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Fast hypergraph regularized nonnegative tensor ring decomposition based on low-rank approximation
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AI
DOI：10.1007/s10489-022-03346-1.png)
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Abstract
En 中文
Tensor ring (TR) decomposition is a highly effective tool for obtaining the low-rank character of multi-way data. Recently, nonnegative tensor ring (NTR) decomposition combined with manifold learning has emerged as a promising approach for exploiting the multi-dimensional structure and extracting features from tensor data. However, an existing method such as graph regularized tensor ring (GNTR) decomposition only models the pair-wise similarities of objects. The graph cannot precisely encode similarity relationships for tensor data with a complex manifold structure. In this paper, to sufficiently utilize the high-dimensional and complex similarities among objects, we add a novel hypergraph regulation into the NTR framework to further enhance feature extraction. Based on this, we propose a hypergraph regularized nonnegative tensor ring decomposition (HGNTR) model. To reduce computational complexity and suppress noise, we apply the low-rank approximation trick to accelerate HGNTR (called LraHGNTR). Our experiment results demonstrate that the proposed HGNTR and LraHGNTR algorithms outperform other state-of-the-art algorithms; additionally, LraHGNTR significantly reduces running time without sacrificing accuracy.
Keywords:
Feature extraction
Low-rank approximation
Hypergraph
Tensor ring decomposition
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