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 simultane-ously performs linear and non-linear feature extraction. A representative algorithm is the Graph Regularized Nonnegative Matrix Factorization (GNMF) for image clustering. However, the normal 2 -order graph can only model the pairwise similarity of objects, which cannot sufficiently exploit the com-plex structures of samples. Thus, we propose a novel method, named Hypergraph Regularized Nonnegative Tensor Factorization (HyperNTF), which utilizes hypergraph to model the complex connec-tions among samples and employs the factor matrix corresponding with last mode of Canonical Polyadic (CP) decomposition as low-dimensional representation of original data. Extensive experiments on syn-thetic 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.(c) 2022 Elsevier B.V. All rights reserved.