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This article will explain in detail what is the use of the PCA algorithm in Matlab. The editor thinks it is very practical, so I share it for you as a reference. I hope you can get something after reading this article.

PCA algorithm is mainly used for dimensionality reduction, that is, to project sample data from high-dimensional space to low-dimensional space, and to represent the original data in low-dimensional space as much as possible. The geometric meaning of PCA can be simply interpreted as:

Dimension 0-PCA: all sample information is projected to a point, so it can not reflect the difference between samples; if you want to use a point to represent all sample data as much as possible, this point must be the mean of the sample. 1D-PCA: equivalent to projecting all the sample information to the straight line of the sample mean; 2D-PCA: regarding the plane distribution of the sample as an elliptical distribution, finding out the major and minor axis direction of the ellipse, and then projecting the sample information onto these two major and short axis directions, that is, two-dimensional PCA. (the projection direction is the major and minor axis direction of the ellipse on the plane); 3D-PCA: the plane distribution of the sample is regarded as an elliptical distribution, and the projection method is the equatorial radius an and b of the ellipsoid, and the polar radius c (along the z axis).

In short, PCA is based on the distribution of input data to re-find orthogonal axes that can better describe this set of data, such as the following picture, for that elliptical distribution, the most convenient axis of this distribution must be the major axis of the ellipse rather than the original x, y axis.

So how to find out the major axis and the minor axis? So linear algebra comes: we need to find out the covariance matrix of this pile of sample data first, and then find the eigenvalue and eigenvector of the covariance matrix. the direction of the eigenvector corresponding to the largest eigenvalue is the direction of the long axis (that is, the principal component), the second largest eigenvalue is the direction of the second principal element, and so on.

To achieve PCA, you can call the Matlab toolbox princomp () function directly, or you can implement the PCA process by yourself. Of course, you can also use the fast PCA algorithm.

(1) method 1: [COEFF SCORE latent] = princomp (X) Parameter description: 1) COEFF is the principal component component, that is, the eigenvector of the sample covariance matrix; 2) SCORE principal component is the representation of sample X in low-dimensional space, that is, the projection of sample X on the principal component COEFF. If you need to reduce k dimensions, only the first k column principal component components need to be taken. 3) latent: a vector containing the eigenvalues of the sample covariance matrix.

Example: suppose there are 8 samples, each sample has 4 features (attributes), use PCA method to reduce dimension (k dimension, k is less than the number of features 4), and extract the features of the first two principal components, that is, the original data is reduced from 4-dimensional space to 2-dimensional space.

%% sample matrix X, there are 8 samples, each sample has 4 features, using PCA dimensionality reduction to extract k main features (k

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