE. An anomaly score is associated with each gene in order to stratify AGE by the severity of aberration. We tested ABEILLE on a semi-synthetic and an experimental dataset demonstrating the importance of the flexibility of the VAE configuration to identify potential pathogenic candidates.https://github.com/UCA-MSI/ABEILLE.ABEILLE source code is freely available at: Bioinformatics online. OutPyR showed good performances in reporting injected AGE on small sample size but the number of total AGE identified was very high leading to a high number of false positives. Consequently, there is an urgent burning to develop novel computational approaches to resolve the diagnostic deadlock and improve our knowledge of rare disorders  and whole-genome sequencing (WGS) has greatly accelerated the identification of variants in previously unknown rare disease genes . This apisorders . Here, wet alRare-disease cohort from Kremer . The RNA-seq raw read counts for this cohort were downloaded from Small datasets. We used the Kremer et al. dataset and we created six smaller sub-datasets of size 110, 90, 60, 30, 20, and 10 samples, respectively, composed of the 6 patients with validated AGE  and the complementary number of patients to arrive to the desired dataset size. For each size, we created 10 datasets randomly selecting the patients without the validated AGE. We then run the two tools ABEILLE and OUTRIDER and we measured how many times they were able to identify any combination of the six AGEs depending on the size of the dataset.GTEx cohort. The Genotype-Tissue Expression (GTEx) project  is a public database of WGS, WES, and RNA-seq data collected post-mortem from 54 non-diseased tissue sites across nearly 1000 individuals. We randomly selected samples from the GTEx database to build the semi-synthetics datasets. We also filtered out samples with RIN < 6 (RNA Integrity Number).Semi-synthetic datasets. Due to the absence of a gold standard real dataset with known AGE, we decided to use a computational strategy to inject AGE in the GTEx cohort. We implemented the same strategy as described in the study of j and sample i to substitute to the original value, j, N is the amplitude of the corrupted count [a random value drawn in a normal distribution characterized by a mean of log(3) and a standard deviation of log(1.6)]. AGEs are injected randomly with probability 10−6, 10−5 or 10−4 resulting in different percentages of injected AGEs  in samples randomly selected from the GTEx database. We created 18 semi-synthetic datasets composed of 50, 75, 125, 250, 500 and 1000 samples with AGE injected with the three different probabilities. For a complete summary of the semi-synthetic dataset characteristics see With ABEILLE is a computational framework to identify AGEs . It is cABEILLE main and ABEILLE decision tree. Hence, a labeled dataset with known AGEs must be used. In absence of that, as it is the case for us, a semi-synthetic dataset can be built. AGEs can be simulated as described in The purpose of this phase is to determine the thresholds of parameters implemented in ABEILLE model to discriminate AGEs respect to normal gene expression (NGE). For this phase, we use two modules: ABEILLE main. The core of ABEILLE is composed by a VAE followed by a linear regression model.VAEs are generative models, which means they learn to approximate a data generating distribution. Through approximation and compression, these models have been shown to capture an underlying data manifold  and disentangle sources of variation from different classes of data.et al. study  and let the model generate the reconstructed counts (R_expr) . AGEs prj and sample i, j and sample i, Where j and sample i, j.The delta count Δ, that we define here as:For each gene, the divergence score and delta count are plotted for each patient composing the cohort: we expect the points to be agglomerated very close to each other in case of NGE (high reconstruction fidelity) while to see point(s) further from the main agglomeration in case of AGE (low reconstruction fidelity). We thus apply a linear regression model and calculate parameters associated to this model to evaluate its position on the plot and its reconstruction fidelity. These parameters are:Typeerror, the standard residues is the distance between the predicted value on the linear regression and the real value.Dfbetas, are statistics that indicate the effect that deleting each one observation has on the estimates of the regression coefficients associated with the gene.Hat, projection matrix where the value of the diagonal corresponds to leverages. The leverages describe the influence that each response value has on the fitted value for that same observation.CooksD, Cook’s distance is defined as the sum of all the changes in the regression model when observation i is removed from it.ABEILLE decision tree. To avoid to set threshold for the parameters calculated on the linear regression to define the AGE, we used a decision tree approach. Regression parameters calculated on the semi-synthetic datasets were used to feed a decision tree using the CART algorithm .To identify enriched terms in AGEs found in the Kremer dataset by ABEILLE, OUTRIDER and the case-control approach used in the original study, we used the R package enrichR . Briefly, we randomly suppressed samples from the original cohort in order to obtain datasets with sizes: 110, 90, 60, 30, 20 and 10 always keeping the 6 patients with validated AGEs. We repeated the strategy 10 times for each size thus obtaining 60 datasets. We then tested the ability of ABEILLE and OUTRIDER to recall any of the 6 validated AGEs accordingly with the sample size . As expeWe then studied the identification of AGEs by ABEILLE and OUTRIDER. To perform this analysis, we injected simulated AGEs into the GTEx data and counted the number of such AGEs that were recovered as described in Section 2. We simulated AGEs with three different probabilities resulting in different percentages of injected AGEs . The analysis was repeated for six different size datasets: 50, 75, 125, 250, 500, 1000 samples . We calcP-values and Z-scores for OUTRIDER and divergence score and delta count for ABEILLE . Since recall expresses the proportion of correctly found AGEs among the total number of injected AGEs, we can state that ABEILLE performs better in identifying true AGEs. ABEILLE performs better on datasets with very few AGEs, which makes it particularly suitable for rare diseases where a single gene in a patient may be responsible for the pathology and where the available cohorts are small. These results were corroborated by the application on the real data from Kremer et al. dataset. Here ABEILLE showed a higher agreement with AGE found by the original study than OUTRIDER and a higher specificity to detect AGEs experimentally validated. Of note, ABEILLE outperformed OUTRIDER when sample size is smaller than 60 samples: while OUTRIDER cannot identify any of the validated AGE, ABEILLE showed similar performances as observed on the entire cohort. Thus ABEILLE is suitable for AGE identification in the context of rare diseases.Due to the lack of a ‘gold standard’ dataset with known real AGEs, we had to generate We did not compare ABEILLE with other known methods for RNA-Seq data analysis such as DESeq2 (https://zenodo.org/record/6395166). Both tools showed some limitations to handle these data, leading to a large number of genes with very low expression identified as AGE. For OUTRIDER this limitation was already claimed by the authors because of a possible poor fit of the negative binomial model. For ABEILLE, the issue is in the sparsity of the data because we optimized the model for small datasets where we do not expect a high degree of sparsity as in the single-tissue datasets in GTEx. Thus a novel model should be developed to handle single-tissue and multiple-tissues AGE identification, although we do not expect to have data from several tissues for the same patient in the diagnostic context.Finally, we tested ABEILLE and OUTRIDER on finding AGEs in single-tissues of the GTEx dataset  under reference number [ANR-15-IDEX-01].Conflict of Interest: none declared.btac603_Supplementary_DataClick here for additional data file.


Colorectal cancer is a highly heterogeneous disease. Tumor heterogeneity limits the efficacy of cancer treatment. Single-cell RNA-sequencing technology (scRNA-seq) is a powerful tool for studying cancer heterogeneity at cellular resolution. The sparsity, heterogeneous diversity, and fast-growing scale of scRNA-seq data pose challenges to the flexibility, accuracy, and computing efficiency of the differential expression (DE) methods. We proposed HEART (high-efficiency and robust test), a statistical combination test that can detect DE genes with various sources of differences beyond mean expression changes. To validate the performance of HEART, we compared HEART and the other six popular DE methods on various simulation datasets with different settings by two simulation data generation mechanisms. HEART had high accuracy ( Colorectal cancer (CRC) was the world’s third most common cause of cancer mortality, with more than 850000 deaths annually . The Colt-test, z-test, and F-test, have poor results due to the extreme skewness caused by the sparsity of the scRNA-seq datasets. Non-parametric tests, such as the Wilcoxon rank-sum test, adapt for the sparsity of scRNA-seq data. But, they have awful accuracy because of the high heterogeneity and complexity of scRNA-seq data. The probabilities of Type 1 errors of the non-parametric tests vary systematically with the increasing heterogeneous variances and remain relatively constant even if the sample size increases Droplet-based single-cell RNA-sequencing methods measure gene expression on tens or hundreds of thousands of cells at the single-cell level. Gene expression measurements in droplet technology are often in the form of low counts with a large fraction of zero values, and difficult to estimate the exact statistical distribution. We decomposed the gene expression distribution into two parts : the stan” parts . Therefod groups . We test DE gene . Due to Fisher’s  theory op-values p-value p-value of p-values p-values of all genes.We split the complex null hypothesis HEART proposed a combination test to catch various sources of differences in gene expression patterns between two pre-defined groups. To validate the performance of HEART, we used two simulation data generation mechanisms to compare HEART and other six popular DE methods, including five model-based DE methods  and a default test in Seurat (Seurat-W). Simulation details were provided in the “Methods”. Briefly, the artificial simulation tool, Splatter package , generatIn simulation 1, we evaluated the performances of each method on simulation datasets with the same simulation settings. HEART, Monocle3, and NBID perform better than other methods . They hadatasets . Regardip-value estimation for each method  count are two main quantification schemes in single-cell RNA-sequencing technologies and have different statistical characterizations. Some literature  suggestevia bulk RNA-seq (Human brain data (GSE67835)  was a si RNA-seq . DE gene methods . Moreove methods . Figure In this human brain single-cell dataset quantified by read counts, HEART performs best among seven DE methods. Underlying different standards, HEART always had excellent accuracy for DE gene detection. DESeq2 and NBID had high TPRs, but they maybe detect false DE genes because they identified overabundant genes as DE genes.+ Naive T cells (1873 cells) and CD4+ memory T cells  from the PBMC68K  is the most commonly diagnosed cancers in the world.20% of individuals with newly diagnosed colorectal cancer have metastatic disease upon presentation, and another 25% of those who initially have localized illness will eventually acquire metastases . DistantConsequently, we supposed that a series of genes, CTTN, S100A4, S100A6, etc., were potential colorectal cancer metastasis biomarkers. The MK5 subpopulation with highly-expressed above potential biomarkers might be a cluster related to colorectal cancer metastasis and have a circulating tumor cell (CTC). The exact mechanism between MK5 and colorectal tumor metastasis warranted further investigation.+ Naive T cells and CD4+ memory T cells from the PBMC 68k dataset quantified by UMI counts. HEART had less computational time and higher TPRs and Differential expression analysis was a crucial topic in cancer heterogeneity analysis. The new characteristics of scRNA-seq data put forward new challenges for the DE method. Model-based methods methods’ performances are unstable due to strong assumptions and lacked scalability facing the explosive growing scale of single-cell data. Test-based methods were more scalable than model-based methods. However, the accuracy existing in these test-based methods was relatively too low in identifying DE genes due to the sparsity, variability, and complexity of scRNA-seq data. HEART proposed a bio-driven combination test framework that captures comprehensive differences by integrating differential information about gene expression ratio, gene expression level, and variability. Unlike most competitors assuming theoretical statistical distribution (some are complex mixture distributions) for gene expression, HEART used a combination framework of simple statistical tests to test the two parts of the gene expression. We compared HEART and the other six DE methods on various simulation datasets with different sample sizes and DE strength of DE genes. HEART achieved an excellent trade-off between accuracy and computational efficiency. It had higher cterized , the intcterized . In rececterized . KeepingIn summary, HEART is a competitive DE method for scRNA-seq data, which maintains high accuracy, unrivaled computational efficiency, and strong robustness across diverse scRNA-seq datasets.https://support.10xgenomics.com/single-cellgene-expression/datasets. The human brain dataset can be obtained by R package SC2P or the GEO database repository under accession code GSE67835. The scRNA-seq data of one stage III colorectal cancer patient have been deposited in the OMIX, China National Center for Bioinformation / Beijing Institute of Genomics, Chinese Academy of Sciences (https://ngdc.cncb.ac.cn/omix: accession no. OMIX002120). The spatial transcriptomic data of two colorectal cancer patients are available from (http://www.cancerdiversity.asia/scCRLM).We used three actual scRNA-seq datasets in applications. The PBMC68K is available from We used two simulation data generation mechanisms to generate scenarios with different settings. Each design had 20 replications. The popular artificial protocol, Splatter , generatSimulation 2 adopted a semi-simulation mechanism based on actual scRNA datasets to recover the multimodality and biological characteristic complexity of actual scRNA-seq data  Chen et. First,  PBMC68K  as sourc PBMC68K . We geneAll DE gene lists in simulation datasets were artificially set. We calculated all method performance indices according to known DE gene lists. Due to the unattainability of the whole accurate DE genes list of different cell groups in real single-cell data, we used different standards to set three potential DE gene lists and calculated all method performance indices.Standard 1. Known DE genes from the literature.Standard 2. The top 500 genes are ranked by the chosen number of times by all methods.Standard 3. The top 1,000 genes are ranked by the chosen number of times by all methods.For Standard 1, we collected dozens of known DE genes from various experiments based on bulk RNA-seq in the literature . They weOn the basis of the DE gene list in 2.3, we calculated a series of indices: group 1 and group 2 are For this On” state of each gene is involved in calculations. For hypothesis On” state.In terms of hypotheses p-value of each test is recorded as p-values For this


However, the use of MI with continuous data  is sensitive to data size, correlation strength and underlying distributions, and often requires laborious and, at times, ad hoc optimization.A cell exhibits a variety of responses to internal and external cues. These responses are possible, in part, due to the presence of an elaborate gene regulatory network (GRN) in every single cell. In the past 20 years, many groups worked on reconstructing the topological structure of GRNs from large-scale gene expression data using a variety of inference algorithms. Insights gained about participating players in GRNs may ultimately lead to therapeutic benefits. Mutual information (MI) is a widely used metric within this inference/reconstruction pipeline as it can detect any correlation (linear and non-linear) between any number of variables (k-nearest neighbor (kNN) MI estimation results in significant error reduction as compared to commonly used methods based on fixed binning. Second, we demonstrate that implementing the MI-based kNN Kraskov–Stoögbauer–Grassberger (KSG) algorithm leads to a significant improvement in GRN reconstruction for popular inference algorithms, such as Context Likelihood of Relatedness (CLR). Finally, through extensive in-silico benchmarking we show that a new inference algorithm CMIA , inspired by CLR, in combination with the KSG-MI estimator, outperforms commonly used methods.In this work, we first show that estimating MI of a bi- and tri-variate Gaussian distribution using Using three canonical datasets containing 15 synthetic networks, the newly developed method for GRN reconstruction—which combines CMIA, and the KSG-MI estimator—achieves an improvement of 20–35% in precision-recall measures over the current gold standard in the field. This new method will enable researchers to discover new gene interactions or better choose gene candidates for experimental validations.The online version contains supplementary material available at 10.1186/s12859-022-05047-5. Most cells in a multicellular organism contain the same genome, yet they can differentiate into different cell types and adapt to different environmental conditions . These rAdvances in large-scale gene expression data collected from omic-level microarrays and RNA-seq experiments allow the construction of basic networks by clustering co-expressed genes using statistical correlation metrics such as covariance and threshold to determine the statistical significance . Anothern-dimensions).Originally introduced for communication systems by Shannon in the late 40s , mutual i.e., normalized fluorescence intensity data for gene expression) needs to be discretized first to build probability density functions (PDF). This practice is known to be sensitive to data size, correlation strength and underlying distributions  for three MI estimation methods: FB-ML, kNN-KL and kNN-KSG. The code for the three estimators was written in Python 3.8, used built-in functions from Numpy v1.19 and Scipy v1.5, and was run on a single core of a desktop [Intel Xeon E5-1620 @ 3.6 GHz]. As seen in Fig. minet  for different combinations of MI estimator and GRN inference algorithm for the 6 different Yeast networks from DREAM3. Figure S14: Sorted boxplots of percentage AUPR difference (increase or decrease) relative to the gold standard combination  for different combinations of MI estimator and GRN inference algorithm for the 5 different networks of 100 genes from DREAM4. Figure S15: Area Under Precision–Recall curve (AUPR) versus different number of bins or k-neighbors for real E. coli data. Figure S16: AUPR comparison of different combinations of MI estimators and inference algorithms when non-TF-containing interactions are removed from the networks.Additional file 3.Table S1: Median AUPR and %ΔAUPR (AUPR_relative) values for different combinations of MI estimator and GRN inference algorithm for different network sizes. Table S2: Median AUPR and %ΔAUPR (AUPR_relative) values for different combinations of MI estimator and GRN inference algorithm for different organisms. Table S3: Characteristics of the 10 synthetic networks from DREAM3 and statistics of the different 3-node network motifs extracted. Table S4: precision and recall for various Z-score values for the real E. coli network.


Early diagnosis of Alzheimer’s Disease (AD) is critical for disease prevention and cure. However, currently, techniques with the required high sensitivity and specificity are lacking. Recently, with the advances and increased accessibility of data analysis tools, such as machine learning, research efforts have increasingly focused on using these computational methods to solve this challenge. Here, we demonstrate a convolutional neural network (CNN)-based AD diagnosis approach using the surface-enhanced Raman spectroscopy (SERS) fingerprints of human cerebrospinal fluid (CSF). SERS and CNN were combined for biomarker detection to analyze disease-associated biochemical changes in the CSF. We achieved very high reproducibility in double-blind experiments for testing the feasibility of our system on human samples. We achieved an overall accuracy of 92%  based on the clinical diagnosis. Further, we observed an excellent correlation coefficient between our test score and the Clinical Dementia Rating (CDR) score. Our findings offer a substantial indication of the feasibility of detecting AD biomarkers using the innovative combination of SERS and machine learning. We are hoping that this will serve as an incentive for future research in the field. Alzheimer’s disease (AD) affects millions of people worldwide and is increasing drastically due to the aging population ,2,3,4. TCSF provides a means to assess neurodegenerative processes in the brain through the identification of disease-associated molecules. These molecules most often are proteins or protein fragments, including the amyloid β-protein (Aβ) and tau ,25,26,272. The pyramids formed a quasi-periodic array with a hexagonal arrangement that was uniformly distributed across the entire sample surface area of 1 cm × 1 cm. Due to the manner in which the pattern was generated , variations in the spacing between pyramids and the sizes of the pyramids themselves can appear. This variance was estimated to be ±30 nm.Fabrication of the platform was based on sphere lithography . A perioCSF samples were collected and diluted by a factor of 100 and applied to the SERS platform.2 each), as shown in Spectra were acquired using a Renishaw inVia microscope under ambient conditions. The excitation wavelength was 785 nm and the He-Ne laser power was 0.5 mW. The grating used was 1800 lines/mm, and the objective lens used was 50×. We scanned the entire region on the platform occupied by the samples using Raman mapping with a step size of 3 μm . Several characteristics of the patients’ CSF had already been measured, using standard procedures among the ADRCs. These included the levels of Aβ42, total tau, and phospho-tau, as well as the mini-mental state exam (MMSE) and the clinical dementia rating (CDR). A summary of the patient data is shown in The analysis in this work was carried out using R. R was chosen for the Hierarchical Clustering Algorithm (HCA) implementation because it is suitable for statistical learning, and having powerful libraries for data experiment and exploration. Several functions are available in R for HCA, and “hclust” was used because it fulfilled our need for agglomerative hierarchical clustering. The distance matrix was calculated by the function “dist”. The linkage method was changed by adding “method” in the “hclust” function. The results were plotted in dendrogram format with complete linkage. The spectra analyzed using HCA were the average spectra of each CSF sample.A one-dimensional CNN was used to process and classify the SERS spectral data. CNN was used instead of other popular models, such as support vector machines because other works in the field have highlighted that CNN’s offer a much better alternative pipeline . To elabWe started with a dataset size of over 1200 spectra, i.e., at least 80 spectra per sample. To increase the training set, some methods of augmenting the training data were applied: (i) random shifting of each spectrum by a few (1–2) wavenumbers; (ii) introduction of random noise into each spectrum; and (iii) randomly producing linear combinations of spectra collected from the same mapping procedure. The adaptive gradient algorithm (Adagrad) was used for gradient-based optimization while training the model, and early stopping was applied to prevent overfitting. In the model, the learning rate was adapted component-wise by incorporating knowledge of past observations. The Python version used was 3.6.8, and the neural network model was implemented in Tensorflow 1.11.0 , Google’s open-source software library for machine learning. The R version used was 3.6.1. We used the Anaconda coding environment for data analysis and used the matplotlib Python library for plotting.To determine the feasibility of the method, we used 5 distinct sets of CSF samples, where each set contained three replicates. Spectra were acquired from each of the three replicates of each sample set. The study was double-blinded. Neither those providing the samples nor the person carrying out the spectroscopy and data analysis knew the provenance of the samples.–1. SERS mappings with a step size of 3 μm, covering a 9 µm2 area, were carried out. A minimum of 80 spectra were acquired and averaged for each sample. All 15 average spectra are shown in SERS spectra were acquired in the wavenumber range of 550–1650 cm−1 peak from alanine and/or the 870 cm–1 peak from glutamic acid and serine, the 1000 cm–1 phenylalanine peak, the 1171 cm–1 tyrosine peak, the 1465 cm−1 lipid peak, and the 1555 cm−1 tryptophan [Hierarchical cluster analysis (HCA) was used to determine the similarity and differences among the 15 samples quantitatively. Integration normalization was carried out when comparing the samples. The wavenumber of each of the SERS peaks represents one dimension and the peak height represents the corresponding value in that dimension. We grouped the samples using a single linkage of the aggregation HCA. The possible sources of the major peaks that contributed to the formation of different clusters are the—850 cmyptophan ,40,41.HCA clustered the 15 samples into five clearly separated groups . The degWe next studied the ability of the method to distinguish between clinically evident AD and pre-clinical AD (FAD samples) using a “leave-one-out” validation procedure. We trained with all samples save one. We then analyzed the remaining sample. We repeated this procedure until every spectrum was left out once, then the average accuracy across all the data was computed. Leave-one out validation was used mainly because of its low evaluation error and the ease with which it can be used for small sample sizes. The results showed an accuracy of 97.7% for the spectrum of the FAD sample and 93.3% for the spectra of the AD sample, which suggests there was good uniformity over the SERS spectral data of these samples and that they were differentiable. The results of this double-blind study are a significant step forward in establishing the power of the platform for analyzing patient samples, despite intrinsic biological variability.We also performed a leave-one-group-out evaluation on the dataset because a leave-one-out evaluation cannot determine whether our model is capable of exploring the relationship between the SERS testing result for a subject’s CSF sample and the subject’s diagnosed syndrome . This is because the spectral data collected from the same CSF sample are likely to be dependent on that individual sample, thus forming a group of dependent data, so that for an unseen sample that is yet to be classified, the correlation information of its spectral data should not be given to the model during training. Therefore, for each round of evaluation, we needed to make sure that all the spectral data in the test set came from groups that were not represented at all in the corresponding training set. Since we had a total of 17 CSF samples, a leave-one-group-out evaluation was a suitable approach for us to know whether our model could be generalized well to the unseen samples. During each evaluation, the entire SERS spectral data collected from one CSF sample were used for testing, while the rest of the data were used for training. This kind of evaluation was repeated until every group of spectral data had been left out once.The final classification result also took the group dependency into consideration. In each round of evaluation, after the trained CNN made predictions on every testing spectrum, all the predictions were then combined through a majority vote to produce the final prediction, i.e., the class with the highest percentage of predictions was considered to be the predicted class of the testing sample. We used the percentage of predictions leading to the predicted class as a score to represent the likelihood that the testing sample belonged to the predicted class. An overall 94% diagnostic rate was achieved . The norWithin this table, we are able to see that Sample R was the only one with a prediction score less than 50, indicating we were not able to tell if R was a diseased sample. To further understand this sample, we referred to her cognitive test score. Her MMSE score was 25, which should be diagnosed as normal. However, her CDR test score was far away from normal (9 for CDRSUM and 1 for CDRGLOB) . These sTo further understand more complicated situations, such as FAD-related patients, we performed the same test based on our training of normal and diseased patients. FAD-negative samples  had an accuracy of 4/4 (100%) and an average score of 91.25; FAD-positive samples had an accuracy of 4/5 (80%) and an average score of 80.0. The results are shown in Sample D had a test score of 49, indicating we are not able to accurately define whether she was diseased or not. When referring to her medical scores, we found that she had a MMSE score of 28 and CDRSUM of 0.5, indicating that she has mild dementia . More anTo further understand the feasibility of our diagnostic results, we performed a correlation analysis for the diagnostic index and all the AD-related medical parameters. Several parameters were included in the analysis: sex, age, the levels of several biomarkers , and several cognitive test scores .To better analyze the correlation, we first needed to deal with the missing data. In the clinical information provided, the t-tau information of Samples N, R, R, S, T, W, and X were missing, and the p-tau information of Sample R was missing. According to the literature, the t-tau and p-tau levels in CSF are highly correlated, and in the data provided, we saw a highly linear relationship between the concentration of the two types of tau protein with a correlation factor of r = 0.8883. The prediction model can be easily shown by regression:We can see from the figure that our prediction index was highly correlated to all three cognitive test scores. The correlation coefficients were r = 0.79 with MMSE, r = −0.88 with CDRSUM, and r = −0.87 with CDRGLOB. Considering that the CDR scores are taken as an accurate method of diagnosing AD, our prediction index is accurate as a diagnostic. We also observe from the figure that the correlation between single biomarkers  and the cognitive test score (MMSE and CDR) is relatively low. The highest correlation coefficient of a single biomarker was r = 0.47 (between t-tau and MMSE), which is still a low value. This highlights the fact single biomarkers cannot be used to accurately diagnose AD. However, our SERS/AI system has the ability to carry out combinatorial analyses, which allow for much more accurate disease diagnoses, as indicated by the high correlation with the CDR scores.We have presented here a hybrid system of SERS and CNN for diagnosing Alzheimer’s disease with high accuracy. We have achieved excellent reproducibility in double-blind experiments and 92% accuracy in disease diagnosis. The correlation analysis demonstrated that our diagnostic system is more accurate than single-biomarker analyses. The SERS neural network is a novel platform that promises accurate, reliable, and rapid clinical diagnosis of AD. Even though the current study uses a small sample size (due to the limited availability of AD patient CSF samples), the very high accuracy obtained in the double-blind experiments is very encouraging. Our study, therefore, provides an indication of the feasibility of a biological test for AD diagnosis. We are hoping that this will serve as an incentive for much more extensive follow-up research by the Alzheimer’s research community at large. In the future, we expect this approach to allow early-stage AD diagnosis, and we hope this study will be a stepping stone for the SERS/AI technology to find use as a prognostic device and in clinical trials. To that end, subsequent studies will involve larger patient sample sizes, and demonstrate the sensitive and specific diagnostic capability using blood samples.


Single-cell multi-omics sequencing techniques have rapidly developed in the past few years. Clustering analysis with single-cell multi-omics data may give us novel perspectives to dissect cellular heterogeneity. However, multi-omics data have the properties of inherited large dimension, high sparsity and existence of doublets. Moreover, representations of different omics from even the same cell follow diverse distributions. Without proper distribution alignment techniques, clustering methods will encounter less separable clusters easily affected by less informative omics data.We developed MoClust, a novel joint clustering framework that can be applied to several types of single-cell multi-omics data. A selective automatic doublet detection module that can identify and filter out doublets is introduced in the pretraining stage to improve data quality. Omics-specific autoencoders are introduced to characterize the multi-omics data. A contrastive learning way of distribution alignment is adopted to adaptively fuse omics representations into an omics-invariant representation. This novel way of alignment boosts the compactness and separableness of clusters, while accurately weighting the contribution of each omics to the clustering object. Extensive experiments, over both simulated and real multi-omics datasets, demonstrated the powerful alignment, doublet detection and clustering ability features of MoClust.https://doi.org/10.5281/zenodo.7306504.An implementation of MoClust is available from Bioinformatics online. The recent technological innovation of single-cell genomics allows for assaying cellular heterogeneity at an unprecedented resolution. It provides us an unparalleled opportunity to dissect complex biological processes, including cancer  observed in M different omics. Let i from omic m, then the total observation of cell i is K, our objective is to assign the observation set of each cell i, K clusters. For protein data preprocessing, we normalize the counts for each cell after log transforming and finally scale the data. For RNA-seq data, we do the same preprocess and compute the size factor for each cell. For ATAC-seq data, we first generate a rough estimate of the transcriptional activity of each gene by quantifying ATAC-seq counts in the 2 kb-upstream region and gene body. And then we treat the gene activity matrix as RNA-seq data. The raw counts of RNA data and gene activity matrix will also be fed to the model to compute the reconstruction, i.e. NB(ZINB), loss.Suppose our dataset consists of First, we transform each preprocessed π) that represents the weight of the point mass of probability at zero (the probability of dropout events):m. The ZINB model-based autoencoder for m-th omics estimates the parameters mγ refers to the strength of ZINB loss for the m-th omics. We introduce a fusion layer to represent the integrated information of all different omics, which computes a weight averagemw are fusion weights which are contributions of omics to the omic-invariant representation iz. These weights will be adaptively chosen under the guidance of the following contrastive alignment.To capture the character of transcriptomic (scRNA-seq) and epigenomic data, we utilize the same ZINB (In u-th omic with cell i as input. Assume that the predicted soft label of cell i is u and v (i.e. cosine similarity). Compared to the popular Euclidean distance, cosine similarity focus on directions of the vectors rather than absolute values and thus alleviate the problem of inconsistent metrics across different omics. The loss function for a positive pair of latent features For latent feature The contrastive alignment is thus at the sample level. To reduce annoying tuning of parameters, we multiply the contrastive loss by the weight of the least informative omics so that the strength of the contrastive alignment can be automatically adjusted.ih, the hidden representation for cell i. Another fully connected layer with a softmax activation is followed to obtain the k-dimensional soft label aα.To obtain the final cluster assignments, we add a fully connected layer after the fusion layer, producing iz. DDC loss consists of three parts, ensuring the separability and compactness of clusters, closeness of cluster assignments to simplex corners and orthogonality of cluster assignments, respectively.As is admitted in most deep learning clustering methods, we assume that the denoising autoencoder is capable of obtaining a low-dimensional representation which captures most of biological information in the input omics data. Basing on this assumption, we designed three clustering losses to find a better space where the clusters are compact and separable, thus making it easy to distinguish among different clusters. Additionally, we also want the cluster assignments for cells to be deterministic and the assignment vectors for clusters to be orthogonal. Inspired by former works on divergence-based clustering  refers to the strictly upper triangular elements of matrix X. The DDC module consists of inner products between cluster assignment vectors. Cluster assignment vectors are orthogonal if and only if these inner products are zero. Optimizing The third part is designed as the strictly upper triangular elements of The final clustering loss is the sum of these three terms:δ is a hyperparameter which influences the strength of the contrastive loss. Finally, the total loss we use to train MoClust isMoClust can also find doublets efficiently and effectively without manually setting a threshold. Before identifying the doublets, a pretraining process is needed. The pretraining loss to be optimized is:i we define a prototypea. iS consists of all a is assigned to cluster i by MoClust. Given a noise level ϵ, we randomly sample in cells from Gaussian distribution λ is a parameter to control the fusion weights and we fixed Formally, for each cluster α, we compute the α-quantile from experimental distribution acquired from Given a level MoClust is suitable for clustering single-cell RNA-seq and antibody-derived tags data. To validate the effectiveness and efficiency of MoClust clustering CITE-seq data, we selected four real-world CITE-seq datasets, 10X10k, 10XInHouse, Spleen and Lymph datasets. The details of each dataset are listed in We applied several state-of-the-art single-cell multi-omics clustering methods available for transcriptomic and proteomic data over these for datasets for comparison, namely, Seurat V4, CiteFuse  counts according to marker protein. For instance, in We also applied MoClust and competing methods over a series of simulated datasets. By varying the differential expression probability of RNA and protein, we simulated multi-omics datasets of different RNA or protein quality levels. We also generated datasets with different protein numbers and cluster numbers to simulate different circumstances of sequencing. The ARI and NMI of MoClust and competing methods are shown as line charts in To investigate whether MoClust is scalable, we used R package Splatter to simulate a series of CITE-seq datasets with different number of cell samples and features and record the running time of different methods. The RNA DE probability is fixed as 0.15, protein DE probability as 0.7, number of clusters as 10. As is shown in MoClust can also be applied on scRNA-seq and scEpigenome data for integrative analysis. We examined MoClust on three published datasets, including SNARE-seq datasets CellLine and 10XPBMC, as well as SHARE-seq  dataset In 10XPBMC is a published SNARE-seq dataset that can be downloaded from 10X Genetics website. Among all methods, MoClust got the highest ARI applying on 10XPBMC dataset and a NMI only slightly lower than Seurat. As we utilized the Seurat annotations based on transcriptome state as approximate truth, the tiny gap between NMIs of MoClust and Seurat is unsurprising. We also performed all methods over the large-scale SHARE-seq dataset Ma-2020, the detailed results of NMI and ARI can be seen in α, the α-quantile of the empirical distribution obtained from the pseudo counts will serve as a threshold for identifying real doublets. We applied our method on a perturbed 10XInHouse CITE-seq dataset. We randomly chose 80 pairs of cells, each pair from distinct cell types, and averaged the RNA and ADT counts of cells from the same pair to simulate doublets. MoClust implemented an automatic doublet detection module to identify doublets without manually setting a threshold. First, we pretrain MoClust by optimizing σ, τ, δ and γ, which can be seen in τ, δ and γ. We also found that the adequate intervals for σ were similar across different experiments. Optimal hyperparameters for MoClust through all experiments are listed in details in We also verified stability, while varying four hyperparameters introduced in our model, including To investigate the importance of distribution alignment, we trained MoClust without the contrastive loss on CITE-seq datasets 10X10k and 10XInhouse. For 10X10k, without the contrastive module, the ARI deteriorated from 94.5% to 85.9% while the NMI decreased from 89.2% to 83.1%. In To investigate whether the fusion weights is strongly correlated with cell types or they are mainly related to the quality of omics, we selected different subgroups of cell types appeared in 10X10k dataset and applied MoClust on cells from selected cell types. In Through all experiments, we trained each model with the number of clusters the same as the number of different cell types appeared in the dataset. In practice, when the true number of cell types can hardly obtain, we suggest using scRNA-seq analyzing tool SIMLR -cite and BMMC-multiome, with known ground truth labels to conduct grid search for MoClust and all competing deep learning methods. The detailed information of datasets and the criterion for hyperparameters selection are described in the MoClust offers a new perspective of integrative analysis for single-cell transcriptome, epigenome and proteome. Clustering methods for single-cell data have long been obsessed over identifying rare cell types. In 10XInHouse dataset, MoClust also found it hard to distinguish rare cell type ‘CD16 + monocytes’ from ‘CD14 + monocytes’ and we are still making efforts to make MoClust capable of identifying these rare types. To avoid collapse of small clusters, i.e. rare cell types, we added a selective When applied to CITE-seq and SNARE-seq data datasets, MoClust outperforms other state-of-the-art methods for scRNA and protein joint clustering analysis. MoClust shows remarkable NMI, ARI over four different datasets and presents more separable and compact clusters than any other methods. MoClust successfully captured most biological biases and correctly distinguish cells from different cell types in most cases,In practice, single-cell clustering methods are often confused by doublets which typically arise owing to errors in cell sorting or capture. MoClust is armed with an automatic doublet detection module. With experiments over the 10XInHouse dataset, the efficiency and effectiveness of MoClust in detecting doublets and enhancing its clustering performance can be clearly seen. We believe that the deliberately designed representation alignment afford MoClust more practicality and power when compared to any other state-of-the-art methods now available.btac736_Supplementary_DataClick here for additional data file.