Experimental Analysis of Legendre Decomposition in Machine Learning

2020/08/12 by Jianye Pang, Pang, Jianye, Kai Yi +5 · 1 citation
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Computational Physics and Python Applications #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2008.05095

openalex publication_date 2020/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this technical report, we analyze Legendre decomposition for non-negative tensor in theory and application. In theory, the properties of dual parameters and dually flat manifold in Legendre decomposition are reviewed, and the process of tensor projection and parameter updating is analyzed. In application, a series of verification experiments and clustering experiments with parameters on submanifold were carried out, hoping to find an effective lower dimensional representation of the input tensor. The experimental results show that the parameters on submanifold have no ability to be directly used as low-rank representations. Combined with analysis, we connect Legendre decomposition with neural networks and low-rank representation applications, and put forward some promising prospects.

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