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A brain-computer interface (BCI) based on the combination of oddball paradigm and face perception has been introduced. Such BCI mainly exploits three event-related potential (ERP) components, namely vertex positive potential (VPP), N170 and P300 instead of only P300. With different temporal and spatial distributions of the three ERP components, a regularized common spatial pattern (CSP) with Fisher's criterion (FC), named FCCSP, is proposed to extract the most discriminative features for single trial classification of ERP components. With linear discriminant analysis (LDA) classifier, the proposed FCCSP spatial filtering method yields an average classification accuracy of 95.4% on seven healthy subjects for single-trial ERP components, which outperforms no spatial filtering, the CSP and the FC.

Nonnegative matrix factorization (NMF) with minimum-volume-constraint (MVC) is exploited in this paper. Our results show that MVC can actually improve the sparseness of the results of NMF. This sparseness is L(0)-norm oriented and can give desirable results even in very weak sparseness situations, thereby leading to the significantly enhanced ability of learning parts of NMF. The close relation between NMF, sparse NMF, and the MVC_NMF is discussed first. Then two algorithms are proposed to solve the MVC_NMF model. One is called quadratic programming_MVC_NMF (QP_MVC_NMF) which is based on quadratic programming and the other is called negative glow_MVC_NMF (NG_MVC_NMF) because it uses multiplicative updates incorporating natural gradient ingeniously. The QP_MVC_NMF algorithm is quite efficient for small-scale problems and the NG_MVC_NMF algorithm is more suitable for large-scale problems. Simulations show the efficiency and validity of the proposed methods in applications of blind source separation and human face images analysis.

Steady-state visual evoked potential (SSVEP)-based brain computer-interface (BCI) is one of the most popular BCI systems. An efficient SSVEP-based BCI system in shorter time with higher accuracy in recognizing SSVEP has been pursued by many studies. This paper introduces a novel multiway canonical correlation analysis (Multiway CCA) approach to recognize SSVEP. This approach is based on tensor CCA and focuses on multiway data arrays. Multiple CCAs are used to find appropriate reference signals for SSVEP recognition from different data arrays. SSVEP is then recognized by implementing multiple linear regression (MLR) between EEG and optimized reference signals. The proposed Multiway CCA is verified by comparing to the standard CCA and power spectral density analysis (PSDA). Results showed that the Multiway CCA achieved higher recognition accuracy within shorter time than that of the CCA and PSDA.

Nonnegative matrix factorization (NMF) is a widely used method for blind spectral unmixing (SU), which aims at obtaining the endmembers and corresponding fractional abundances, knowing only the collected mixing spectral data. It is noted that the abundance may be sparse (i.e., the endmembers may be with sparse distributions) and sparse NMF tends to lead to a unique result, so it is intuitive and meaningful to constrain NMF with sparseness for solving SU. However, due to the abundance sum-to-one constraint in SU, the traditional sparseness measured by L0/L1-norm is not an effective constraint any more. A novel measure (termed as S-measure) of sparseness using higher order norms of the signal vector is proposed in this paper. It features the physical significance. By using the S-measure constraint (SMC), a gradient-based sparse NMF algorithm (termed as NMF-SMC) is proposed for solving the SU problem, where the learning rate is adaptively selected, and the endmembers and abundances are simultaneously estimated. In the proposed NMF-SMC, there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior. Yet, it does not require the preprocessing of dimension reduction in which some useful information may be lost. Experiments based on synthetic mixtures and real-world images collected by AVIRIS and HYDICE sensors are performed to evaluate the validity of the proposed method.

Recently, nonnegative matrix factorization (NMF) attracts more and more attentions for the promising of wide applications. A problem that still remains is that, however, the factors resulted from it may not necessarily be realistically interpretable. Some constraints are usually added to the standard NMF to generate such interpretive results. In this paper, a minimum-volume constrained NMF is proposed and an efficient multiplicative update algorithm is developed based on the natural gradient optimization. The proposed method can be applied to the blind source separation (BSS) problem, a hot topic with many potential applications, especially if the sources are mutually dependent. Simulation results of BSS for images show the superiority of the proposed method.

To make the results reasonable, existing joint diagonalization algorithms have imposed a variety of constraints on diagonalizers. Actually, those constraints can be imposed uniformly by minimizing the condition number of diagonalizers. Motivated by this, the approximate joint diagonalization problem is reviewed as a multiobjective optimization problem for the first time. Based on this, a new algorithm for nonorthogonal joint diagonalization is developed. The new algorithm yields diagonalizers which not only minimize the diagonalization error but also have as small condition numbers as possible. Meanwhile, degenerate solutions are avoided strictly. Besides, the new algorithm imposes few restrictions on the target set of matrices to be diagonalized, which makes it widely applicable. Primary results on convergence are presented and we also show that, for exactly jointly diagonalizable sets, no local minima exist and the solutions are unique under mild conditions. Extensive numerical simulations illustrate the performance of the algorithm and provide comparison with other leading diagonalization methods. The practical use of our algorithm is shown for blind source separation (BSS) problems, especially when ill-conditioned mixing matrices are involved.

In traditional method to blindly extract interesting source signals sequentially, the second-order or higher-order statistics of signals are often utilized. However, for impulsive sources, both of the second-order and higher-order statistics may degenerate. Therefore, it is necessary to exploit new method for the blind extraction of impulsive sources. Based on the best compression-reconstruction principle, a novel model is proposed in this work, together with the corresponding algorithm. The proposed method can be used for blind extraction of sources which are distributed from alpha stable process. Simulations are given to illustrate availability and robustness of our algorithm.

Based on the fact that the temporal predictability of signals is often different, new algorithm using second order statistics for blind source separation (BSS) is proposed in this work. The novel measure of signal temporal predictability is developed. Based on which, the proposed method is less time-consuming and requires minimal assumptions regarding the probability density functions of the source signals. Also, the online mode is provided. Simulations show that the proposed algorithm is robust with the best precision for batch mode, and its convergence is quite well for online mode.

Non-negative tensor factorization (NTF) has been successfully applied to analyze event-related potentials (ERPs), and shown superiority in terms of capturing multi-domain features. However, the time-frequency representation of ERPs by higher-order tensors are usually large-scale, which prevents the popularity of most tensor factorization algorithms. To overcome this issue, we introduce a non-negative canonical polyadic decomposition (NCPD) based on low-rank approximation (LRA) and hierarchical alternating least square (HALS) techniques. We applied NCPD (LRAHALS and benchmark HALS) and CPD to extract multi-domain features of a visual ERP. The features and components extracted by LRAHALS NCPD and HALS NCPD were very similar, but LRAHALS NCPD was 70 times faster than HALS NCPD. Moreover, the desired multi-domain feature of the ERP by NCPD showed a significant group difference (control versus depressed participants) and a difference in emotion processing (fearful versus happy faces). This was more satisfactory than that by CPD, which revealed only a group difference.

Canonical correlation analysis (CCA) has been one of the most popular methods for frequency recognition in steady-state visual evoked potential (SSVEP)-based brain–computer interfaces (BCIs). Despite its efficiency, a potential problem is that using pre-constructed sine-cosine waves as the required reference signals in the CCA method often does not result in the optimal recognition accuracy due to their lack of features from the real electro-encephalo-gram (EEG) data. To address this problem, this study proposes a novel method based on multiset canonical correlation analysis (MsetCCA) to optimize the reference signals used in the CCA method for SSVEP frequency recognition. The MsetCCA method learns multiple linear transforms that implement joint spatial filtering to maximize the overall correlation among canonical variates, and hence extracts SSVEP common features from multiple sets of EEG data recorded at the same stimulus frequency. The optimized reference signals are formed by combination of the common features and completely based on training data. Experimental study with EEG data from 10 healthy subjects demonstrates that the MsetCCA method improves the recognition accuracy of SSVEP frequency in comparison with the CCA method and other two competing methods (multiway CCA (MwayCCA) and phase constrained CCA (PCCA)), especially for a small number of channels and a short time window length. The superiority indicates that the proposed MsetCCA method is a new promising candidate for frequency recognition in SSVEP-based BCIs.