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典型相关分析的最小二乘公式

A Least Squares Formulation for Canonical Correlation Analysis
课程网址: http://videolectures.net/icml08_ji_alsf/  
主讲教师: Shuiwang Ji
开课单位: 华盛顿州立大学
开课时间: 2008-08-29
课程语种: 英语
中文简介:
典型相关分析（CCA）是用于找到两组多维变量之间的相关性的众所周知的技术。它将两组变量投影到一个较低维度的空间中，在这些空间中它们最大程度地相关。 CCA通常用于监督维数减少，其中多维变量之一是从类标签导出的。已经表明，CCA可以被公式化为二元类情况中的最小二乘问题。然而，他们在更一般的环境中的关系仍不清楚。在本文中，我们表明，在温和的条件下，往往容纳高维数据，多标签分类中的CCA可以表示为最小二乘问题。基于这种等价关系，我们提出了几种CCA扩展，包括使用1范数正则化的稀疏CCA。多标签数据集上的实验证实了已建立的等价关系。结果还证明了提议的CCA扩展的有效性
课程简介: Canonical Correlation Analysis (CCA) is a well-known technique for finding the correlations between two sets of multi-dimensional variables. It projects both sets of variables into a lower-dimensional space in which they are maximally correlated. CCA is commonly applied for supervised dimensionality reduction, in which one of the multi-dimensional variables is derived from the class label. It has been shown that CCA can be formulated as a least squares problem in the binary-class case. However, their relationship in the more general setting remains unclear. In this paper, we show that, under a mild condition which tends to hold for high-dimensional data, CCA in multi-label classifications can be formulated as a least squares problem. Based on this equivalence relationship, we propose several CCA extensions including sparse CCA using 1-norm regularization. Experiments on multi-label data sets confirm the established equivalence relationship. Results also demonstrate the effectiveness of the proposed CCA extensions
关 键 词: 典型相关分析; 多维变量; 最小二乘
课程来源: 视频讲座网
最后编审: 2019-04-19：lxf
阅读次数: 137

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