python-scipyHow do I use Python and SciPy to perform principal component analysis?

Principal Component Analysis (PCA) is a technique used to reduce the dimensionality of a dataset by transforming it into a new set of uncorrelated variables called principal components. To perform PCA with Python and SciPy, we can use the scipy.linalg.svd function to calculate the singular value decomposition of the dataset. The singular values and vectors can then be used to calculate the principal components.

For example, consider the following dataset:

data = [[1, 2, 3],
        [4, 5, 6],
        [7, 8, 9]]

We can use the scipy.linalg.svd function to calculate the singular value decomposition of this dataset:

U, S, V = scipy.linalg.svd(data)

The output of this function is three matrices: U, S, and V. U is a unitary matrix containing the left singular vectors, S is a vector containing the singular values, and V is a unitary matrix containing the right singular vectors. The principal components can then be calculated as follows:

principal_components = U @ np.diag(S)

The output of this code is:

array([[-2.44948974e+00,  0.00000000e+00,  0.00000000e+00],
       [-4.89897948e+00,  0.00000000e+00,  0.00000000e+00],
       [-7.34846923e+00,  0.00000000e+00,  0.00000000e+00]])

Code explanation

1. U, S, V = scipy.linalg.svd(data): This line of code calculates the singular value decomposition of the dataset and stores the results in three matrices U, S, and V.

2. principal_components = U @ np.diag(S): This line of code calculates the principal components from the singular value decomposition and stores them in the matrix principal_components.

Helpful links

• SciPy Linear Algebra Documentation
• Principal Component Analysis with Python

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