---
title: "A Convengent Solution to Tensor Subspace Learning"
authors:
  - "Huan Wang"
  - "Shuicheng Yan"
  - "Thomas S. Huang"
  - "Xiaoou Tang"
doi: ""
url: "https://ijcai.org/proceedings/2007/100"
pdf: "https://ijcai.org/proceedings/2007/0100.pdf"
venue: "Proceedings of the Twentieth International Joint Conference on Artificial Intelligence"
year: 2007
pages: "629-633"
track: ""
keywords:
---

# A Convengent Solution to Tensor Subspace Learning

Huan Wang, Shuicheng Yan, Thomas S. Huang, Xiaoou Tang

*Proceedings of the Twentieth International Joint Conference on Artificial Intelligence*, pages 629-633.

## Abstract

Recently, substantial efforts have been devoted to the subspace learning techniques based on tensor representation, such as 2DLDA, DATER and Tensor Subspace Analysis (TSA). In this context, a vital yet unsolved problem is that the computational convergency of these iterative algorithms is not guaranteed. In this work, we present a novel solution procedure for general tensor-based subspace learning, followed by a detailed convergency proof of the solution projection matrices and the objective function value. Extensive experiments on real-world databases verify the high convergence speed of the proposed procedure, as well as its superiority in classification capability over traditional solution procedures.