HyperNTF: A Hypergraph Regularized Nonnegative Tensor Factorization for Dimensionality Reduction

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.