Summary of PCA Learning

Source: Internet
Author: User

1. PCA Holistic Thinking

Pca,principle componet analysis, PCA, mainly used for data dimensionality reduction. By calculating the eigenvalues and eigenvectors of the covariance matrix of a given data set, it obtains the most critical direction of the dataset (the projection variance of the dataset is the largest in this direction, which can keep the most information), and the first k-dimensional space is selected from the key direction, in which the original data is re-represented to achieve the purpose of dimensionality reduction.

2. Derivation process


3. Basic steps of the algorithm

Input: DataSet X (DxN)

Output: Eigenvalues E (Dx1), Eigenvector V (DxD, eigenvectors stored in columns), sample mean for each dimension (DX1)

Procedure: 1. Calculates the covariance matrix C for X

2. Find the eigenvalues E and eigenvectors V of C and arrange them in descending order of eigenvalues

3. Select the first k eigenvector (i.e. the first k column) of V to form the matrix P (DXK)

4. The X element x is projected on the front k eigenvectors of P, resulting in XX (k,1), resulting in a projection matrix Z (KXN) of X on K eigenvectors.

5. Reconstruct xx with Z and compare with X to calculate the reconstruction error

4. MATLAB implementation of PCA

[V, E] = Eig (cov (X ')) [E index] = sort (Diag (e), ' descend '); v = V (:, index); Meanx = mean (X ') '; P=v (:, [1:k]) [r,c] = size (X); Y = P ' * (X-repmat (meanx,1,c)); [R,c] = size (Y); XX = P * Y + repmat (Meanx, 1, c);

5. PCA main Application

Face recognition, handwriting recognition with relatively more.

a fairly good copy of PCA profile:

Summary of PCA Learning

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