HyperNTF: A Hypergraph Regularized Nonnegative Tensor Factorization for Dimensionality Reduction

• URL: http://arxiv.org/abs/2101.06827v2
• Date: Tue, 26 Jan 2021 16:08:29 GMT
• Title: HyperNTF: A Hypergraph Regularized Nonnegative Tensor Factorization for Dimensionality Reduction
• Authors: Wanguang Yin, Zhengming Ma, Quanying Liu
• Abstract summary: We propose a novel method, called Hypergraph Regularized Nonnegative Factorization (HyperNTF) HyperNTF can preserve nonnegativity in tensor factorization, and uncover the higher-order relationship among the nearest neighborhoods. Experiments show that HyperNTF robustly outperforms state-of-the-art algorithms in clustering analysis.
• Score: 2.1485350418225244
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Most methods for dimensionality reduction are based on either tensor representation or local geometry learning. However, the tensor-based methods severely rely on the assumption of global and multilinear structures in high-dimensional data; and the manifold learning methods suffer from the out-of-sample problem. In this paper, bridging the tensor decomposition and manifold learning, we propose a novel method, called Hypergraph Regularized Nonnegative Tensor Factorization (HyperNTF). HyperNTF can preserve nonnegativity in tensor factorization, and uncover the higher-order relationship among the nearest neighborhoods. Clustering analysis with HyperNTF has low computation and storage costs. The experiments on four synthetic data show a desirable property of hypergraph in uncovering the high-order correlation to unfold the curved manifolds. Moreover, the numerical experiments on six real datasets suggest that HyperNTF robustly outperforms state-of-the-art algorithms in clustering analysis.

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