A Progressive Hierarchical Alternating Least Squares Method for Symmetric Nonnegative Matrix Factorization.

In this article, we study the symmetric nonnegative matrix factorization (SNMF) which is a powerful tool in data mining for dimension reduction and clustering. The main contributions of the present work include: (i) a new descent direction for the rank-one SNMF is derived and a strategy for choosing the step size along this descent direction is established; (ii) a progressive hierarchical alternating least squares (PHALS) method for SNMF is developed, which is parameter-free and updates the variables column by column. Moreover, every column is updated by solving a rank-one SNMF subproblem; and (iii) the convergence to the Karush-Kuhn-Tucker (KKT) point set (or the stationary point set) is proved for PHALS. Several synthetical and real data sets are tested to demonstrate the effectiveness and efficiency of the proposed method. Our PHALS provides better performance in terms of the computational accuracy, the optimality gap, and the CPU time, compared with a number of state-of-the-art SNMF methods.

Dual modification of BiVO4 photoanode by enriching bulk and surface oxygen vacancies for enhanced photoelectrochemical performance.

The introduction of oxygen vacancies (Ov) into photoanodes has been considered an effective method to enhance the photoelectrochemical (PEC) water splitting performance. The efficiency of water splitting is related to light absorption, charge separation to the electrode surface, and charge injection into the electrolyte. However, introducing Ov from a single level cannot meet the above objectives. In this work, we present the fabrication of BiVO4 (BVO) photoanodes with bulk and surface Ov, and their respective roles in the PEC performance have been studied. The bulk OV of the photoanode could increase the carrier density and improve the separation efficiency of photogenerated electrons and holes. The surface Ov provide abundant surface active sites, and enhance the charge injection efficiency. Charge separation efficiency of the nitrogen-treated BVO (N:BVO) (69.1 % at 0.75 V vs RHE and 85.1 % at 1.23 V vs RHE) has a noticeable increase compared with that of BVO (51.2 % at 0.75 V vs RHE and 64.6 % at 1.23 V vs RHE), nevertheless, only a minor enhancement of charge injection efficiency (from 49.1 % to 56.5 % at 1.23 V vs RHE). After the deposition of NiFeOOH, the photoanodes present superior charges injection efficiency in the whole range of applied potential. The as-synthesized N:BVO/U-NiFeOOH photoanode exhibits a photocurrent density of 5.52 mA·cm-2 at 1.23 V vs RHE with a 97 % Faradaic efficiency for O2/H2 evolution. Thus, there is a synergistic effect between the bulk OV and surface OV on the BVO photoanode, exhibiting highly promoted PEC water splitting activity relative to the individual OV decorated BVO for oxygen evolution reaction, which provides a promising strategy for fabricating efficient solar water splitting systems.

A Fast Frequent Directions Algorithm for Low Rank Approximation.

Recently a deterministic method, frequent directions (FD) is proposed to solve the high dimensional low rank approximation problem. It works well in practice, but experiences high computational cost. In this paper, we establish a fast frequent directions algorithm for the low rank approximation problem, which implants a randomized algorithm, sparse subspace embedding (SpEmb) in FD. This new algorithm makes use of FD's natural block structure and sends more information through SpEmb to each block in FD. We prove that our new algorithm produces a good low rank approximation with a sketch of size linear on the rank approximated. Its effectiveness and efficiency are demonstrated by the experimental results on both synthetic and real world datasets, as well as applications in network analysis.

Incremental Linear Discriminant Analysis: A Fast Algorithm and Comparisons.

It has always been a challenging task to develop a fast and an efficient incremental linear discriminant analysis (ILDA) algorithm. For this purpose, we conduct a new study for linear discriminant analysis (LDA) in this paper and develop a new ILDA algorithm. We propose a new batch LDA algorithm called LDA/QR. LDA/QR is a simple and fast LDA algorithm, which is obtained by computing the economic QR factorization of the data matrix followed by solving a lower triangular linear system. The relationship between LDA/QR and uncorrelated LDA (ULDA) is also revealed. Based on LDA/QR, we develop a new incremental LDA algorithm called ILDA/QR. The main features of our ILDA/QR include that: 1) it can easily handle the update from one new sample or a chunk of new samples; 2) it has efficient computational complexity and space complexity; and 3) it is very fast and always achieves competitive classification accuracy compared with ULDA algorithm and existing ILDA algorithms. Numerical experiments based on some real-world data sets demonstrate that our ILDA/QR is very efficient and competitive with the state-of-the-art ILDA algorithms in terms of classification accuracy, computational complexity, and space complexity.

Sparse canonical correlation analysis: new formulation and algorithm.

In this paper, we study canonical correlation analysis (CCA), which is a powerful tool in multivariate data analysis for finding the correlation between two sets of multidimensional variables. The main contributions of the paper are: 1) to reveal the equivalent relationship between a recursive formula and a trace formula for the multiple CCA problem, 2) to obtain the explicit characterization for all solutions of the multiple CCA problem even when the corresponding covariance matrices are singular, 3) to develop a new sparse CCA algorithm, and 4) to establish the equivalent relationship between the uncorrelated linear discriminant analysis and the CCA problem. We test several simulated and real-world datasets in gene classification and cross-language document retrieval to demonstrate the effectiveness of the proposed algorithm. The performance of the proposed method is competitive with the state-of-the-art sparse CCA algorithms.

Sparse representation classifier steered discriminative projection with applications to face recognition.

A sparse representation-based classifier (SRC) is developed and shows great potential for real-world face recognition. This paper presents a dimensionality reduction method that fits SRC well. SRC adopts a class reconstruction residual-based decision rule, we use it as a criterion to steer the design of a feature extraction method. The method is thus called the SRC steered discriminative projection (SRC-DP). SRC-DP maximizes the ratio of between-class reconstruction residual to within-class reconstruction residual in the projected space and thus enables SRC to achieve better performance. SRC-DP provides low-dimensional representation of human faces to make the SRC-based face recognition system more efficient. Experiments are done on the AR, the extended Yale B, and PIE face image databases, and results demonstrate the proposed method is more effective than other feature extraction methods based on the SRC.

Discriminant analysis in pairwise kernel learning for SVM classification.

Multiple kernel learning arises when different types of kernels are employed simultaneously. In particular, in the situation that the data are from heterogeneous sources. In this study, we developed a new framework for determining the coefficients in learning pairwise kernels for classification in Support Vector Machines (SVM). The effectiveness of the proposed method was then demonstrated through the prediction of self-renewal and pluripotency mESCs stemness membership genes. It was also tested on the power of discrimination in DNA repair gene data. The promising formulation in learning coefficients for pairwise kernel learning was shown via experimental evaluation. This may provide a novel perspective for kernel learning in future applications.