计算机科学与探索 ›› 2010, Vol. 4 ›› Issue (7): 654-661.DOI: 10.3778/j.issn.1673-9418.2010.07.009

• 学术研究 • 上一篇    下一篇

稀疏低秩双线性判别模型及其应用*

蒋 琳+;谭晓阳;刘 俊

  

  1. 南京航空航天大学 信息科学与技术学院, 南京 210016
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2010-07-14 发布日期:2010-07-14
  • 通讯作者: 蒋 琳

Sparse Low Rank Bilinear Discriminative Model and its Application*

JIANG Lin+; TAN Xiaoyang; LIU Jun

  

  1. College of Computer Science & Technology, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China
  • Received:1900-01-01 Revised:1900-01-01 Online:2010-07-14 Published:2010-07-14
  • Contact: JIANG Lin

摘要: “高维度小样本”问题是模式识别应用中的主要障碍之一。跨越这一障碍的有效方法之一是采用参数矩阵的低秩逼近, 目的是控制模型复杂度。常用的低秩逼近方法需要预先指定目标矩阵秩的大小(如主成分分析)。提出了一种新的基于稀疏约束的低秩判别模型, 此模型通过对目标参数进行矩阵分解, 然后分别对子成分施加低秩(稀疏)约束, 从而达到低秩逼近的目的。进一步将这一思想嵌入一个双边判别模型, 并用坐标下降法对目标函数进行优化, 使得算法在低秩逼近的同时还有效利用了输入数据的空间特性, 从而得到更好的推广性能。其有效性在一个安全生物识别应用上得到了验证。

关键词: 稀疏低秩逼近, 双边判别框架, 主成分分析

Abstract: “High dimensionality and small size samples” is widely encountered in many real world machine learning applications. Low rank approximation to parametric matrix has recently been proven to be an effective method to control the complexity of models. Most of the previous low rank methods are required to specify the target rank by hand beforehand (e.g., principal component analysis), however, imposing the sparsity constraints on the parametric matrix can avoid this. In particular, under a bilinear discriminative framework, decomposing the parametric matrix and simultaneously constraining their ranks with the sparsity-inducing regularization will perform well. The result-ing problem can be efficiently solved with coordinate descent. This method is able to take the spatial information of structured data into account, leading to improved generalization capability. The feasibility and effectiveness of the proposed method is demonstrated on a security biometric application.

Key words: sparse low rank approximation, bilinear discriminative framework, principal component analysis

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