The intersubject variability present in electroencephalographic (EEG) signals can affect the performance of the brain–computer interface (BCI) systems. Despite the significant progress in the field, the variability in neural data remains one of the most critical challenges in constructing accurate predictive models of human intention. As a result, the majority of the previous studies have focused either on devising subject-specific signal processing and machine learning algorithms, used some data from a target user to update and calibrate a pretrained classifier, or have used data collected from a relatively large number of training subjects to construct generic classifiers for new subjects. In this work, we investigate the feasibility of using a relatively small number of training subjects to achieve subject-independent classification of event-related potentials (ERPs) in P300-based BCIs. To this end, we employ convolutional neural networks (CNNs) and propose a leave-one-subject-out cross-validation (LOSO-CV) for model selection; that is to say, for tuning CNN hyperparameters including number of layers, filters, kernel size, and epoch. The utility of the proposed model selection is warranted because LOSO-CV simulates the effect of subject-independent classification within the training data. The entire process of training (including model selection) is validated by applying another LOSO-CV external to the training process. Our empirical results obtained on four publicly available datasets confirm the capability of LOSO-CV model selection with CNN to capture intrinsic ERP features from a small group of subjects to classify observations collected from unseen subjects.

Predicting attention-modulated brain responses is a major area of investigation in brain–computer interface (BCI) research that aims to translate neural activities into useful control and communication commands. Such studies involve collecting electroencephalographic (EEG) data from subjects to train classifiers for decoding users’ mental states. However, various sources of inter or intrasubject variabilities in brain signals render training classifiers in BCI systems challenging. From a machine learning perspective, this model training generally follows a common methodology: 1) apply some type of feature extraction, which can be time-consuming and may require domain knowledge and 2) train a classifier using extracted features. The advent of deep learning technologies has offered unprecedented opportunities to not only construct remarkably accurate classifiers but also to integrate the feature extraction stage into the classifier construction. Although integrating feature extraction, which is generally domain-dependent, into the classifier construction is a considerable advantage of deep learning models, the process of architecture selection for BCIs generally depends on domain knowledge. In this study, we examine the feasibility of conducting a systematic model selection combined with mainstream deep learning architectures to construct accurate classifiers for decoding P300 event-related potentials. In particular, we present the results of 232 convolutional neural networks (CNNs) (4 datasets$\times58$structures), 36 long short-term memory cells (LSTMs) (4 datasets$\times9$structures), and 320 hybrid CNN-LSTM models (4 datasets$\times80$structures) of varying complexity. Our empirical results show that in the classification of P300 waveforms, the constructed predictive models can outperform the current state-of-the-art deep learning architectures, which are partially or entirely inspired by domain knowledge. The source codes and constructed models are available athttps://github.com/berdakh/P3Net.

A salient problem in machine learning is transforming categorical variables into efficient numerical features. This focus is warranted due to the ubiquity of categorical data in real-world applications but, on the contrary, the development of many machine learning methods based on the assumption of having numerical variables. Perhaps the most popular existing categorical to numerical conversion techniques include one-hot encoding, thermometer encoding, and ordinal (integer) encoding. One-hot and thermometer encodings become computationally inefficient and may lead to ill-conditioning for high-cardinality categorical variables as they create high-dimensional data matrices. As ordinal encoding does not change data dimensionality, it is significantly more memory-efficient; however, the spurious ordering induced by ordinal encoding among unordered categorical values can hamstring the performance of constructed predictive models. In this paper, we propose a new encoding technique, namely complex encoding, that provides a symmetric representation of categorical values in the complex plane. To show the efficacy of the complex encoding in terms of error rate and memory usage, we conducted a set of numerical experiments using real datasets and the family of linear discriminant functions for complex Gaussian distributions. Empirical results show that not only complex encoding avoids the ill-conditioning problem of one-hot and thermometer encodings, it can generally lead to a comparable or higher classification accuracy with respect to others (when they are applicable) at the expense of only about two-fold increase in memory usage with respect to ordinal encoding.

Interpreting results of a transformer frequency response analysis (FRA) is quite challenging. One of the common methods to summarize FRA data is to employ statistical indicators (SIs) over FRA spectra. However, SI-specific boundary conditions for various operational modes of transformers are left unexplored. The lack of such boundary conditions renders interpretation of SIs difficult and subjective. In this article, in an attempt to find data-driven boundary conditions, first the conventional measurement setup of FRA technique is modified to emulate interturn winding short-circuit. Then, the boundary conditions of various SIs for normal, suspicious, and critical operational modes of transformers under fault are obtained. Nevertheless, the price of moving subjective boundaries to their objective data-driven counterparts is paid in an intrinsic uncertainty introduced by the process of data collection per se. In order to capture and quantify this uncertainty, a novel solution inspired by bolstered error estimation used in pattern recognition is proposed. In particular, the proposed method allows reporting the level of confidence that an observed magnitude of SI belongs to a specific operational mode. Having this confidence level is also warranted from an operational perspective because it enables utility operators to enhance the decision-making process and estimate the severity of transformer faulty conditions.

In this letter, the theory of random matrices of increasing dimension is used to construct a form of regularized linear discriminant analysis (RLDA) that asymptotically yields the lowest overall risk with respect to the bias of the discriminant in cost-sensitive classification of two multivariate Gaussian distributions. Numerical experiments using both synthetic and real data show that even in finite-sample settings, the proposed classifier can uniformly outperform RLDA in terms of achieving a lower risk as a function of regularization parameter and misclassification costs.

Constructing accurate predictive models is at the heart of brain-computer interfaces (BCIs) because these models can ultimately translate brain activities into communication and control commands. The majority of the previous work in BCI use spatial, temporal, or spatiotemporal features of event-related potentials (ERPs). In this study, we examined the discriminatory effect of their spatiospectral features to capture the most relevant set of neural activities from electroencephalographic recordings that represent users' mental intent. In this regard, we model ERP waveforms using a sum of sinusoids with unknown amplitudes, frequencies, and phases. The effect of this signal modeling step is to represent high-dimensional ERP waveforms in a substantially lower dimensionality space, which includes their dominant power spectral contents. We found that the most discriminative frequencies for accurate decoding of visual attention modulated ERPs lie in a spectral range less than 6.4 Hz. This was empirically verified by treating dominant frequency contents of ERP waveforms as feature vectors in the state-of-the-art machine learning techniques used herein. The constructed predictive models achieved remarkable performance, which for some subjects was as high as 94% as measured by the area under curve. Using these spectral contents, we further studied the discriminatory effect of each channel and proposed an efficient strategy to choose subject-specific subsets of channels that generally led to classifiers with comparable performance.

BACKGROUND: Time-Frequency (TF) analysis has been extensively used for the analysis of non-stationary numeric signals in the past decade. At the same time, recent studies have statistically confirmed the non-stationarity of genomic non-numeric sequences and suggested the use of non-stationary analysis for these sequences. The conventional approach to analyze non-numeric genomic sequences using techniques specific to numerical data is to convert non-numerical data into numerical values in some way and then apply time or transform domain signal processing algorithms. Nevertheless, this approach raises questions regarding the relative magnitudes under numeric transforms, which can potentially lead to spurious patterns or misinterpretation of results. RESULTS: In this paper, using the notion of interpretive signal processing (ISP) and by redefining correlation functions for non-numeric sequences, a general class of TF transforms are extended and applied to non-numerical genomic sequences. The technique has been successfully evaluated on synthetic and real DNA sequences. CONCLUSION: The proposed framework is fairly generic and is believed to be useful for extracting quantitative and visual information regarding local and global periodicity, symmetry, (non-) stationarity and spectral color of genomic sequences. The notion of interpretive time-frequency analysis introduced in this work can be considered as the first step towards the development of a rigorous mathematical construct for genomic signal processing.

Half a century ago, Chow and Liu proved that the distribution of the first-order dependence tree that optimally approximates an arbitrary joint distribution in terms of Kullback-Leibler cross entropy is the distribution of the maximum-weight dependence tree (MWDT). In a p-dimensional space, this is a tree with p-1 branches between pairs of variables with each branch having a weight equal to the mutual information between variables at both ends. Today, MWDTs have applications that are more important in classification than only being used to model first-order dependence structure among variables. Nevertheless, whether the MWDT is the optimal first-order tree in classification has been left unexplored so far. In this letter, we study the optimality of the MWDT structure from the stand-point of classification.

MOTIVATION: The biomarker discovery process in high-throughput genomic profiles has presented the statistical learning community with a challenging problem, namely learning when the number of variables is comparable or exceeding the sample size. In these settings, many classical techniques including linear discriminant analysis (LDA) falter. Poor performance of LDA is attributed to the ill-conditioned nature of sample covariance matrix when the dimension and sample size are comparable. To alleviate this problem, regularized LDA (RLDA) has been classically proposed in which the sample covariance matrix is replaced by its ridge estimate. However, the performance of RLDA depends heavily on the regularization parameter used in the ridge estimate of sample covariance matrix. RESULTS: We propose a range-search technique for efficient estimation of the optimum regularization parameter. Using an extensive set of simulations based on synthetic and gene expression microarray data, we demonstrate the robustness of the proposed technique to Gaussianity, an assumption used in developing the core estimator. We compare the performance of the technique in terms of accuracy and efficiency with classical techniques for estimating the regularization parameter. In terms of accuracy, the results indicate that the proposed method vastly improves on similar techniques that use classical plug-in estimator. In that respect, it is better or comparable to cross-validation-based search strategies while, depending on the sample size and dimensionality, being tens to hundreds of times faster to compute. AVAILABILITY AND IMPLEMENTATION: The source code is available at https://github.com/danik0411/optimum-rlda CONTACT: [email protected] information: Supplementary materials are available at Bioinformatics online.

MOTIVATION: It is commonly assumed in pattern recognition that cross-validation error estimation is 'almost unbiased' as long as the number of folds is not too small. While this is true for random sampling, it is not true with separate sampling, where the populations are independently sampled, which is a common situation in bioinformatics. RESULTS: We demonstrate, via analytical and numerical methods, that classical cross-validation can have strong bias under separate sampling, depending on the difference between the sampling ratios and the true population probabilities. We propose a new separate-sampling cross-validation error estimator, and prove that it satisfies an 'almost unbiased' theorem similar to that of random-sampling cross-validation. We present two case studies with previously published data, which show that the results can change drastically if the correct form of cross-validation is used. AVAILABILITY AND IMPLEMENTATION: The source code in C++, along with the Supplementary Materials, is available at: http://gsp.tamu.edu/Publications/supplementary/zollanvari13/.

This paper provides, for the first time, exact analytical expressions for the first moment of the true error of linear discriminant analysis (LDA) when the data are univariate and taken from two stochastic Gaussian processes. We assume a general setting in which the sample data from each class do not need to be identically distributed or independent within or between classes. As an application of this framework, we characterize the performance of LDA in situations that the data are generated from autoregressive models of the first order.

Recent advances in high-throughput biotechnologies have led to the rapid growing research interest in reverse engineering of biomolecular systems (REBMS). 'Data-driven' approaches, i.e. data mining, can be used to extract patterns from large volumes of biochemical data at molecular-level resolution while 'design-driven' approaches, i.e. systems modeling, can be used to simulate emergent system properties. Consequently, both data- and design-driven approaches applied to -omic data may lead to novel insights in reverse engineering biological systems that could not be expected before using low-throughput platforms. However, there exist several challenges in this fast growing field of reverse engineering biomolecular systems: (i) to integrate heterogeneous biochemical data for data mining, (ii) to combine top-down and bottom-up approaches for systems modeling and (iii) to validate system models experimentally. In addition to reviewing progress made by the community and opportunities encountered in addressing these challenges, we explore the emerging field of synthetic biology, which is an exciting approach to validate and analyze theoretical system models directly through experimental synthesis, i.e. analysis-by-synthesis. The ultimate goal is to address the present and future challenges in reverse engineering biomolecular systems (REBMS) using integrated workflow of data mining, systems modeling and synthetic biology.

Error estimation must be used to find the accuracy of a designed classifier, an issue that is critical in biomarker discovery for disease diagnosis and prognosis in genomics and proteomics. This paper presents, for what is believed to be the first time, the analytical formulation for the joint sampling distribution of the actual and estimated errors of a classification rule. The analysis presented here concerns the linear discriminant analysis (LDA) classification rule and the resubstitution and leave-one-out error estimators, under a general parametric Gaussian assumption. Exact results are provided in the univariate case, and a simple method is suggested to obtain an accurate approximation in the multivariate case. It is also shown how these results can be applied in the computation of condition bounds and the regression of the actual error, given the observed error estimate. In contrast to asymptotic results, the analysis presented here is applicable to finite training data. In particular, it applies in the small-sample settings commonly found in genomics and proteomics applications. Numerical examples, which include parameters estimated from actual microarray data, illustrate the analysis throughout.

The complex Chebyshev error criterion is usually used as a general constraint in design of peak constraint weighted least square error (PCWLSE) filters. It applies an upper bound on the maximum magnitude of error between the desired and designed transfer functions of the filter. Therefore, it confines the corresponding maximum phase error as well. However, it imposes an over restricted constraint which reduces the feasibility region of the filter design problem. In this paper, a new and comprehensive class of constraints is proposed for design of PCWLSE filters that provides a larger feasible region than that of the complex Chebyshev constraint. Hence, the filter weights acquire larger feasible space to search and select better optimal values and consequently boost up the performance of the designed filter by achieving less weighted least square error. Simulation results show superiority of the proposed constraints over that of the complex Chebyshev criterion.

BACKGROUND: Nanomaterials are being manufactured on a commercial scale for use in medical, diagnostic, energy, component and communications industries. However, concerns over the safety of engineered nanomaterials have surfaced. Humans can be exposed to nanomaterials in different ways such as inhalation or exposure through the integumentary system. RESULTS: The interactions of engineered nanomaterials with primary human cells was investigated, using a systems biology approach combining gene expression microarray profiling with dynamic experimental parameters. In this experiment, primary human epidermal keratinocytes cells were exposed to several low-micron to nano-scale materials, and gene expression was profiled over both time and dose to compile a comprehensive picture of nanomaterial-cellular interactions. Very few gene-expression studies so far have dealt with both time and dose response simultaneously. Here, we propose different approaches to this kind of analysis. First, we used heat maps and multi-dimensional scaling (MDS) plots to visualize the dose response of nanomaterials over time. Then, in order to find out the most common patterns in gene-expression profiles, we used self-organizing maps (SOM) combined with two different criteria to determine the number of clusters. The consistency of SOM results is discussed in context of the information derived from the MDS plots. Finally, in order to identify the genes that have significantly different responses among different levels of dose of each treatment while accounting for the effect of time at the same time, we used a two-way ANOVA model, in connection with Tukey's additivity test and the Box-Cox transformation. The results are discussed in the context of the cellular responses of engineered nanomaterials. CONCLUSION: The analysis presented here lead to interesting and complementary conclusions about the response across time of human epidermal keratinocytes after exposure to nanomaterials. For example, we observed that gene expression for most treatments become closer to the expression of the baseline cultures as time proceeds. The genes found to be differentially-expressed are involved in a number of cellular processes, including regulation of transcription and translation, protein localization, transport, cell cycle progression, cell migration, cytoskeletal reorganization, signal transduction, and development.

This paper is concerned with the design of peak constrained weighted least square error (PCWLSE) FIR filters. Successive use of Caratheodory's theorem and Farkas' lema leads us to a new approach which is an extended epsiv-perturbation method to solve the resultant semi-infinite quadratic optimization problems of this type of filter design. The approach does not need the calculation of Lagrange multipliers which may require the inversion of ill-conditioned matrixes. The new proposed method is able to deal with design of both symmetric and asymmetric FIR filters. The computational procedure is illustrated by solving an example

The design of peak-constrained weighted least-square error (PCWLSE) Laguerre filters is of interest in signal processing applications. The formulation of such Laguerre filters ends up as a semi-infinite problem with two uncountable variables. Here, an efficient method is proposed to deal with this. Therefore, one can design PCWLSE Laguerre filters to satisfy all the continuous constraints of the problem. Furthermore, the desired phase response is also guaranteed. The proposed method has been developed based on exploiting the dual parameterization scheme derived directly from the Karush-Kuhn-Tucker condition. This approach may also be used to design similar asymmetric FIR filters