148 lines
4.0 KiB
Python
148 lines
4.0 KiB
Python
"""Principal Component Analysis
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Created on Tue Sep 29 20:11:23 2009
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Author: josef-pktd
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TODO : add class for better reuse of results
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"""
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import numpy as np
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def pca(data, keepdim=0, normalize=0, demean=True):
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'''principal components with eigenvector decomposition
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similar to princomp in matlab
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Parameters
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----------
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data : ndarray, 2d
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data with observations by rows and variables in columns
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keepdim : int
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number of eigenvectors to keep
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if keepdim is zero, then all eigenvectors are included
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normalize : bool
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if true, then eigenvectors are normalized by sqrt of eigenvalues
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demean : bool
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if true, then the column mean is subtracted from the data
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Returns
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-------
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xreduced : ndarray, 2d, (nobs, nvars)
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projection of the data x on the kept eigenvectors
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factors : ndarray, 2d, (nobs, nfactors)
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factor matrix, given by np.dot(x, evecs)
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evals : ndarray, 2d, (nobs, nfactors)
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eigenvalues
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evecs : ndarray, 2d, (nobs, nfactors)
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eigenvectors, normalized if normalize is true
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Notes
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-----
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See Also
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--------
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pcasvd : principal component analysis using svd
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'''
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x = np.array(data)
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#make copy so original does not change, maybe not necessary anymore
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if demean:
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m = x.mean(0)
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else:
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m = np.zeros(x.shape[1])
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x -= m
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# Covariance matrix
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xcov = np.cov(x, rowvar=0)
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# Compute eigenvalues and sort into descending order
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evals, evecs = np.linalg.eig(xcov)
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indices = np.argsort(evals)
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indices = indices[::-1]
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evecs = evecs[:,indices]
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evals = evals[indices]
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if keepdim > 0 and keepdim < x.shape[1]:
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evecs = evecs[:,:keepdim]
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evals = evals[:keepdim]
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if normalize:
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#for i in range(shape(evecs)[1]):
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# evecs[:,i] / linalg.norm(evecs[:,i]) * sqrt(evals[i])
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evecs = evecs/np.sqrt(evals) #np.sqrt(np.dot(evecs.T, evecs) * evals)
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# get factor matrix
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#x = np.dot(evecs.T, x.T)
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factors = np.dot(x, evecs)
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# get original data from reduced number of components
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#xreduced = np.dot(evecs.T, factors) + m
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#print x.shape, factors.shape, evecs.shape, m.shape
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xreduced = np.dot(factors, evecs.T) + m
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return xreduced, factors, evals, evecs
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def pcasvd(data, keepdim=0, demean=True):
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'''principal components with svd
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Parameters
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----------
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data : ndarray, 2d
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data with observations by rows and variables in columns
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keepdim : int
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number of eigenvectors to keep
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if keepdim is zero, then all eigenvectors are included
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demean : bool
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if true, then the column mean is subtracted from the data
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Returns
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-------
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xreduced : ndarray, 2d, (nobs, nvars)
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projection of the data x on the kept eigenvectors
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factors : ndarray, 2d, (nobs, nfactors)
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factor matrix, given by np.dot(x, evecs)
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evals : ndarray, 2d, (nobs, nfactors)
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eigenvalues
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evecs : ndarray, 2d, (nobs, nfactors)
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eigenvectors, normalized if normalize is true
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See Also
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--------
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pca : principal component analysis using eigenvector decomposition
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Notes
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-----
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This does not have yet the normalize option of pca.
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'''
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nobs, nvars = data.shape
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#print nobs, nvars, keepdim
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x = np.array(data)
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#make copy so original does not change
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if demean:
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m = x.mean(0)
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else:
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m = 0
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## if keepdim == 0:
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## keepdim = nvars
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## "print reassigning keepdim to max", keepdim
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x -= m
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U, s, v = np.linalg.svd(x.T, full_matrices=1)
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factors = np.dot(U.T, x.T).T #princomps
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if keepdim:
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xreduced = np.dot(factors[:,:keepdim], U[:,:keepdim].T) + m
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else:
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xreduced = data
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keepdim = nvars
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"print reassigning keepdim to max", keepdim
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# s = evals, U = evecs
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# no idea why denominator for s is with minus 1
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evals = s**2/(x.shape[0]-1)
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#print keepdim
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return xreduced, factors[:,:keepdim], evals[:keepdim], U[:,:keepdim] #, v
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__all__ = ['pca', 'pcasvd']
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