Although these methods, especially deep learning, perform well in data classification, they usually require large amounts of data for model training and have limitations in interpretability. Besides, as cancer is a complex systemic disease, the phenotypic difference between cancer samples can hardly be fully understood by only analyzing single molecules, and differential expression-based molecular subtyping methods are reportedly not conserved. To address the above issues, we present here a new framework for molecular subtyping of cancer through identifying a robust specific co-expression module for each subtype of cancer, generating network features for each sample by perturbing correlation levels of specific edges, and then training a deep neural network for multi-class classification. When applied to breast cancer (BRCA) and stomach adenocarcinoma (STAD) molecular subtyping, it has superior classification performance over existing methods. In addition to improving classification performance, we consider the specific co-expressed modules selected for subtyping to be biologically meaningful, which potentially offers new insight for diagnostic biomarker design, mechanistic studies of cancer, and individualized treatment plan selection.Molecular subtyping of cancer is recognized as a critical and challenging step towards individualized therapy. Most existing computational methods solve this problem  Precision cancer medicine aims to characterize the distinct biology of an individual or a group of cancer patients sharing certain commonalities and treat them by targeting the specific oncogenic event shared by such a group . Using bCancer subtyping through applications of machine learning techniques has been done by numerous authors on multiple cancer types. Cascianelli et al. developed a classification method for breast cancer subtyping that employs several machine learning classifiers to solve the multi-classification task for breast cancer subtyping . Markus While these methods, such as deep learning, have powerful capabilities in data classification, most of these methods have limitations in interpretability and tend to require large amounts of data for model training , which hA few papers have been published on cancer subtyping based on co-expression information, which classify cancer samples based on the general characteristics of the relevant co-expression networks . Jiang eIn this paper, we present a new cancer molecular subtype classification framework based on a specific co-expression module and a deep neural network (DNN) named SCM-DNN, which can identify a robust, distinct co-expression module for each subtype of a cancer. A co-expression module is a set of genes whose expressions highly correlate with each other , and a dWe present a new computational framework, SCM-DNN, shown in RNA-seq data and clinical information of breast cancer and stomach cancer tissue and normal samples are downloaded from the TCGA database . These cX = , Xi is the expression value of gene X of the ith sample. Clearly, the more similar the expression levels of a gene are across all samples, the closer its “mad” value is to zero. For our analyses, we only keep the top 90% genes with the largest “mad” values. Overall, 14,439 and 7,761 genes are kept for BRCA and STAD, respectively.For each cancer type, we first construct gene co-expression networks for each subtype; that is, for a cancer type with T molecular subtypes, T co-expression networks need to be constructed. The Spearman correlation coefficient is used to construct the co-expression networks. According to , althougs1, s2, ...sT}, we have performed F-fold sampling to calculate the correlations for each subset, with each fold having Ns samples. Ns should be smaller than min {s1, s2, ...sT}, and F should be large enough to ensure that all samples are selected at least one time. For the fth fold in lth subset, p-values. The final correlation values and p-values of lth subset are defined as Formula (2) and (3):Given the sample sizes of each subtype {p-value >0.01) and genes that do not connect with any other genes in the network. In the end, we have obtained T co-expression networks {MeanNet1, MeanNet2, ...MeanNetT} for each subtype. For each MeanNet, we apply WGCNA to divide it into several co-expression modules. We set the soft thresholds according to the scale free topology fitting index R2 coefficient for each subtype. It reweights the MeanNet by adjusting the coefficient of each co-expression pair to make the network satisfy the scale-free property. All the genes are then hierarchically clustered into different groups based on the weighted network, and the genes that can’t cluster together with other genes are stored in Module0.Furthermore, we have removed gene pairs in the network whose associations are not significant . In order to avoid the bias caused by the number of genes in each module, we will calculate the overlap ratio between Score 1: Specific aggregation score. If genes of one subset are concentrated in a module of one subtype but they are scattered in many different modules for all the other subtypes, it indicates that these genes have a specific co-expression pattern in this subtype. According to this idea, we perform a cross calculation among all the modules of different subtypes to evaluate the specificity of each module. For module Overlapratios,t,i,j). If some edges in For a certain module i, j) in the specific co-expression module, their correlation values on all subtypes are denoted as As the sizes of specific modules are different and there are many edges in each specific module, it is necessary for us to select the most specific edges that are highly co-expressed only in one subtype to represent the character of each specific module. In addition, selecting same number of edges for each subclass can improve the comparability. If we want to select E specific edges for each specific module, following steps can be taken. For a gene pairs . For each subsampling, a reference network set is generated, including T reference networks corresponding to T subtypes, and we randomly select P samples from each subtype several times and generate several reference network sets, shown in Then, one cancer sample is added to a reference set, which is T reference networks, to construct T new co-expression networks, called expanded networks. The perturbation value of a specific edge is obtained by calculating the difference between an expanded network and a reference network.ith specific edge of subtype x, ith specific edge of subtype x in the expanded network and reference network, respectively. ith specific edge. Then, for one cancer sample, it’s T *E perturbation values are merged into a vector, where E is the number of specific edges selected for each subtype, generating a piece of network feature data.Here, i is the One piece of network feature data shows the characteristics of a sample at the co-expression network level. In order to augment the sample size, we add each training sample to several reference network sets. Hence, we can obtain enough network feature data for model training even though there are few cancer samples, which guarantees the classifiers are able to learn sufficient information for each subtype. For each test sample, it is also randomly added to the reference network sets to generate its corresponding new sample(s). It is worth noting that all the reference networks are constructed from samples of training sets.We build a fully connected feed forward neural network classifier with cross-entropy loss function.y depends on the true label of data i. Let h be a neural network, in which the activation function of hidden layers and output layer are ReLu and softmax, respectively. pic is the probability of the data i belonging to subtype c. N is the size of the data. The optimization algorithm is stochastic gradient descent. We apply an early stop strategy to avoid over-fitting in the training process and take 10-fold cross validation to verify the performance of the classification method. In prediction, when adding each testing sample into different reference networks, it generates several new samples and then gets multiple prediction labels, voting strategy are used to obtain final prediction label of this sample.Here, the value of We compared our method, SCM-DNN with three traditional filter feature selection methods , and one state-of-the-art wrapper feature selection method, (HSIC-Lasso) following with DNN. In addition, we also compared our method with one of the few co-expression-based cancer subtyping methods. Moreover, we compared our method with one of the few co-expression-based cancer subtyping methods (SCP), which predicted a sample’s label through calculating its perturbation on the most specific edges of each subclass-representing network. In addition, we also compared our method with DeepCC, which is a deep learning-based framework integrating functional spectra quantifying activities of biological pathways for molecular subtyping of cancer .14439 and 7761 genes were used for the construction of co-expression networks for BRCA and STAD, respectively. We decompose the co-expression network into several modules for each cancer subtype. The number of co-expression modules for each cancer subtype, and the number of genes and edges in each specific co-expression module are shown in To evaluate the discerning power and stability of each co-expression module between each subtype and the samples of the other subtypes of a cancer, we have used accuracy, macro-average recall and macro-average F1-score to avoid possible issues created by imbalanced sample sizes among the subtypes, defined as follow.#i is the sample size of ith group; TP is for true positives, FP for false positives, FN for false negatives, and TN for true negatives.Here, For BRCA subtyping, we have conducted two experiments by selecting the top 100 and top 200 distinguishing co-expressed edges from each co-expression module to evaluate their discerning power. Considering the relatively small sample size and the number of features, a neural network with two-hidden layers is employed to train a classifier, which has 50 and 10 nodes on the first and the second layer, respectively. We have compared the performance of our approach with six other published classifiers (see Methods), each employing the same number of features as our approach.The subtyping performance of our method on BRCA samples along with the performance by other five methods are shown in vs. the other six methods is comparable to that on BRCA, with our method performing the best as detailed in For STAD subtyping, we set the same experimental parameters, including the organization of the neural networks as for BRCA breast cancer molecular subtyping task. The performance by our method Overall, the results reveal that our method gives the best and stable subtyping performance, particularly for the subtyping problems with highly imbalanced sample sizes. We found that our method always performs best specially in recall and F1-score, the reason is: we generate sufficient network feature data for neural network model training, and it avoids the situation that the classifier only learns sufficient information for the category with largest scale, instead of categories with small scale. Hence, our method is superior to other methods when predict the subtype with smallest scale. In addition, network feature data can reflect the characteristics of each individual subtypes. It also proves that specific modules with differentiation and robustness are conducive to improving classification performance. We display network feature data in the form of heat map and find that the samples of the same subtype naturally gather into one block. Details are shown in the To elucidate the possibly unique biology for each cancer subtype, a pathway enrichment analysis is conducted over edges of the identified co-expression module for each subtype. It is worth noting that the number of genes in specific modules of each molecular subtype is different. Specifically, there are 171, 86, 281 and 205 genes in the specific modules of control, ER+, HER2+ and triple negative BRCA samples, respectively, with detailed gene lists given in vs. BRCA cancer samples in terms of their functionalities, namely cell-cell adhesion , interactions with immune cells . Similar can be said about neural functions , cell polarity  and inflammation signaling (leukotriene biosynthesis). Similarly, the most enriched pathways for ER+ samples are growth related , muscle development , and a specific type of immune response (HTLV-I infection). And the most enriched pathways for HER2+ are related to xenobiotic metabolism , oxidative stress (glutathione biosynthesis), and cell morphogenesis changes. The pathways uniquely enriched by triple negative samples involve neural systems, a general indicator for the level of malignancy of a cancer type, and phosphatidylinositol 3-kinase signaling (a key regulator of cell polarity), also strongly indicating the level of malignancy of the cancer subtype.The most enriched pathways in each distinct set of samples shown in For STAD, 72, 81,67,119, and 217 genes and their co-expressed gene pairs are selected as distinguishing features for the control, CIN, EBV, MSI, and GS STAD samples, respectively. The enrichment results by each gene set are shown in The distinct biology of each of the four subtypes of STAD samples, as indicated by their enriched pathways, is striking. For CIN subtype, we see strong indication of toxicity and detoxification in their cells, e.g., by response to toxic substance, sulfation, intracellular protein transport and steroid metabolic process. In EBV samples, the distinct characteristics are dealing with oxidative stress as shown by response to ionizing radiation, valine, leucine, and isoleucine degradation, activation of cysteine-type endopeptidase activity, and upregulation of spliceosome. In MSI, we see that all signals are related to inflammation and immune response in immune response, response to interferon-gamma, type I interferon signaling pathway, and inflammatory response. In GS, the key distinguishing characteristic is rapid cell division, as indicated by cell division, cell cycle, nuclear division, chromatid cohesion and G2/M transition.We have compared the consistency and differences among the top 100 selected features obtained by each of the five methods, including ours, with results summarized in Through further performing differential gene expression analyses on the genes obtained by SCM-DNN, we find their expression have little changes among different subtypes of the same cancer type. This result reveals that differential gene expression-based methods have clear limitations in characterizing changes in biological systems. Hence co-expression-based analyses for cancer subtyping and possibly many other cancer omic data analysis problems could prove to be the way to go.We have also analyzed the connectivity of the selected genes in the co-expression modules. In our subtyping prediction, we used only the top 100 and 200 co-expressed gene pairs. An interesting observation is that all the selected genes could be connected using at most two additional genes in the relevant module, suggesting that the selected feature genes are strongly functionally associated. However, regarding the genes selected by traditional gene expression based feature selection methods, they are generally highly dispersed across a co-expression module.Additionally, due to the transmissibility of information in a network, it’s not hard to control the whole module by managing a few nodes. Moreover, since these modules are specific to each molecular subtype, in other words, they are probably the most striking features of this disease. Hence, they are expected to be the most effective drug targets for individualized therapy.In this paper, we proposed a computational classification method for cancer molecular subtyping based on co-expression network features of each cancer sample. It has been recognized that the phenotypic difference in cancer samples can hardly be fully understood by only analyzing single molecules, and it is the relevant system or specific network that is ultimately responsible for such a phenomenon . MoreoveThe classification performance of our method is superior to conventional molecule biomarker-based methods, when applied to breast and stomach cancer molecular subtyping, under several evaluation indexes. It is a universal framework and is expected to perform well in molecular subtyping task for other cancer types. Besides, it is also easy to transfer to other subtyping tasks, such as cancer sample staging and grading classification. Similarly, through constructing co-expression networks and extracting specific co-expression modules for each cancer stage or grade, a sample could be accurately classified according to its network features generated by calculating the perturbation effect of this sample on each background class-specific module. We assume that specific module of each cancer stage (or grade) can capture the essential distinguishing property of its samples. And adding a sample of a different class to the specific module will induce large disturbance, while adding a sample of its same class will not disturb too much. One of the advantages of this study is that it doesn’t need too many training samples. Prior knowledge in the basis of satisfying the statistical significance indicates that the sample number of each subtype reaching 15 is enough to construct co-expression networks for each subtype. Then, a large number of new samples with a network feature can be generated.Omics data have enabled the unbiased characterization of the molecular features of multiple human diseases, particularly in cancer. Multi-omics may provide molecular insights beyond the sum of individual omics, and it is becoming increasingly common to characterize multiple omics layers to gain biological insights spanning multiple types of cellular processes . Hence, We present here a new framework, SCM-DNN, to identify each molecular subtype’s robust, specific co-expression modules that could efficiently and steadily predict patients’ molecular subtypes of breast and stomach cancer. Compared with traditional gene expression based feature selection methods for multi-classification, SCM-DNN performs better under all the metrics even the sample size of each class is extremely imbalanced. Additionally, these specific genes identified by SCM-DNN could probably represent the striking characteristics of individual subtypes; meanwhile, they are concentrated in the co-expression network. Hence, they are promised to assist us to better understand the underlying mechanism of molecular subtyping and potentially guide individualized medicine.Multi-omics data and their integration are recognized as an effective way to explore the biological mechanism. In future studies, we will make full use of those data to develop a more comprehensive and robust classification method by integrating multi-omics data to construct subtype-specific correlation networks for molecular subtyping of cancers, expecting a deeper mechanism to be discovered.


However, integrating information from different experiments remains challenging because of the batch effect generated by various technological and biological variations in the transcriptome. Numerous batch-correction methods to deal with this batch effect have been developed in the past. However, a user-friendly workflow to select the most appropriate batch-correction method for the given set of experiments is still missing. We present the SelectBCM tool that prioritizes the most appropriate batch-correction method for a given set of bulk transcriptomic experiments, improving biological clustering and gene differential expression analysis. We demonstrate the applicability of the SelectBCM tool on analyses of real data for two common diseases, rheumatoid arthritis and osteoarthritis, and one example to characterize a biological state, where we performed a meta-analysis of the macrophage activation state. The R package is available at  Over the last two decades, high-throughput transcriptome studies have resulted in a vast accumulation of bulk gene-expression experiments in public repositories and value-added resources, including microarray and RNA-seq data . The potHowever, there are several challenges before fully harnessing this wealth of data for scientific investigation; one of the most critical is the ‘batch effect’ in collated transcriptome datasets ,11. BatcGiven the tremendous potential buried in the available bulk transcriptome datasets, we aimed to develop a freely available R-based tool to facilitate gene-expression integration. Here, we present the SelectBCM tool to choose the appropriate BCM for the given set of bulk transcriptomic data. Integrating different BCM tools and assessment strategies into the same framework, the SelectBCM tool, will increase the reusability and reproducibility of these BCMs for batch correction and allow the user to compare and select the top BCM for their chosen datasets. We also demonstrate the application of SelectBCM through case studies and compare differentially expressed genes (DEGs) obtained after batch correction with the traditional meta-analysis approach.Homo sapiens  tool to estimate the batch effect and biological variability of interest in the SelectBCM tool in a given meta-experiment . In summs(i) can range from –1 to 1, with s as an indicator of the presence or absence of ‘batch effects’.To assess the clustering pattern of biosamples before and after batch correction, we compute the silhouette coefficient . TheoretTo estimate the linear batch effect, we perform linear regression using the top 20 principal components (PCs) obtained from PCA as a default setting against a batch  variable. For the estimation purpose, we use the scaled pcRegression score by scaling it by the total variance of the top 20 PCs, as suggested in the κBET package .We compute the regional entropy of batch mixing before and after batch correction using the first two PCs, as indicated in the MNN package . In our Highly variable genes (HVGs) contribute to cell-to-cell variation within a homogeneous cell population and represent true biological heterogeneity ,24. We qTo rank BCMs, we compute sumRank using results obtained from evaluation steps as parameters Figure . In the PVCA: batch  for visualization purposes. We then compute sumRank using the evaluation matrix explained below:where Therefore, sumRank provides the final ranking of BCMs for the given meta-experiment in descending order. BCM ranked higher across evaluation methods will get a higher weightage and, therefore, first rank among others (Output 3).We used visual and DEG analysis approaches to qualitatively assess the impact of the top 3 BCMs on biological inferences. To visually assess the impact of batch correction on biological clustering, we applied PCA on a meta-experiment obtained after batch correction and compared how well biosamples from different batches were mixed. We perform DEG analysis to assess the impact of the batch correction on identifying relevant biological signals. We also compare DEGs identified by BCMs with those determined by the traditional meta-analysis approach (MetaVolcanoR), where people study each experiment individually and then statistically combine the list of significant genes . We provhttps://github.com/ebi-gene-expression-group/selectBCM) implements a flexible framework in R to select the best BCMs for transcriptomic experiments  and osteoarthritis (OA) diseases as examples to demonstrate the usability of SelectBCM for microarray experiments. We curated microarray experiments for RA and OA from synovial fluid or bone specimens for For RA disease, we selected E-GEOD-1919, E-GEOD-55235, E-GEOD-48780, E-GEOD-12021, E-GEOD-55457 and E-MTAB-3201 experiments contributing at least RA or control synovial specimen samples or both. SelectBCM performs batch correction and evaluation for the RA meta-experiment. We observe that the evaluation methods did not produce a consensus among themselves to identify the best BCM Figure . Even thTo assess the impact of the top 3 BCMs shortlisted by the SelectBCM on biological clustering, we carried out a PCA Figure . We firsWe assess the impact of the batch correction on differential gene analysis by comparing DEGs obtained after applying the top 3 BCMs with DEGs obtained from the traditional meta-analysis approach. As expected, different BCMs resulted in different sets of DEGs having minimal overlap  Figure . We alsocis-regulatory region sequence-specific DNA binding, RNA polymerase II transcription regulatory region sequence-specific DNA binding and double-stranded DNA binding were the top 5 downregulated molecular functions among top BCMs and MetaVolcanoR  and downregulated (13 genes) using the EnrichR tool . The topR Figure  30). Ev. Evcis-rFinally, we also checked the tissue specificity of these common DEGs using the Jensen tissue score from EnrichR . Jensen Based on biological clustering, DEG recovery, molecular functions and tissue specificity of common DEGs, we concluded that the top 3 BCMs could capture biologically relevant processes while retaining tissue-specific information for the RA study. However, depending on the choice of BCM, some methods (such as limma) will require a more stringent statistical cut-off to filter DEGs.We performed a similar analysis for OA and provided a detailed study description in in vitro monocyte-derived macrophage (MDM) activation state models as a case study to demonstrate the application of the SelectBCM tool for bulk RNA-seq experiments. We choose the MDM study as macrophages represent heterogeneous immune cell populations in the context of tissue and diseases, and most studies use in vitro MDMs to understand the stimulant-associated heterogeneity , we again observed that all three BCMs captured the right direction of differential expression changes of marker genes of the IL-4 stimulation but failed to capture it in the uncorrected meta-experiment Figure . HoweverBelow we discuss the key challenges and limitations of performing batch correction in the bulk transcriptome. This study has emphasized the challenges associated with how biological heterogeneity interferes with the batch-correction outcome. Through a meta-analysis study of systemic juvenile idiopathic arthritis , we demonstrate a scenario where biological heterogeneity (active and inactive states of illness) is present, the study design is unbalanced and the sample size is small. We observe that clustering did not improve after batch correction in both studies . We alsoWe designed the SelectBCM tool to solve the old problem of selecting the suitable BCM for bulk transcriptomic experiments. We implemented >9 state-of-the-art batch-correction algorithms in our workflow designed to handle bulk transcriptomes from microarray and RNA-seq technology. We showcase the useability of our workflow to address the problem of choosing the most appropriate BCM and the importance of having multiple evaluation methods. Using RA and OA datasets, we observed that Q_ComBat and ComBat1 were the top BCMs for better DEG recovery, and downstream biological inferences agreed with the traditional meta-analysis approach. For the bulk RNA-seq experiment, we observed that ComBat_seq is better for retaining biological signals. We expect our tool will speed up the bulk transcriptomic data integration process, starting from filtering the datasets based on metadata to batch correction and allowing users to focus on deciphering biological signals.https://hub.docker.com/r/yysong123/selectbcm. All datasets and analyses used in the paper are public, referenced and downloadable at https://doi.org/10.5281/zenodo.7482141.The docker image of the tool is available at lqad014_Supplemental_FileClick here for additional data file.


Insects have been a food source for humans for millennia, and they are actively consumed in various parts of the world. This paper aims to ascertain the feasibility of portable near-infrared (NIR) spectroscopy as a reliable and fast candidate for the classification of insect powder samples and the prediction of their major components. Commercially-available insect powder samples were analyzed using two miniaturized NIR instruments. The samples were analyzed as they are and after grinding, to study the effect of the granulometry on the spectroscopic analyses. A homemade sample holder was designed and optimized for making reliable spectroscopic measurements. Classification was then performed using three classification strategies, and partial least squares (PLS) regression was used to predict the macronutrients. The results obtained confirmed that both spectroscopic sensors were able to classify insect powder samples and predict macronutrients with an adequate detection limit. Over the last decade, rapid population growth and the problems of undernourishment, mainly in underdeveloped countries, are creating the need to find new and sustainable food sources, and a new perspective is being demanded to address this issue. Insect-based products seem to match this priority ,2, by inTenebrio molitor, declared safe by the European Food Safety Authority (EFSA) in January 2021. However, if edible insect powders have previously reached national markets based on national regulations, they can still be found in these national markets. The overlapping of the new European regulation (and the list of novel foods) and previous national regulations, mean that it is difficult nowadays to find a wide variety of edible insect powders in Europe.Unfortunately, even if the consumption of edible insects started nearly 7000 years ago and many insects have been eaten worldwide , consumeThe diffusion of a new type of food requires new analytical strategies for its analysis, and to control the quality of such food. This paper tries to address this problem, proposing a rapid and low-cost methodology for the modern insect-based food industry and consumers. A few reports can be found in the literature that analyze insect-based products ,8,9, shoThe choice of miniaturized NIR spectroscopy arises from several considerations, since this technology has proved its suitability in many applications, and has solved analytical problems relevant to food analysis ,11,12,13NIR miniaturized spectroscopy is non-destructive, fast, cheap, and almost no chemicals are needed, all of which greatly reduce the impact the technique and the analysis have on the environment. It is portable and it can be used directly on the field or in the plant, and by the end-user without any sample pretreatment, once the necessary chemometric models for data analysis have been developed. The use of multivariate analysis goes hand in hand with NIR spectroscopy.Most currently available NIR miniaturized sensors are not designed to analyze powder samples , and theThis research explores the analytical complexities encountered when analyzing insect powder samples and proposes a reproducible way for their analysis without any pretreatment using two different portable NIR spectrometers , with quite different characteristics and modes of operation.Five commercially available insect powder samples were purchased, and their differentiation and classification were carried out using principal components analysis (PCA), partial least squares 2-discriminant analysis (PLS2-DA), and linear discriminant analysis (LDA) algorithms. Finally, PLS regression was used to predict the content of macronutrients in the samples.A SCiO spectrometer  and a Neospectra Micro Development Kit (MDK) device  were used for the insect powder analysis.The SCiO is a miniaturized NIR device that uses a molecular sensor with dimensions of 67.7 mm × 40.2 mm × 18.8 mm and weighs 35 g. It works in the wavelength range of 740 to 1070 nm, and it is controlled by a smartphone (Android and IOS) through the application ‘SCiO Lab’ via Bluetooth. The default scan time for SCiO measurements is between 2 and 5 s, and it cannot be set manually. The data recorded are stored in the cloud. The resolution of the SCiO device is not available from the manufacturer .The NeoSpectra MDK consists of a monolithic microelectromechanical system (MEMS) Michelson interferometer and a single InGaAs photodetector. The dimensions of the device are 32 mm × 32 mm × 22 mm and it weighs 17 g. The wavelength range is 1350 to 2558 nm with a resolution of 16 nm. The NeoSpectra Micro is connected to a Raspberry Pi single-board computer that acts as a host and allows connection via a universal serial bus (USB) to a laptop. The software (Windows and Linux) allows the user to set a limited number of parameters, such as the scan time, run mode (single or continuous), or data interpolation in each spectrum collected. The NeoSpectra has to be calibrated each time the software is started. The scan time was optimized to 5 s.A background  was performed before any analytical session as suggested by the manufacturers for both sensors. In the case of the SCiO, the reflectance material is included on the back side of the cover. The analytical sessions started after 20 min warming for the NeoSpectra MDK sensor.® 2 Desktop 3D Printer  was used to fabricate the holder lateral sides, while in the intermediate bottom of the cell, interchangeable coverslips of 22 mm × 22 mm pieces of borosilicate glass of hydrolytic class 1 with a thickness of 0.13–0.17 mm  were used.Reflectance mode analysis was employed for both instruments. A homemade cell was used as the sample holder . A MakerBot ReplicatorA coffee grinder  was employed to grind the insect powder samples.-Acheta domesticus , class A1-Acheta domesticus , class A2-Tenebrio molitor , class T-Alphitobius diaperinis, , class AD-Locusta migratoria, , class LFive types of commercial edible insect powders were purchased. The insect type, the producer or importer, and the label/class assigned to these types are:Details of the samples reproduced from the commercial labels are reported in The samples were analyzed without any sample pretreatment and after grinding . Sample bags were only opened immediately before the analysis, and after opening, the sample bags were stored under a nitrogen atmosphere and in a temperature-controlled (4 °C) and dark environment to prevent any unwanted and unpredictable changes. Stored samples were analyzed when they reached ambient temperature. Measurements were carried out at ambient temperature and without any special precautions. An instrumental background was performed prior to any analytical session. Fifteen aliquots of each bag were sampled and analyzed in three independent analytical sessions (on different days), except for A2. Three bags of sample A2 were purchased and five aliquots for each bag were sampled—a bag for each analytical session. In any session, all the insect powders were investigated. In all sessions, data were collected with both spectrometers.Calculations were performed using PLS Toolbox 9.0  running under the Matlab 2021a  environment.X matrices.Two data matrices were built, one for signals recorded with the SCiO sensor  and one for signals obtained with the NeoSpectra MDK . The average of five spectra recorded for each insect powder sample, collected after resampling, were used to build the 2 and Q statistics calculated in the PCA models built for each class, (2) classification using PLS2-DA, and (3) classification using LDA. PLS regression was employed to predict major components in the insect powder samples.PCA was used for exploratory data analysis. Classification of the different types of insect powder was carried out following three strategies: (1) one-class classification using TSeveral spectral preprocessing techniques were evaluated to improve classification and prediction model performances. Standard normal variate (SNV), multiplicative scatter correction (MSC), Savitzky-Golay smoothing (from 7 to 25 smoothing points), and derivatives (first and second order) were tested. Prior to any model calculation, data were mean-centered. In the case of PLS and PLS2-DA, the Venetian blinds method (with 10 data splits and 4 samples per blind) was used for cross-validation of the training set.Samples were analyzed on three different days . Calibration samples were analyzed during the first two analytical sessions. Validation samples were analyzed in the third analytical session. For A2, three different bags were available: samples from two bags were used to calibrate the model, and samples from the third bag were employed to validate the model. Ground samples were analyzed in independent sessions from non-ground samples. The reason for performing measurements on different days was to capture the between-day variability, if present, and to obtain a validation set of samples  as indeIn this section, the instrumental setup for the NeoSpectra MDK and SCiO will be respectively discussed.-allow for reproducible reflectance analysis,-cover the entire measurement window,-and allow for easy cleaning of the cell.The NeoSpectra MDK sensor is designed to be used in contact with the sample and there is no commercially available sample holder for powder samples. For this reason, a homemade cell or sample holder was optimized to:Concerning the last point, some of the insect powders appeared to be oily. This suggested using an easily washable or economically disposable material such as the coverslips to make the lower part of the cell (the part that is in contact with the measurement windows). The coverslip does not affect the spectra as already observed , is a loAccurate length measurements were taken to build a cell able to cover the whole measurement window and to fit perfectly into the sensor to avoid any movement/shift during the analysis. The key feature to optimize was the thickness of the cell . Several experiments were carried out putting in a first cell prototype different quantities of a sample (different thicknesses) and using a reflective material on the top of the sample to detect changes in the signal according to the different optical paths of the radiation. From these experiments, a cell height of 5 mm was found to allow the obtaining of reproducible spectra without any external light influence  using a sample quantity easy to manage but without excessive waste. The transflection mode of analysis was also considered but results were not satisfactory in terms of reproducibility of the spectroscopic signal: the measurement window is quite large and adding the minimum amount of sample to allow the radiation to pass through it twice and at the same time covering the entire window was not trivial. For these reasons, the external reflection mode was preferred. The same cell was tested on wheat flour and corn flour and the 5 mm height was also suitable for these other types of powder samples. A scheme of the homemade cell is depicted in After the optimization of the homemade sample holder, optimization of the scanning time was carried out.Five seconds of scanning time was the shortest time that ensured reproducible spectra, while less time resulted in noisier spectra. Ten instrumental replicates were collected for each sample, and each sample was repositioned five times to get the final average spectrum to be considered for calculations. As previously said, samples were stored in a controlled atmosphere (nitrogen), light conditions (dark), and temperature (4 °C), to avoid unwanted changes that would have added more variability to the system. These storage conditions became necessary after observing that the samples stored in the air for several days lost moisture during the analysis with the NeoSpectra MDK.This spectral variation could be explained considering the high temperature of the measuring window, which evidently affects the sample moisture even if the sample is not in direct contact with the window (the cover slip placed at the bottom of the homemade cell lies between the measuring window and the sample). This behavior was not observed when samples were analyzed immediately after opening the sample bag, or after reaching ambient temperature after the proper storage previously described. The same behavior was observed with all types of insect powders when analyzing them with the NeoSpectra MDK.The optimized homemade cell was also used in the data collection using the SCiO sensor. It should be noted that for measurements with this kind of sensor it is very important to maintain a perfectly vertical position of the sensor . A fixeIn this case, it was not possible to optimize the sampling time since this is automatically set by the SCiO. Five replicates with sample repositioning were registered for each insect powder aliquot and the average spectrum was used for the calculations.-1495 nm, N-H stretch 1st overtone, NH: amide, proteins-2: lipids1723/1726 nm, C-H stretch 1st overtone, CH-1924 nm, O-H stretch + O-H deformation: water-2054, N-H asymmetric stretch + amide II: proteins-2164, N-H symmetric stretch + amide II: proteins-2298, 2x amide I + amide III: proteins-2301, C-H bending: lipids-2468, C-H combination: lipidsFor the NeoSpectra MDK a, the spThe SCiO spectral bands b are morX matrices (one for each instrument). Data were then preprocessed according to the characteristics of the different spectroscopic signals to obtain the highest values of explained variance in the first PCs, which corresponded to the best separation between classes in PCA models.The average spectra obtained for each insect powder aliquot were used to build the Data obtained from the NeoSpectra MDK gave the best results after smoothing (21 points) and the first derivative, while SCiO data did not need any preprocessing. In both cases, a good separation between the different insect powder samples can be observed. The information is distributed on the two first PCs in the case of the NeoSpectra MDK data  while PC1 dominates the variability of the samples in the case of the SCiO sensor (99%). The loading plots for the two PCA models can be found in the An interesting observation emerges from both models. Looking at the different groups of samples, they seem to have the same intrinsic variability: in other words, they occupy a comparable area in the PC1 vs PC2 score plot. As previously mentioned, aliquots of insect powder A2 (labeled as green squares in the plots) were collected from 3 different bags . A2 samples do not show any behavior according to the different bags, nor do A2 samples show a very different variability from others. No trends with respect to the three bags are observed. This suggests that the variability between different bags is comparable to the estimated variability within the same bag.As previously mentioned, the purchased insect powders showed different textures, some of them appearing as fine powders, and others as coarser powders. As the miniaturized NIR instruments employed in this research work in reflectance mode (as in many of the applications of miniaturized NIR sensors), the registered spectra may be affected by the physical characteristics of the samples. While this aspect is often overlooked in many studies, the influence of the sample texture on the modeling was investigated.A dimensional homogenization of the insect powder samples was performed. All the samples except sample A2, which was a very fine powder, were treated using a commercial coffee grinder. To avoid any unwanted change in the samples  the insect powders were ground in four 30 s consecutive sessions, with a pause of 10 s between each session.When building the PCA models with the ground and non-ground insect powders, data obtained from the NeoSpectra MDK gave the best results after smoothing (21 points), while SCiO data did not need any preprocessing. Very interesting results can be observed in the PCA scores obtained d—SCiO. IAcheta domesticus. When insect powder A1 is ground, its position in the score plot moves towards insect powder A2, which appears as a very fine powder as previously mentioned .Looking at the PCA model built with NeoSpectra MDK data c, the grThis has two important implications. The first is that, as expected, the spectroscopic signal depends on the physical, as well as the chemical, characteristics of the powders. The second is that using portable NIR spectroscopy and chemometric analysis, the classification of insect powders may be possible only by taking into account the granulometric characteristics of the samples.These results are confirmed also by data collected with the SCiO sensor. In the scores plot d samples2 and Q statistics calculated in PCA models, while the other two strategies were developed using two supervised methods of classification: PLS2-DA and LDA.Three different classification strategies were tested and validated. The first one is based on an unsupervised method, Hotelling’s TFor the classification of the different insect powders, we decided to focus on the type of insect, introducing in the same class the different producers and grinding levels. The aim was to develop classification models able to classify different types of insect powders regardless of their provenance or grinding level .Acheta domesticus from two different producers and with different grinding levels) were all labeled as class A. Samples from classes AD and AD_G were labeled as class AD. Samples from classes T and T_G were labeled as class T. Samples from classes L and L_G were labeled as class L.Therefore, samples from classes A1, A2, and A1_G , 4 PCs-class AD: no preprocessing, 1 PC-class L: no preprocessing, 1 PC-class T: first derivative, 3 PCs.The preprocessing used for the different classes and the number of required PCs using NeoSpectra MDK data were:2 and Q confidence intervals (lower-left part of each subfigure defined by the dashed lines) for each one of the classes built with the NeoSpectra MDK data. For the PCA models, more than 90% of the variance was explained for classes AD and L, and more than 95% of the variance was explained for classes A and T. For all models, samples belonging to a particular class were correctly classified in that class with the exception of one sample in class AD and one sample in class L. 2 and Q confidence intervals, showing that those samples are correctly classified as not belonging to that class. The sensitivity (the ability of the model to correctly classify samples of its class) [s class)  is 100% 2 and Q confidence intervals for each one of the classes built with the SCiO data. In all cases, one PC was required to define the classes, and it is possible to see that all the samples belonging to that class are correctly classified and that samples from other classes lie away from the confidence intervals. The sensitivity and the specificity are therefore 100% for the four classes. Data obtained from the SCiO data gave the best results without any preprocessing. X is correlated to a vector y, which is the sample property to be predicted. In PLS-DA algorithms, the vector y is substituted by a dummy variable consisting of only +1 and 0 denoting in-class and out-class respectively [Y is a K-column dummy matrix, where K is the class number.A PLS2-DA classification strategy was also used to classify the insect powder samples. Data collected with the two sensors were modeled separately. In general, the PLS-DA algorithm is an evolution of PLS, which is an algorithm proposed to solve regression problems. In PLS, a data matrix ectively ,23,24. WIdeally, in a multi-class problem, several PLS-DAs could be performed to model each class separately: each time only one class is of concern (in-class) while the other classes are grouped as out-class. The advantage of PLS2-DA is that the algorithm considers all classes simultaneously and produces only one classification model .When building the PLS2-DA models, data obtained from the NeoSpectra MDK gave the best results after smoothing (15 points) and the second derivative, while SCiO data did not need any preprocessing.Y. Four LVs were needed in the PLS2-DA model with SCiO data to account for 88.50% of the information in Y. Five latent variables (LVs) were needed in the PLS2-DA model with the NeoSpectra MDK data to account for 69.13% of the information in For comparison purposes, to the best of our knowledge PLS2-DA has not been applied to classification in food analysis using miniaturized NIR instruments, but PLS-DA has been used in other related studies. For instance, considering food samples, different coffee samples were successfully classified (sensitivities and specificities ranging from 0.84 to 1 for the test set) , adulterTo show the usefulness of miniaturized NIR instruments for the classification of edible insect powders, we also tried another classification method (LDA) not based on the decomposition of data into latent variables. When applying LDA, data obtained from the NeoSpectra MDK gave the best results after smoothing (19 points), while SCiO data did not need any preprocessing. In all cases for all four classes  and the training and test sets in both NeoSpectra MDK and SCiO, the sensitivities and specificities were all 1.LDA has not been applied as widely as PLS-DA for the classification of food samples using miniaturized NIR instruments, although some studies have been performed. For example, nitrogen-based adulterants in whey protein powder were classified with accuracies of 80% .One of the major advantages of using chemometric data analysis is that from the same dataset several different models can be developed, depending on the specific purpose. The same spectra recorded on the insect powder samples were used to predict their major constituents.X matrix, while the values reported on the bags (declared by the producers) were used as the y values. For each macronutrient, a model was performed by optimizing data preprocessing and choosing the best compromise between model parsimony and prediction error. Samples were divided exactly as in the classification models: samples coming from the two first analytical sessions were used to calibrate the models, while samples analyzed in the third session were used to validate the model .Protein, fatty acids, carbohydrates, and fiber contents in the investigated samples (no pretreatment) were predicted using PLS regression. Spectra recorded with the NeoSpectra NDK and the SCiO sensors were used as the 2pred value of the regression line between the predicted and the measured values (R2 corresponds to the square of the correlation coefficient of the regression line), and the smaller number of factors. 2CV value of the regression line between the predicted and the measured values of the training set in the different cross-validation steps. The different regression lines between the predicted and the measured values are shown in the In all cases, the best model was chosen as the best compromise between the lower root mean square error of prediction (RMSEP) for the test set, the higher R-proteins: first-order polynomial smoothing with 15 points followed by the Savitzky–Golay first derivative.-fatty acids: zero-order polynomial smoothing with 21 points followed by the Savitzky–Golay second derivative.-carbohydrates: first-order polynomial smoothing with 11 points followed by SNV-fiber: second-order polynomial smoothing with 21 points followed by the Savitzky–Golay first derivative.For the PLS models built with the SCiO data, no preprocessing was needed. For the NeoSpectra data, the best combinations of data preprocessing were:To check the performance of these prediction models, two parameters, the ratio of performance to deviation (RPD) and range error ratio (RER), were used. Both RPD and RER are dimensionless parameters, where RPD is calculated as the ratio of the standard deviation of the reference values of the samples in the validation set to the RMSEP, and RER is calculated as the ratio of the range of the reference values in the validation set to the RMSEP . Higher PLS for macronutrient prediction has been extensively used in food matrices analyzed by miniaturized NIR instruments. Details can be found in very recently published reviews on the field ,31. MostThis manuscript describes for the first time the application of miniaturized NIR instruments to the classification of edible insect powders. The two NIR instruments used have proved their usefulness in the classification of different insect powders, regardless of their provenance or grinding degree. Depending on the type of samples used, measuring with miniaturized NIR instruments may be a challenging task to optimize the instrumental signal, and a homemade cell using a 3D printer was designed and built for this task.Three different methods of classification were applied to successfully discriminate the different classes of insect powders. Very good results were obtained using all three methods. The results suggest that both devices have the potential to be used, e.g., in the quality control phases in the insect food industry. At the time of this study, obtaining insect powders was difficult due to changes in European regulations mentioned in the introduction. The new regulation requires that edible insects be included in the list of authorized novel foods before being introduced to the market, which only allowed access to a limited number of insect powders that had previously reached national markets based on national regulations. The goal of this study was the development of an analytical procedure for the analysis (including classification and prediction of macronutrients) of insect powders using miniaturized NIR spectroscopy, and this goal has been pursued with the currently available insect powders. Future studies dealing with a larger set of samples should be carried out to validate it.Prediction of the macronutrients also gave very encouraging results. It should be noted that values declared by the producers were used as reference values, and the precision of this data influenced the quantification errors.The exploitation of miniaturized NIR instruments is a field of very rapid expansion, and they are increasingly being applied to a wide variety of analyzes in many different environments and situations. In all cases, the operational conditions must be optimized to obtain the best instrumental signal and, therefore, the best results. This may involve intensive work optimizing and developing suitable measurement conditions considering the specific properties of the samples to be measured and the specific characteristics of the instruments used. This optimization process may require extensive experience in analytical measurement and the use of chemometric methods, although once the chemometric methods have been developed they can be used by non-experienced users such as final consumers.


Coronavirus disease 2019 (COVID19) has triggered a global pandemic affecting millions of people. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causing the COVID-19 disease is hypothesized to gain entry into humans via the airway epithelium, where it initiates a host response. The expression levels of genes at the upper airway that interact with the SARS-CoV-2 could be a telltale sign of virus infection. However, gene expression data have been flagged as suspicious of containing different contamination errors via techniques for extracting such information, and clinical diagnosis may contain labelling errors due to the specificity and sensitivity of diagnostic tests. We propose to fit the regularized logistic regression model as a classifier for COVID-19 diagnosis, which simultaneously identifies genes related to the disease and predicts the COVID-19 cases based on the expression values of the selected genes. We apply a robust estimating methods based on the density power divergence to obtain stable results ignoring the effects of contamination or labelling errors in the data and compare its performance with respect to the classical maximum likelihood estimator with different penalties, including the LASSO and the general adaptive LASSO penalties. Coronaviruses (CoVs) are a group of enveloped, single, positive-stranded RNA viruses causing mild to severe respiratory illnesses in humans. Coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV2), has lead to a global pandemic affecting millions of people and causing high mortality rates worldwide. Nonetheless, the actual knowledge about COVID19 is limited, and numerous studies have been carried out to identify genes involved in the host response to the SARS-CoV-2 infection, so as to determine mechanisms of pathogenicity and potential therapeutic targets . Genetic variation may contribute to disease largely through misregulation of gene expression. Metagenomic Next-Generation Sequencing (mNGS) is an useful tool providing clinically actionable information for predicting causes of an infection, evaluating infectious disease risk and successful diagnosing. Therefore, genetic information may be used to build novel respiratory diagnostics that integrate host transcriptional signatures of infection. Conversely, gene expression profiling involves a large number of features, often much larger than the sample size. High feature dimensionality and paucity of samples possess a challenge for predictive classification and marker identification methodologies. Therefore, techniques for high dimensional data analysis need to be applied.Despite the potential of mNGS, it presents some crucial barriers, including data cleanliness. Contamination of samples during specimen collection is a large concern given the increased analytical sensitivity of mNGS in comparison with standard culture methods. Accordingly, robust statistical analysis appears appropriate for the classification of COVID19 patients and identification of genes involved in patient’s response to the infection using mNGS data.Among the existing high dimensional statistical techniques, the regularized logistic regression model provides simultaneous gene identification and patient classification through a likelihood of suffering from the disease. The low dimensional logistic regression model has been widely used as a powerful classifier, but classical estimation design is ill-posed in the high dimensional set-up and regularized methods need to be applied. Regularization techniques assume that only a few number of explanatory variables are actually involved in the true model underlying the data, so they perform variable selection and parameter estimation by combining a model-based loss function with a penalization on the absolute value of the model parameters. Several penalties have been explored in the literature. The LASSO (Least Absolute Shrinkage and Selection Operator) procedure  stands wWhile classical estimating methods are based on the maximum likelihood estimator (MLE), recent literature has shown the advantage of using divergence-based methods in terms of robustness, with an unavoidable (but often not quite significant) loss of efficiency. Robust methods for logistic regression based on bounded deviances have been introduced in Bianco and Yohai . CantoniIn this paper, we propose to develop a COVID19 patients classifier through their upper airway gene expression using the penalized logistic regression model, which simultaneously carries out important gene selection. We apply different estimation methods, namely the classical MLE and the MDPDEs penalized with the LASSO, Ad-LASSO and AW-LASSO penalties  as deveThe outline of the paper is as follows. Section k-dimensional vector of explanatory variables, Let us consider dichotomous and independent response variables As discussed in Sect. and Basu  presenteOn the other hand, dealing with high dimensional data requires additional assumptions on the model parameters. In particular, we assume that the true regression vector is assumed to be sparse, that is, having few non-null elements. Explanatory variables with zero regression coefficient are not significant for the model. Thus, variable selection needs to be performed jointly with the parameter estimation. Regularization methods are characterized by combining a loss function (from the model) and a penalty function that induces zero estimation of many coefficients.The classical penalized (regularized) LASSO estimator of e et al. . The choFokianos , Park anFokianos , Plan anFokianos , Zhu andFokianos  and Sun Fokianos  are inteBasu et al.  extendedn and Li ). Since n and Li  proposedmentclass2pt{minim and Lee  and refeThe idea of weighting the LASSO penalization can be extended to a more general framework, yielding the adaptive weighted LASSO estimator with objective functionThe adaptive and weighted adaptive LASSO procedure can be easily adapted to the DPD-based loss function leading to an objective function of the formu et al. , and nonu et al.  empiricaWe study the upper airway host transcriptional response in patients with COVID19 , specificity  and correct classification rate (CCR). The explicit formulas areKitagawa , to seleglmnet, AW-LASSO is fitted using ncvreg package and we fit the DPD-based estimators with our own implemented code available at https://github.com/MariaJaenada/awDPDlasso. Finally, to examine the robustness of the methods, the logistic regression model is fitted with original and contaminated data and then, evaluated with the original data (without outliers) in both settings.To compute the LASSO and Ad-LASSO methods, we use the R package Further, to assess the dependence of the model on the data, we fit the logistic model with the whole dataset and with 5 subsamples containing all observations except for 5 predefined folds, and we report the accuracy measures of the model fitted with the whole data, and the mean of the measures produced by the 5 different models fitted with each fold. The last one allows us to better assess the estimation dependency of the data, since some subsamples would contain more outlier observations than others.We first examine the performance of the different methods when differentiating COVID19 patients from patients suffering other viral and non-viral disease. Table We also study the accuracy by fitting a Receiver Operating Characteristic (ROC) curve of the model and reporting its area under the curve (AUC). The AUC is a robust overall measure to evaluate the performance of score classifiers because its calculation relies on the complete ROC curve and thus involves all possible classification thresholds. Figure Complementary to the accuracy study of the model, it is also interesting to examine common genes selected in each method, and the stability in the selection, in the case of DPD loss-based methods by varying the parameter entclass1pt{minimaConversely, selected genes changed when contaminating the data even when fitting the model with the same estimating method, as our contamination scheme uses the set of important variables to introduce leverage points. Nonetheless, both sets of genes are highly correlated, as shown in Fig. IFI6 and IF44L have the greatest OR value in adaptive methods and standard LASSO, respectively. Those genes are two of the most statistically significant genes upregulated by SARS-CoV-2, according to Mick et al. [IFI6 and IF44L. In addition, DPD-based methods find some other important genes in the classification. Besides IFI6 and IF44L genes, TIMP1, FAM83ATRO and WDR74 have been flagged to be specifically upregulated in COVID-19 patients compared to both other viral and non-viral ARIs according to [TIMP1 has been shown to be related to SARS-CoV-2 infection with lower expression level during pathogenesis  may be used to compare the relative odds of the occurrence of the disease given the expression level of a certain gene. The Odds can be interpreted as the risk or importance of a gene in the diagnostic, so they allow comparison of the magnitude of the risk entailed by different genes for the COVID19 disease. Accordingly, each regression coefficient associated with a gene can be interpreted as the estimated relative increase in the log odds of the outcome per unit increase in the level of that gene. Then, the exponential function of the regression coefficient is the odds ratio associated with a one-unit increase in the expression level. Of course, zero-estimated coefficients, resulting in unit OR, imply that these genes do not affect to the diagnose. Table k et al. . In contrding to , 29. In genesis , which The identified genes in our analysis mostly coincide with some biomarkers discussed in the literature. In particular, 20 of the 23 genes identified using LASSO penalized MLE were also selected in Mick et al. [The previous results were calculated with the aggregated data, where the class NO-COVID19 included viral and non-viral ARIs. We now study the performance of the logistic model in differentiating COVID19 from other viral diseases. In this case, only TIMP1, TRO, WDR74, AL928654.3,ICAM4, and IGLL5 were also identified by at least one of the DPD-based methods, and LGR6,SMARCA1 and PCSK5 were identified by the classical LASSO estimator.Table Robust penalized logistic regression is specially convenient when dealing with gene-based classification problems. From our results, DPD-based robust methods outperform classical ones when training data are contaminated with leverage points or mislabelled observations, which is quite common in genetic datasets. In particular, when the MLE is used, correct diagnosis of the COVID19 is highly affected by this data contamination and only a The accuracy loss of the non-robust methods under data contamination is emphasized when differentiating between viral ARIs. In this scenario, penalized MLEs lose their ability to detect viral diseases other than COVID, whereas robust estimators manage to maintain sufficiently high specificity. Weighted adaptive DPD-based estimators show the best performance in this case. All these results presented in this paper illustrate the benefit of using the robust DPD-based procedures which can be used routinely in any future real-life analysis of high-dimensional gene expression data and associated classification problems.