典型相关分析 [英] Cannonical Correlation Analysis

问题描述

我刚刚开始在Matlab中使用CCA.我有两个维度为60x1920和60x1536的向量X和Y，样本数量为60，不同向量集合中的变量分别为1920和1536.我想知道CCA将它们缩小到子空间，然后进行特征匹配.

I have just started working using CCA in Matlab. I have two vectors X and Y of dimension 60x1920 and 60x1536 with the number of samples being 60 and variables in the different set of vectors being 1920 and 1536 respectively. I want to know do CCA for reducing them to the subspace and then do feature matching.

我正在使用此命令.

%% DO CCA
[A,B,r,U,V] = canoncorr(X,Y);

我得到的输出是这样:

  Name         Size             Bytes  Class     Attributes

  A         1920x58            890880  double              
  B         1536x58            712704  double              
  U           60x58             27840  double              
  V           60x58             27840  double              
  r            1x58               464  double       

谁能告诉我这些变量的含义.我已经浏览了几次文档，但仍不清楚.据我了解，CCA发现了两个线性投影矩阵Wx和Wy，使得X和Y在Wx和Wy上的投影具有最大的相关性.

Can anyone please tell me what these variables mean. I have gone over the documentation several times and still is unclear about them. As I understand CCA finds two linear projection matrices Wx and Wy such that the projection of X and Y on Wx and Wy are maximally correlated.

1)谁能告诉我以下哪些矩阵?

1) Could anyone please tell me which of the following matrices are these?

2)另外，如何在CCA的学习子空间中找到投影矢量?

2) Also how can I find the projected vectors in the learned subspace of CCA?

任何帮助将不胜感激.预先感谢.

Any help will be appreciated. Thanks in advance.

推荐答案

据我了解，以X和Y为原始数据矩阵，A和B是执行系数的集合改变基础以最大程度地关联您的原始数据.您的数据在新的基准中表示为矩阵U和V.

As I understand it, with X and Y being your original data matrices, A and B are the sets of coefficients that perform a change of basis to maximally correlate your original data. Your data is represented in the new bases as the matrices U and V.

所以回答您的问题:

1. 您要查找的投影矩阵为A和B，因为它们将X和Y转换为新的空间.

1. The projection matrices you are looking for would be A and B since they transform X and Y into the new space.

X和Y在新空间中的最终投影分别为U和V. (r向量表示U和V之间的相关矩阵的项，它是对角矩阵.)

The resulting projections of X and Y into the new space would be U and V, respectively. (The r vector represents the entries of the correlation matrix between U and V, which is a diagonal matrix.)

MATLAB文档表示，可以使用以下公式完成此转换，其中N是观察数:

The The MATLAB documentation says this transformation can be done with the following formulae, where N is the number of observations:

U = (X-repmat(mean(X),N,1))*A
V = (Y-repmat(mean(Y),N,1))*B

此页面很好地列出了流程，因此您可以看到每个系数意味着在转型过程中.

This page lays out the process nicely so you can see what each coefficient means in the transformation process.

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