Identification of drug-side effect association via restricted Boltzmann machines with penalized term.

In the entire life cycle of drug development, the side effect is one of the major failure factors. Severe side effects of drugs that go undetected until the post-marketing stage leads to around two million patient morbidities every year in the United States. Therefore, there is an urgent need for a method to predict side effects of approved drugs and new drugs. Following this need, we present a new predictor for finding side effects of drugs. Firstly, multiple similarity matrices are constructed based on the association profile feature and drug chemical structure information. Secondly, these similarity matrices are integrated by Centered Kernel Alignment-based Multiple Kernel Learning algorithm. Then, Weighted K nearest known neighbors is utilized to complement the adjacency matrix. Next, we construct Restricted Boltzmann machines (RBM) in drug space and side effect space, respectively, and apply a penalized maximum likelihood approach to train model. At last, the average decision rule was adopted to integrate predictions from RBMs. Comparison results and case studies demonstrate, with four benchmark datasets, that our method can give a more accurate and reliable prediction result.

Temporal generative models for learning heterogeneous group dynamics of ecological momentary assessment data.

One of the goals of precision psychiatry is to characterize mental disorders in an individualized manner, taking into account the underlying dynamic processes. Recent advances in mobile technologies have enabled the collection of ecological momentary assessments that capture multiple responses in real-time at high frequency. However, ecological momentary assessment data are often multi-dimensional, correlated, and hierarchical. Mixed-effect models are commonly used but may require restrictive assumptions about the fixed and random effects and the correlation structure. The recurrent temporal restricted Boltzmann machine (RTRBM) is a generative neural network that can be used to model temporal data, but most existing RTRBM approaches do not account for the potential heterogeneity of group dynamics within a population based on available covariates. In this paper, we propose a new temporal generative model, the HDRBM, to learn the heterogeneous group dynamics and demonstrate the effectiveness of this approach on simulated and real-world ecological momentary assessment datasets. We show that by incorporating covariates, HDRBM can improve accuracy and interpretability, explore the underlying drivers of the group dynamics of participants, and serve as a generative model for ecological momentary assessment studies.

The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System's Configurations from a Given Temperature.

The restricted Boltzmann machine (RBM) is a generative neural network that can learn in an unsupervised way. This machine has been proven to help understand complex systems, using its ability to generate samples of the system with the same observed distribution. In this work, an Ising system is simulated, creating configurations via Monte Carlo sampling and then using them to train RBMs at different temperatures. Then, 1. the ability of the machine to reconstruct system configurations and 2. its ability to be used as a detector of configurations at specific temperatures are evaluated. The results indicate that the RBM reconstructs configurations following a distribution similar to the original one, but only when the system is in a disordered phase. In an ordered phase, the RBM faces levels of irreproducibility of the configurations in the presence of bimodality, even when the physical observables agree with the theoretical ones. On the other hand, independent of the phase of the system, the information embodied in the neural network weights is sufficient to discriminate whether the configurations come from a given temperature well. The learned representations of the RBM can discriminate system configurations at different temperatures, promising interesting applications in real systems that could help recognize crossover phenomena.

Reviewing Evolution of Learning Functions and Semantic Information Measures for Understanding Deep Learning.

A new trend in deep learning, represented by Mutual Information Neural Estimation (MINE) and Information Noise Contrast Estimation (InfoNCE), is emerging. In this trend, similarity functions and Estimated Mutual Information (EMI) are used as learning and objective functions. Coincidentally, EMI is essentially the same as Semantic Mutual Information (SeMI) proposed by the author 30 years ago. This paper first reviews the evolutionary histories of semantic information measures and learning functions. Then, it briefly introduces the author's semantic information G theory with the rate-fidelity function R(G) (G denotes SeMI, and R(G) extends R(D)) and its applications to multi-label learning, the maximum Mutual Information (MI) classification, and mixture models. Then it discusses how we should understand the relationship between SeMI and Shannon's MI, two generalized entropies (fuzzy entropy and coverage entropy), Autoencoders, Gibbs distributions, and partition functions from the perspective of the R(G) function or the G theory. An important conclusion is that mixture models and Restricted Boltzmann Machines converge because SeMI is maximized, and Shannon's MI is minimized, making information efficiency G/R close to 1. A potential opportunity is to simplify deep learning by using Gaussian channel mixture models for pre-training deep neural networks' latent layers without considering gradients. It also discusses how the SeMI measure is used as the reward function (reflecting purposiveness) for reinforcement learning. The G theory helps interpret deep learning but is far from enough. Combining semantic information theory and deep learning will accelerate their development.

Thermodynamics of the Ising Model Encoded in Restricted Boltzmann Machines.

The restricted Boltzmann machine (RBM) is a two-layer energy-based model that uses its hidden-visible connections to learn the underlying distribution of visible units, whose interactions are often complicated by high-order correlations. Previous studies on the Ising model of small system sizes have shown that RBMs are able to accurately learn the Boltzmann distribution and reconstruct thermal quantities at temperatures away from the critical point Tc. How the RBM encodes the Boltzmann distribution and captures the phase transition are, however, not well explained. In this work, we perform RBM learning of the 2d and 3d Ising model and carefully examine how the RBM extracts useful probabilistic and physical information from Ising configurations. We find several indicators derived from the weight matrix that could characterize the Ising phase transition. We verify that the hidden encoding of a visible state tends to have an equal number of positive and negative units, whose sequence is randomly assigned during training and can be inferred by analyzing the weight matrix. We also explore the physical meaning of the visible energy and loss function (pseudo-likelihood) of the RBM and show that they could be harnessed to predict the critical point or estimate physical quantities such as entropy.

Multi-Class Classification of Medical Data Based on Neural Network Pruning and Information-Entropy Measures.

Medical data includes clinical trials and clinical data such as patient-generated health data, laboratory results, medical imaging, and different signals coming from continuous health monitoring. Some commonly used data analysis techniques are text mining, big data analytics, and data mining. These techniques can be used for classification, clustering, and machine learning tasks. Machine learning could be described as an automatic learning process derived from concepts and knowledge without deliberate system coding. However, finding a suitable machine learning architecture for a specific task is still an open problem. In this work, we propose a machine learning model for the multi-class classification of medical data. This model is comprised of two components-a restricted Boltzmann machine and a classifier system. It uses a discriminant pruning method to select the most salient neurons in the hidden layer of the neural network, which implicitly leads to a selection of features for the input patterns that feed the classifier system. This study aims to investigate whether information-entropy measures may provide evidence for guiding discriminative pruning in a neural network for medical data processing, particularly cancer research, by using three cancer databases: Breast Cancer, Cervical Cancer, and Primary Tumour. Our proposal aimed to investigate the post-training neuronal pruning methodology using dissimilarity measures inspired by the information-entropy theory; the results obtained after pruning the neural network were favourable. Specifically, for the Breast Cancer dataset, the reported results indicate a 10.68% error rate, while our error rates range from 10% to 15%; for the Cervical Cancer dataset, the reported best error rate is 31%, while our proposal error rates are in the range of 4% to 6%; lastly, for the Primary Tumour dataset, the reported error rate is 20.35%, and our best error rate is 31%.

A multimodal deep learning-based drug repurposing approach for treatment of COVID-19.

Recently, various computational methods have been proposed to find new therapeutic applications of the existing drugs. The Multimodal Restricted Boltzmann Machine approach (MM-RBM), which has the capability to connect the information about the multiple modalities, can be applied to the problem of drug repurposing. The present study utilized MM-RBM to combine two types of data, including the chemical structures data of small molecules and differentially expressed genes as well as small molecules perturbations. In the proposed method, two separate RBMs were applied to find out the features and the specific probability distribution of each datum (modality). Besides, RBM was used to integrate the discovered features, resulting in the identification of the probability distribution of the combined data. The results demonstrated the significance of the clusters acquired by our model. These clusters were used to discover the medicines which were remarkably similar to the proposed medications to treat COVID-19. Moreover, the chemical structures of some small molecules as well as dysregulated genes' effect led us to suggest using these molecules to treat COVID-19. The results also showed that the proposed method might prove useful in detecting the highly promising remedies for COVID-19 with minimum side effects. All the source codes are accessible using https://github.com/LBBSoft/Multimodal-Drug-Repurposing.git.

An Underwater Acoustic Target Recognition Method Based on Restricted Boltzmann Machine.

This article focuses on an underwater acoustic target recognition method based on target radiated noise. The difficulty of underwater acoustic target recognition is mainly the extraction of effective classification features and pattern classification. Traditional feature extraction methods based on Low Frequency Analysis Recording (LOFAR), Mel-Frequency Cepstral Coefficients (MFCC), Gammatone-Frequency Cepstral Coefficients (GFCC), etc. essentially compress data according to a certain pre-set model, artificially discarding part of the information in the data, and often losing information helpful for classification. This paper presents a target recognition method based on feature auto-encoding. This method takes the normalized frequency spectrum of the signal as input, uses a restricted Boltzmann machine to perform unsupervised automatic encoding of the data, extracts the deep data structure layer by layer, and classifies the acquired features through the BP neural network. This method was tested using actual ship radiated noise database, and the results show that proposed classification system has better recognition accuracy and adaptability than the hand-crafted feature extraction based method.

Towards Modified Entropy Mutual Information Feature Selection to Forecast Medium-Term Load Using a Deep Learning Model in Smart Homes.

Over the last decades, load forecasting is used by power companies to balance energy demand and supply. Among the several load forecasting methods, medium-term load forecasting is necessary for grid's maintenance planning, settings of electricity prices, and harmonizing energy sharing arrangement. The forecasting of the month ahead electrical loads provides the information required for the interchange of energy among power companies. For accurate load forecasting, this paper proposes a model for medium-term load forecasting that uses hourly electrical load and temperature data to predict month ahead hourly electrical loads. For data preprocessing, modified entropy mutual information-based feature selection is used. It eliminates the redundancy and irrelevancy of features from the data. We employ the conditional restricted Boltzmann machine (CRBM) for the load forecasting. A meta-heuristic optimization algorithm Jaya is used to improve the CRBM's accuracy rate and convergence. In addition, the consumers' dynamic consumption behaviors are also investigated using a discrete-time Markov chain and an adaptive k-means is used to group their behaviors into clusters. We evaluated the proposed model using GEFCom2012 US utility dataset. Simulation results confirm that the proposed model achieves better accuracy, fast convergence, and low execution time as compared to other existing models in the literature.

DIRECT: RNA contact predictions by integrating structural patterns.

BACKGROUND: It is widely believed that tertiary nucleotide-nucleotide interactions are essential in determining RNA structure and function. Currently, direct coupling analysis (DCA) infers nucleotide contacts in a sequence from its homologous sequence alignment across different species. DCA and similar approaches that use sequence information alone typically yield a low accuracy, especially when the available homologous sequences are limited. Therefore, new methods for RNA structural contact inference are desirable because even a single correctly predicted tertiary contact can potentially make the difference between a correct and incorrectly predicted structure. Here we present a new method DIRECT (Direct Information REweighted by Contact Templates) that incorporates a Restricted Boltzmann Machine (RBM) to augment the information on sequence co-variations with structural features in contact inference. RESULTS: Benchmark tests demonstrate that DIRECT achieves better overall performance than DCA approaches. Compared to mfDCA and plmDCA, DIRECT produces a substantial increase of 41 and 18%, respectively, in accuracy on average for contact prediction. DIRECT improves predictions for long-range contacts and captures more tertiary structural features. CONCLUSIONS: We developed a hybrid approach that incorporates a Restricted Boltzmann Machine (RBM) to augment the information on sequence co-variations with structural templates in contact inference. Our results demonstrate that DIRECT is able to improve the RNA contact prediction.

CBN-VAE: A Data Compression Model with Efficient Convolutional Structure for Wireless Sensor Networks.

Data compression is a useful method to reduce the communication energy consumption in wireless sensor networks (WSNs). Most existing neural network compression methods focus on improving the compression and reconstruction accuracy (i.e., increasing parameters and layers), ignoring the computation consumption of the network and its application ability in WSNs. In contrast, we pay attention to the computation consumption and application of neural networks, and propose an extremely simple and efficient neural network data compression model. The model combines the feature extraction advantages of Convolutional Neural Network (CNN) with the data generation ability of Variational Autoencoder (VAE) and Restricted Boltzmann Machine (RBM), we call it CBN-VAE. In particular, we propose a new efficient convolutional structure: Downsampling-Convolutional RBM (D-CRBM), and use it to replace the standard convolution to reduce parameters and computational consumption. Specifically, we use the VAE model composed of multiple D-CRBM layers to learn the hidden mathematical features of the sensing data, and use this feature to compress and reconstruct the sensing data. We test the performance of the model by using various real-world WSN datasets. Under the same network size, compared with the CNN, the parameters of CBN-VAE model are reduced by 73.88% and the floating-point operations (FLOPs) are reduced by 96.43% with negligible accuracy loss. Compared with the traditional neural networks, the proposed model is more suitable for application on nodes in WSNs. For the Intel Lab temperature data, the average Signal-to-Noise Ratio (SNR) value of the model can reach 32.51 dB, the average reconstruction error value is 0.0678 °C. The node communication energy consumption can be reduced by 95.83%. Compared with the traditional compression methods, the proposed model has better compression and reconstruction accuracy. At the same time, the experimental results show that the model has good fault detection performance and anti-noise ability. When reconstructing data, the model can effectively avoid fault and noise data.

Hybrid IRBM-BPNN Approach for Error Parameter Estimation of SINS on Aircraft.

To realize the error parameter estimation of strap-down inertial navigation system (SINS) and improve the navigation accuracy for aircraft, a hybrid improved restricted Boltzmann machine BP neural network (IRBM-BPNN) approach, which combines restricted Boltzmann machine (RBM) and BP neural network (BPNN), is proposed to forecast the inertial measurement unit (IMU) instrument errors and initial alignment errors of SINS. Firstly, the error generation mechanism of SINS is analyzed, and initial alignment error model and IMU instrument error model are established. Secondly, an unsupervised RBM method is introduced to initialize BPNN to improve the forecast performance of the neural network. The RBM-BPNN model is constructed through the information fusion of SINS/GPS/CNS integrated navigation system by using the sum of position deviation, the sum of velocity deviation and the sum of attitude deviation as the inputs and by using the error parameters of SINS as the outputs. The RBM-BPNN structure is improved to enhance its forecast accuracy, and the pulse signal is increased as the input of the neural network. Finally, we conduct simulation experiments to forecast and compensate the error parameters of the proposed IRBM-BPNN method. Simulation results show that the artificial neural network method is feasible and effective in forecasting SINS error parameters, and the forecast accuracy of SINS error parameters can be effectively improved by combining RBM and BPNN methods and improving the neural network structure. The proposed IRBM-BPNN method has the optimal forecast accuracy of SINS error parameters and navigation accuracy of aircraft compared with the radial basis function neural network method and BPNN method.

[Automatic classification method of arrhythmia based on discriminative deep belief networks].

Existing arrhythmia classification methods usually use manual selection of electrocardiogram (ECG) signal features, so that the feature selection is subjective, and the feature extraction is complex, leaving the classification accuracy usually affected. Based on this situation, a new method of arrhythmia automatic classification based on discriminative deep belief networks (DDBNs) is proposed. The morphological features of heart beat signals are automatically extracted from the constructed generative restricted Boltzmann machine (GRBM), then the discriminative restricted Boltzmann machine (DRBM) with feature learning and classification ability is introduced, and arrhythmia classification is performed according to the extracted morphological features and RR interval features. In order to further improve the classification performance of DDBNs, DDBNs are converted to deep neural network (DNN) using the Softmax regression layer for supervised classification in this paper, and the network is fine-tuned by backpropagation. Finally, the Massachusetts Institute of Technology and Beth Israel Hospital Arrhythmia Database (MIT-BIH AR) is used for experimental verification. For training sets and test sets with consistent data sources, the overall classification accuracy of the method is up to 99.84% ± 0.04%. For training sets and test sets with inconsistent data sources, a small number of training sets are extended by the active learning (AL) method, and the overall classification accuracy of the method is up to 99.31% ± 0.23%. The experimental results show the effectiveness of the method in arrhythmia automatic feature extraction and classification. It provides a new solution for the automatic extraction of ECG signal features and classification for deep learning.

Latent source mining in FMRI via restricted Boltzmann machine.

Blind source separation (BSS) is commonly used in functional magnetic resonance imaging (fMRI) data analysis. Recently, BSS models based on restricted Boltzmann machine (RBM), one of the building blocks of deep learning models, have been shown to improve brain network identification compared to conventional single matrix factorization models such as independent component analysis (ICA). These models, however, trained RBM on fMRI volumes, and are hence challenged by model complexity and limited training set. In this article, we propose to apply RBM to fMRI time courses instead of volumes for BSS. The proposed method not only interprets fMRI time courses explicitly to take advantages of deep learning models in latent feature learning but also substantially reduces model complexity and increases the scale of training set to improve training efficiency. Our experimental results based on Human Connectome Project (HCP) datasets demonstrated the superiority of the proposed method over ICA and the one that applied RBM to fMRI volumes in identifying task-related components, resulted in more accurate and specific representations of task-related activations. Moreover, our method separated out components representing intermixed effects between task events, which could reflect inherent interactions among functionally connected brain regions. Our study demonstrates the value of RBM in mining complex structures embedded in large-scale fMRI data and its potential as a building block for deeper models in fMRI data analysis.

Self-Organizing Traffic Flow Prediction with an Optimized Deep Belief Network for Internet of Vehicles.

To assist in the broadcasting of time-critical traffic information in an Internet of Vehicles (IoV) and vehicular sensor networks (VSN), fast network connectivity is needed. Accurate traffic information prediction can improve traffic congestion and operation efficiency, which helps to reduce commute times, noise and carbon emissions. In this study, we present a novel approach for predicting the traffic flow volume by using traffic data in self-organizing vehicular networks. The proposed method is based on using a probabilistic generative neural network techniques called deep belief network (DBN) that includes multiple layers of restricted Boltzmann machine (RBM) auto-encoders. Time series data generated from the roadside units (RSUs) for five highway links are used by a three layer DBN to extract and learn key input features for constructing a model to predict traffic flow. Back-propagation is utilized as a general learning algorithm for fine-tuning the weight parameters among the visible and hidden layers of RBMs. During the training process the firefly algorithm (FFA) is applied for optimizing the DBN topology and learning rate parameter. Monte Carlo simulations are used to assess the accuracy of the prediction model. The results show that the proposed model achieves superior performance accuracy for predicting traffic flow in comparison with other approaches applied in the literature. The proposed approach can help to solve the problem of traffic congestion, and provide guidance and advice for road users and traffic regulators.

Voiceprint Identification for Limited Dataset Using the Deep Migration Hybrid Model Based on Transfer Learning.

The convolutional neural network (CNN) has made great strides in the area of voiceprint recognition; but it needs a huge number of data samples to train a deep neural network. In practice, it is too difficult to get a large number of training samples, and it cannot achieve a better convergence state due to the limited dataset. In order to solve this question, a new method using a deep migration hybrid model is put forward, which makes it easier to realize voiceprint recognition for small samples. Firstly, it uses Transfer Learning to transfer the trained network from the big sample voiceprint dataset to our limited voiceprint dataset for the further training. Fully-connected layers of a pre-training model are replaced by restricted Boltzmann machine layers. Secondly, the approach of Data Augmentation is adopted to increase the number of voiceprint datasets. Finally, we introduce fast batch normalization algorithms to improve the speed of the network convergence and shorten the training time. Our new voiceprint recognition approach uses the TLCNN-RBM (convolutional neural network mixed restricted Boltzmann machine based on transfer learning) model, which is the deep migration hybrid model that is used to achieve an average accuracy of over 97%, which is higher than that when using either CNN or the TL-CNN network (convolutional neural network based on transfer learning). Thus, an effective method for a small sample of voiceprint recognition has been provided.

Multi-Modal Deep Hand Sign Language Recognition in Still Images Using Restricted Boltzmann Machine.

In this paper, a deep learning approach, Restricted Boltzmann Machine (RBM), is used to perform automatic hand sign language recognition from visual data. We evaluate how RBM, as a deep generative model, is capable of generating the distribution of the input data for an enhanced recognition of unseen data. Two modalities, RGB and Depth, are considered in the model input in three forms: original image, cropped image, and noisy cropped image. Five crops of the input image are used and the hand of these cropped images are detected using Convolutional Neural Network (CNN). After that, three types of the detected hand images are generated for each modality and input to RBMs. The outputs of the RBMs for two modalities are fused in another RBM in order to recognize the output sign label of the input image. The proposed multi-modal model is trained on all and part of the American alphabet and digits of four publicly available datasets. We also evaluate the robustness of the proposal against noise. Experimental results show that the proposed multi-modal model, using crops and the RBM fusing methodology, achieves state-of-the-art results on Massey University Gesture Dataset 2012, American Sign Language (ASL). and Fingerspelling Dataset from the University of Surrey's Center for Vision, Speech and Signal Processing, NYU, and ASL Fingerspelling A datasets.

Deep learning methods for protein torsion angle prediction.

BACKGROUND: Deep learning is one of the most powerful machine learning methods that has achieved the state-of-the-art performance in many domains. Since deep learning was introduced to the field of bioinformatics in 2012, it has achieved success in a number of areas such as protein residue-residue contact prediction, secondary structure prediction, and fold recognition. In this work, we developed deep learning methods to improve the prediction of torsion (dihedral) angles of proteins. RESULTS: We design four different deep learning architectures to predict protein torsion angles. The architectures including deep neural network (DNN) and deep restricted Boltzmann machine (DRBN), deep recurrent neural network (DRNN) and deep recurrent restricted Boltzmann machine (DReRBM) since the protein torsion angle prediction is a sequence related problem. In addition to existing protein features, two new features (predicted residue contact number and the error distribution of torsion angles extracted from sequence fragments) are used as input to each of the four deep learning architectures to predict phi and psi angles of protein backbone. The mean absolute error (MAE) of phi and psi angles predicted by DRNN, DReRBM, DRBM and DNN is about 20-21° and 29-30° on an independent dataset. The MAE of phi angle is comparable to the existing methods, but the MAE of psi angle is 29°, 2° lower than the existing methods. On the latest CASP12 targets, our methods also achieved the performance better than or comparable to a state-of-the art method. CONCLUSIONS: Our experiment demonstrates that deep learning is a valuable method for predicting protein torsion angles. The deep recurrent network architecture performs slightly better than deep feed-forward architecture, and the predicted residue contact number and the error distribution of torsion angles extracted from sequence fragments are useful features for improving prediction accuracy.

Identify Huntington's disease associated genes based on restricted Boltzmann machine with RNA-seq data.

BACKGROUND: Predicting disease-associated genes is helpful for understanding the molecular mechanisms during the disease progression. Since the pathological mechanisms of neurodegenerative diseases are very complex, traditional statistic-based methods are not suitable for identifying key genes related to the disease development. Recent studies have shown that the computational models with deep structure can learn automatically the features of biological data, which is useful for exploring the characteristics of gene expression during the disease progression. RESULTS: In this paper, we propose a deep learning approach based on the restricted Boltzmann machine to analyze the RNA-seq data of Huntington's disease, namely stacked restricted Boltzmann machine (SRBM). According to the SRBM, we also design a novel framework to screen the key genes during the Huntington's disease development. In this work, we assume that the effects of regulatory factors can be captured by the hierarchical structure and narrow hidden layers of the SRBM. First, we select disease-associated factors with different time period datasets according to the differentially activated neurons in hidden layers. Then, we select disease-associated genes according to the changes of the gene energy in SRBM at different time periods. CONCLUSIONS: The experimental results demonstrate that SRBM can detect the important information for differential analysis of time series gene expression datasets. The identification accuracy of the disease-associated genes is improved to some extent using the novel framework. Moreover, the prediction precision of disease-associated genes for top ranking genes using SRBM is effectively improved compared with that of the state of the art methods.

Multiple functional networks modeling for autism spectrum disorder diagnosis.

Despite countless studies on autism spectrum disorder (ASD), diagnosis relies on specific behavioral criteria and neuroimaging biomarkers for the disorder are still relatively scarce and irrelevant for diagnostic workup. Many researchers have focused on functional networks of brain activities using resting-state functional magnetic resonance imaging (rsfMRI) to diagnose brain diseases, including ASD. Although some existing methods are able to reveal the abnormalities in functional networks, they are either highly dependent on prior assumptions for modeling these networks or do not focus on latent functional connectivities (FCs) by considering discriminative relations among FCs in a nonlinear way. In this article, we propose a novel framework to model multiple networks of rsfMRI with data-driven approaches. Specifically, we construct large-scale functional networks with hierarchical clustering and find discriminative connectivity patterns between ASD and normal controls (NC). We then learn features and classifiers for each cluster through discriminative restricted Boltzmann machines (DRBMs). In the testing phase, each DRBM determines whether a test sample is ASD or NC, based on which we make a final decision with a majority voting strategy. We assess the diagnostic performance of the proposed method using public datasets and describe the effectiveness of our method by comparing it to competing methods. We also rigorously analyze FCs learned by DRBMs on each cluster and discover dominant FCs that play a major role in discriminating between ASD and NC. Hum Brain Mapp 38:5804-5821, 2017. © 2017 Wiley Periodicals, Inc.