Haixian Wang

L1-Norm-Based Common Spatial Patterns

Common spatial patterns (CSP) is a commonly used method of spatial filtering for multichannel electroencephalogram (EEG) signals. The formulation of the CSP criterion is based on variance using L2-norm, which implies that CSP is sensitive to outliers. In this paper, we propose a robust version of CSP, called CSP-L1, by maximizing the ratio of filtered dispersion of one class to the other class, both of which are formulated by using L1-norm rather than L2-norm. The spatial filters of CSP-L1 are obtained by introducing an iterative algorithm, which is easy to implement and is theoretically justified. CSP-L1 is robust to outliers. Experiment results on a toy example and datasets of BCI competitions demonstrate the efficacy of the proposed method.

Fisher Discriminant Analysis With L1-Norm

Fisher linear discriminant analysis (LDA) is a classical subspace learning technique of extracting discriminative features for pattern recognition problems. The formulation of the Fisher criterion is based on the L2-norm, which makes LDA prone to being affected by the presence of outliers. In this paper, we propose a new method, termed LDA-L1, by maximizing the ratio of the between-class dispersion to the within-class dispersion using the L1-norm rather than the L2-norm. LDA-L1 is robust to outliers, and is solved by an iterative algorithm proposed. The algorithm is easy to be implemented and is theoretically shown to arrive at a locally maximal point. LDA-L1 does not suffer from the problems of small sample size and rank limit as existed in the conventional LDA. Experiment results of image recognition confirm the effectiveness of the proposed method.

Locality-Preserved Maximum Information Projection

Dimensionality reduction is usually involved in the domains of artificial intelligence and machine learning. Linear projection of features is of particular interest for dimensionality reduction since it is simple to calculate and analytically analyze. In this paper, we propose an essentially linear projection technique, called locality-preserved maximum information projection (LPMIP), to identify the underlying manifold structure of a data set. LPMIP considers both the within-locality and the between-locality in the processing of manifold learning. Equivalently, the goal of LPMIP is to preserve the local structure while maximize the out-of-locality (global) information of the samples simultaneously. Different from principal component analysis (PCA) that aims to preserve the global information and locality-preserving projections (LPPs) that is in favor of preserving the local structure of the data set, LPMIP seeks a tradeoff between the global and local structures, which is adjusted by a parameter alpha, so as to find a sub- space that detects the intrinsic manifold structure for classification tasks. Computationally, by constructing the adjacency matrix, LPMIP is formulated as an eigenvalue problem. LPMIP yields orthogonal basis functions, and completely avoids the singularity problem as it exists in LPP. Further, we develop an efficient and stable LPMIP/QR algorithm for implementing LPMIP, especially, on high-dimensional data set. Theoretical analysis shows that conventional linear projection methods such as (weighted) PCA, maximum margin criterion (MMC), linear discriminant analysis (LDA), and LPP could be derived from the LPMIP framework by setting different graph models and constraints. Extensive experiments on face, digit, and facial expression recognition show the effectiveness of the proposed LPMIP method.

Local Temporal Common Spatial Patterns for Robust Single-Trial EEG Classification

In this paper, we propose a novel optimal spatio-temporal filter, termed local temporal common spatial patterns (LTCSP), for robust single-trial elctroencephalogram (EEG) classification. Different from classical common spatial patterns (CSP) that uses only global spatial covariances to compute the optimal filter, LTCSP considers temporally local information in the variance modelling. The underlying manifold variances of EEG signals contain more discriminative information. LTCSP is an extension to CSP in the sense that CSP can be derived from LTCSP under a special case. By constructing an adjacency matrix, LTCSP is formulated as an eigenvalue problem. So, LTCSP is computationally as straightforward as CSP. However, LTCSP has better discrimination ability than CSP and is much more robust. Simulated experiment and real EEG classification demonstrate the effectiveness of the proposed LTCSP method.

L1-Norm Kernel Discriminant Analysis Via Bayes Error Bound Optimization for Robust Feature Extraction

A novel discriminant analysis criterion is derived in this paper under the theoretical framework of Bayes optimality. In contrast to the conventional Fishers discriminant criterion, the major novelty of the proposed one is the use of L1 norm rather than L2 norm, which makes it less sensitive to the outliers. With the L1-norm discriminant criterion, we propose a new linear discriminant analysis (L1-LDA) method for linear feature extraction problem. To solve the L1-LDA optimization problem, we propose an efficient iterative algorithm, in which a novel surrogate convex function is introduced such that the optimization problem in each iteration is to simply solve a convex programming problem and a close-form solution is guaranteed to this problem. Moreover, we also generalize the L1-LDA method to deal with the nonlinear robust feature extraction problems via the use of kernel trick, and hereafter proposed the L1-norm kernel discriminant analysis (L1-KDA) method. Extensive experiments on simulated and real data sets are conducted to evaluate the effectiveness of the proposed method in comparing with the state-of-the-art methods.

Investigating univariate temporal patterns for intrinsic connectivity networks based on complexity and low-frequency oscillation: A test–retest reliability study

Intrinsic connectivity networks (ICNs) are composed of spatial components and time courses. The spatial components of ICNs were discovered with moderate-to-high reliability. So far as we know, few studies focused on the reliability of the temporal patterns for ICNs based their individual time courses. The goals of this study were twofold: to investigate the test-retest reliability of temporal patterns for ICNs, and to analyze these informative univariate metrics. Additionally, a correlation analysis was performed to enhance interpretability. Our study included three datasets: (a) short- and long-term scans, (b) multi-band echo-planar imaging (mEPI), and (c) eyes open or closed. Using dual regression, we obtained the time courses of ICNs for each subject. To produce temporal patterns for ICNs, we applied two categories of univariate metrics: network-wise complexity and network-wise low-frequency oscillation. Furthermore, we validated the test-retest reliability for each metric. The network-wise temporal patterns for most ICNs (especially for default mode network, DMN) exhibited moderate-to-high reliability and reproducibility under different scan conditions. Network-wise complexity for DMN exhibited fair reliability (ICC<0.5) based on eyes-closed sessions. Specially, our results supported that mEPI could be a useful method with high reliability and reproducibility. In addition, these temporal patterns were with physiological meanings, and certain temporal patterns were correlated to the node strength of the corresponding ICN. Overall, network-wise temporal patterns of ICNs were reliable and informative and could be complementary to spatial patterns of ICNs for further study.

Local and Weighted Maximum Margin Discriminant Analysis

In this paper, we propose a new approach, called local and weighted maximum margin discriminant analysis (LWMMDA), to performing object discrimination. LWMMDA is a subspace learning method that identifies the underlying nonlinear manifold for discrimination. The goal of LWMMDA is to seek a transformation such that data points of different classes are projected as far as possible while points within a same class are as compact as possible. The projections are obtained by maximizing a new discriminant criterion, called local and weighted maximum margin criterion (LWMMC). Different from previous maximum margin criterion (MMC) which seeks only the globally Euclidean structure of data points, LWMMC takes the local property into account, which makes LWMMC more accurate in finding discriminant information. LWMMC has an additional weighted parameter beta that further broadens the average margin between different classes. Computationally, LWMMDA completely avoids the singularity problem. Besides, LWMMDA couples the QR-decomposition into its framework, which makes LWMMDA very efficient and stable in implementation. Finally, LWMMDA framework is straightforwardly extended into the reproducing kernel Hilbert space induced by a nonlinear function Phi. Experiments on digit visualization, face recognition, and facial expression recognition are presented to show the effectiveness of the proposed method.

Probabilistic two-dimensional principal component analysis and its mixture model for face recognition

Recently, two-dimensional principal component analysis (2DPCA) as a novel eigenvector-based method has proved to be an efficient technique for image feature extraction and representation. In this paper, by supposing a parametric Gaussian distribution over the image space (spanned by the row vectors of 2D image matrices) and a spherical Gaussian noise model for the image, we endow the 2DPCA with a probabilistic framework called probabilistic 2DPCA (P2DPCA), which is robust to noise. Further, by using the probabilistic perspective of P2DPCA, we extend the P2DPCA to a mixture of local P2DPCA models (MP2DPCA). The MP2DPCA offers us a method of being able to model faces in unconstrained (complex) environment. The model parameters could be fitted on the basis of maximum likelihood (ML) estimation via the expectation maximization (EM) algorithm. The experimental recognition results on UMIST, AR face database, and the face recognition (FR) data collected at University of Essex confirm the effectivity of the proposed methods.

Regularized Filters for L1-Norm-Based Common Spatial Patterns

The ℓ1-norm-based common spatial patterns (CSP-L1) approach is a recently developed technique for optimizing spatial filters in the field of electroencephalogram (EEG)-based brain computer interfaces. The ℓ1-norm-based expression of dispersion in CSP-L1 alleviates the negative impact of outliers. In this paper, we further improve the robustness of CSP-L1 by taking into account noise which does not necessarily have as large a deviation as with outliers. The noise modelling is formulated by using the waveform length of the EEG time course. With the noise modelling, we then regularize the objective function of CSP-L1, in which the ℓ1-norm is used in two folds: one is the dispersion and the other is the waveform length. An iterative algorithm is designed to resolve the optimization problem of the regularized objective function. A toy illustration and the experiments of classification on real EEG data sets show the effectiveness of the proposed method.

Localization of neural efficiency of the mathematically gifted brain through a feature subset selection method

Based on the neural efficiency hypothesis and task-induced EEG gamma-band response (GBR), this study investigated the brain regions where neural resource could be most efficiently recruited by the math-gifted adolescents in response to varying cognitive demands. In this experiment, various GBR-based mental states were generated with three factors (level of mathematical ability, task complexity, and short-term learning) modulating the level of neural activation. A feature subset selection method based on the sequential forward floating search algorithm was used to identify an “optimal” combination of EEG channel locations, where the corresponding GBR feature subset could obtain the highest accuracy in discriminating pairwise mental states influenced by each experiment factor. The integrative results from multi-factor selections suggest that the right-lateral fronto–parietal system is highly involved in neural efficiency of the math-gifted brain, primarily including the bilateral superior frontal, right inferior frontal, right-lateral central and right temporal regions. By means of the localization method based on single-trial classification of mental states, new GBR features and EEG channel-based brain regions related to mathematical giftedness were identified, which could be useful for the brain function improvement of children/adolescents in mathematical learning through brain–computer interface systems.