Zhengming Ma

Xinlong Lu, Zhengming Ma, Yuanping Lin

Reproducing Kernel Hilbert Space (RKHS) is the common mathematical platform for various kernel methods in machine learning. The purpose of kernel learning is to learn an appropriate RKHS according to different machine learning scenarios and training samples. Because RKHS is uniquely generated by the kernel function, kernel learning can be regarded as kernel function learning. This paper proposes a Domain Adaptive Learning method based on Sample-Dependent and Learnable Kernels (SDLK-DAL). The first contribution of our work is to propose a sample-dependent and learnable Positive Definite Quadratic Kernel function (PDQK) framework. Unlike learning the exponential parameter of Gaussian kernel function or the coefficient of kernel combinations, the proposed PDQK is a positive definite quadratic function, in which the symmetric positive semi-definite matrix is the learnable part in machine learning applications. The second contribution lies on that we apply PDQK to Domain Adaptive Learning (DAL). Our approach learns the PDQK through minimizing the mean discrepancy between the data of source domain and target domain and then transforms the data into an optimized RKHS generated by PDQK. We conduct a series of experiments that the RKHS determined by PDQK replaces those in several state-of-the-art DAL algorithms, and our approach achieves better performance.

Wanguang Yin, Zhengming Ma, Quanying Liu

Linear discriminant analysis (LDA) is a widely used algorithm in machine learning to extract a low-dimensional representation of high-dimensional data, it features to find the orthogonal discriminant projection subspace by using the Fisher discriminant criterion. However, the traditional Euclidean-based methods for solving LDA are easily convergent to spurious local minima and hardly obtain an optimal solution. To address such a problem, in this paper, we propose a novel algorithm namely Riemannian-based discriminant analysis (RDA) for subspace learning. In order to obtain an explicit solution, we transform the traditional Euclidean-based methods to the Riemannian manifold space and use the trust-region method to learn the discriminant projection subspace. We compare the proposed algorithm to existing variants of LDA, as well as the unsupervised tensor decomposition methods on image classification tasks. The numerical results suggest that RDA achieves state-of-the-art performance in classification accuracy.

Wanguang Yin, Youzhi Qu, Zhengming Ma et al.

Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by tensors. However, most of tensor decomposition methods are the linear feature extraction techniques, which are unable to reveal the nonlinear structure within high-dimensional data. To address such problem, a lot of algorithms have been proposed for simultaneously performs linear and non-linear feature extraction. A representative algorithm is the Graph Regularized Non-negative Matrix Factorization (GNMF) for image clustering. However, the normal 2-order graph can only models the pairwise similarity of objects, which cannot sufficiently exploit the complex structures of samples. Thus, we propose a novel method, named Hypergraph Regularized Non-negative Tensor Factorization (HyperNTF), which utilizes hypergraph to encode the complex connections among samples and employs the factor matrix corresponding with last mode of Canonical Polyadic (CP) decomposition as low-dimensional representation. Extensive experiments on synthetic manifolds, real-world image datasets, and EEG signals, demonstrating that HyperNTF outperforms the state-of-the-art methods in terms of dimensionality reduction, clustering, and classification.