Manually Calculate Principal Component Analysis

PCA.py

## PCA

There is no pca() function in NumPy, but we can easily calculate the Principal Component Analysis step-by-step using NumPy functions.
The example below defines a small 3×2 matrix, centers the data in the matrix, calculates the covariance matrix of the centered data, and then the eigendecomposition of the covariance matrix. The eigenvectors and eigenvalues are taken as the principal components and singular values and used to project the original data.


    from numpy import array
    from numpy import mean
    from numpy import cov
    from numpy.linalg import eig

    # define a matrix
    A = array([[1, 2], [3, 4], [5, 6]])
    print(A)
    # calculate the mean of each column
    M = mean(A.T, axis=1)
    print(M)
    # center columns by subtracting column means
    C = A - M
    print(C)
    # calculate covariance matrix of centered matrix
    V = cov(C.T)
    print(V)
    # eigendecomposition of covariance matrix
    values, vectors = eig(V)
    print(vectors)
    print(values)
    # project data
    P = vectors.T.dot(C.T)
    print(P.T)