Fast Hypergraph Regularized Nonnegative Tensor Ring Factorization Based on Low-Rank Approximation

TL;DR

This paper introduces a hypergraph regularized nonnegative tensor ring decomposition method, enhanced with low-rank approximation, to better capture complex multi-dimensional similarities in high-dimensional data for improved clustering performance.

Contribution

The paper proposes a novel hypergraph regularized NTR method and its accelerated version using low-rank approximation, addressing limitations of pair-wise similarity modeling and reducing computational costs.

Findings

HGNTR outperforms existing algorithms in clustering accuracy.

LraHGNTR significantly reduces running time.

Both methods achieve higher performance in complex data structures.

Abstract

For the high dimensional data representation, nonnegative tensor ring (NTR) decomposition equipped with manifold learning has become a promising model to exploit the multi-dimensional structure and extract the feature from tensor data. However, the existing methods such as graph regularized tensor ring decomposition (GNTR) only models the pair-wise similarities of objects. For tensor data with complex manifold structure, the graph can not exactly construct similarity relationships. In this paper, in order to effectively utilize the higher-dimensional and complicated similarities among objects, we introduce hypergraph to the framework of NTR to further enhance the feature extraction, upon which a hypergraph regularized nonnegative tensor ring decomposition (HGNTR) method is developed. To reduce the computational complexity and suppress the noise, we apply the low-rank approximation trick to accelerate HGNTR (called LraHGNTR). Our experimental results show that compared with other state-of-the-art algorithms, the proposed HGNTR and LraHGNTR can achieve higher performance in clustering tasks, in addition, LraHGNTR can greatly reduce running time without decreasing accuracy.