sparsepca 0.2.3

Sparse Principal Component Analysis in Python

Uses an alternating manifold proximal gradient (A-ManPG) method to find sparse principal component loadings from the given data or covariance matrix.

Requires numpy to be installed.

The GitHub repository can be found here.

Usage

spca(z, lambda1, lambda2, 
     x0=None, y0=None, k=0, gamma=0.5, type=0, 
     maxiter=1e4, tol=1e-5, f_palm=1e5,
	 normalize=True, verbose=False):

Arguments

Name	Type	Description
z	numpy.ndarray	Either the data matrix or sample covariance matrix
lambda1	float list	List of parameters of length n for L1-norm penalty
lambda2	float or numpy.inf	L2-norm penalty term
x0	numpy.ndarray	Initial x-values for the gradient method, default value is the first n right singular vectors
y0	numpy.ndarray	Initial y-values for the gradient method, default value is the first n right singular vectors
k	int	Number of principal components desired, default is 0 (returns min(n-1, p) principal components)
gamma	float	Parameter to control how quickly the step size changes in each iteration, default is 0.5
type	int	If 0, b is expected to be a data matrix, and otherwise b is expected to be a covariance matrix; default is 0
maxiter	int	Maximum number of iterations allowed in the gradient method, default is 1e4
tol	float	Tolerance value required to indicate convergence (calculated as difference between iteration f-values), default is 1e-5
f_palm	float	Upper bound for the F-value to reach convergence, default is 1e5
normalize	bool	Center and normalize rows to Euclidean length 1 if True, default is True
verbose	bool	Function prints progress between iterations if True, default is False

Value

Returns a dictionary with the following key-value pairs:

Key	Value Type	Value
loadings	numpy.ndarray	Loadings of the sparse principal components
f_manpg	float	Final F-value
x	numpy.ndarray	Corresponding ndarray in subproblem to the loadings
iter	int	Total number of iterations executed
sparsity	float	Number of sparse loadings (loadings == 0) divided by number of all loadings
time	float	Execution time in seconds

Authors

Shixiang Chen, Justin Huang, Benjamin Jochem, Shiqian Ma, Lingzhou Xue, and Hui Zou

References

Chen, S., Ma, S., Xue, L., and Zou, H. (2020) "An Alternating Manifold Proximal Gradient Method for Sparse Principal Component Analysis and Sparse Canonical Correlation Analysis" INFORMS Journal on Optimization 2:3, 192-208.

Zou, H., Hastie, T., & Tibshirani, R. (2006). Sparse principal component analysis. Journal of Computational and Graphical Statistics, 15(2), 265-286.

Zou, H., & Xue, L. (2018). A selective overview of sparse principal component analysis. Proceedings of the IEEE, 106(8), 1311-1320.

Example

See sparsepca.py for a more in-depth example.

import numpy as np
from sparsepca import spca_amanpg

k = 4  # columns
d = 500  # dimensions
m = 1000  # sample size
lambda1 = 0.1 * np.ones((k, 1))
lambda2 = 1

np.random.seed(10)
a = np.random.normal(0, 1, size=(m, d))  # generate random normal 1000x500 matrix
fin_sprout = spca_amanpg(a, lambda1, lambda2, k=k)
print(f"Finite: {fin_sprout['iter']} iterations with final value 
		{fin_sprout['f_manpg']}, sparsity {fin_sprout['sparsity']}, 
		timediff {fin_sprout['time']}.")

fin_sprout['loadings']

inf_sprout = spca_amanpg(a, lambda1, np.inf, k=4)
print(f"Infinite: {inf_sprout['iter']} iterations with final value 
		{inf_sprout['f_manpg']}, sparsity {inf_sprout['sparsity']}, 
		timediff {inf_sprout['time']}.")

inf_sprout['loadings']

History

0.2.3

• Doc fixes

0.2.2

• Doc fixes
• PyPI metadata fixes

0.2.1

• Doc fixes

0.2.0

• Initial PyPI release