Calculation of feature vectors in Pca Covariance Matrix

Dimensions n> Number of samples m of the matrix in face recognition.

 

Calculate the principal component of matrix A. According to the principle of PCA, it is to calculate the feature values and feature vectors of the covariance matrix a' A of A, But A' A may be relatively large, therefore, according to the size of a' A, the feature values of A' or A' A can be calculated. The feature values of the original Matrix and Its transpose matrix are the same, but the feature vectors are different.

Assume that our data is stored by row. A is a matrix of M * n, n> M, M is the number of samples, and N is a dimension. Then, the covariance matrix should be a', a' A is a matrix of N * n dimensions. This matrix is very large and is not conducive to finding feature values and feature vectors. Therefore, first obtain the feature value of A', which is a matrix of M * m dimension.

By Matrix properties, the feature value of a' is the feature value of a'. The relationship between the feature vectors of a' A and those of a' is derived below.

 

B = A' A; C = ';

C * Y = C * Y-> AA '* Y = C * Y; left by'

A' A * (a' * y) = C * (a' * y) --> B * (a' * y) = C * (a' * y );

Therefore, the feature vector a' * y of B has the same feature value as C.