r_pca.py

'''
Code from https://github.com/dganguli/robust-pca

MIT License

Copyright (c) 2019 Deep Ganguli

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
'''


from __future__ import division, print_function

import numpy as np

try:
    from pylab import plt
except ImportError:
    print('Unable to import pylab. R_pca.plot_fit() will not work.')

try:
    # Python 2: 'xrange' is the iterative version
    range = xrange
except NameError:
    # Python 3: 'range' is iterative - no need for 'xrange'
    pass


class R_pca:

    def __init__(self, D, mu=None, lmbda=None):
        self.D = D
        self.S = np.zeros(self.D.shape)
        self.Y = np.zeros(self.D.shape)

        if mu:
            self.mu = mu
        else:
            self.mu = np.prod(self.D.shape) / (4 * np.linalg.norm(self.D, ord=1))

        self.mu_inv = 1 / self.mu

        if lmbda:
            self.lmbda = lmbda
        else:
            self.lmbda = 1 / np.sqrt(np.max(self.D.shape))

    @staticmethod
    def frobenius_norm(M):
        return np.linalg.norm(M, ord='fro')

    @staticmethod
    def shrink(M, tau):
        return np.sign(M) * np.maximum((np.abs(M) - tau), np.zeros(M.shape))

    def svd_threshold(self, M, tau):
        U, S, V = np.linalg.svd(M, full_matrices=False)
        return np.dot(U, np.dot(np.diag(self.shrink(S, tau)), V))

    def fit(self, tol=None, max_iter=1000, iter_print=100):
        iter = 0
        err = np.Inf
        Sk = self.S
        Yk = self.Y
        Lk = np.zeros(self.D.shape)

        if tol:
            _tol = tol
        else:
            _tol = 1E-7 * self.frobenius_norm(self.D)

        #this loop implements the principal component pursuit (PCP) algorithm
        #located in the table on page 29 of https://arxiv.org/pdf/0912.3599.pdf
        while (err > _tol) and iter < max_iter:
            Lk = self.svd_threshold(
                self.D - Sk + self.mu_inv * Yk, self.mu_inv)                            #this line implements step 3
            Sk = self.shrink(
                self.D - Lk + (self.mu_inv * Yk), self.mu_inv * self.lmbda)             #this line implements step 4
            Yk = Yk + self.mu * (self.D - Lk - Sk)                                      #this line implements step 5
            err = self.frobenius_norm(self.D - Lk - Sk)
            iter += 1
            if (iter % iter_print) == 0 or iter == 1 or iter > max_iter or err <= _tol:
                print('iteration: {0}, error: {1}'.format(iter, err))

        self.L = Lk
        self.S = Sk
        return Lk, Sk

    def plot_fit(self, size=None, tol=0.1, axis_on=True):

        n, d = self.D.shape

        if size:
            nrows, ncols = size
        else:
            sq = np.ceil(np.sqrt(n))
            nrows = int(sq)
            ncols = int(sq)

        ymin = np.nanmin(self.D)
        ymax = np.nanmax(self.D)
        print('ymin: {0}, ymax: {1}'.format(ymin, ymax))

        numplots = np.min([n, nrows * ncols])
        plt.figure()

        for n in range(numplots):
            plt.subplot(nrows, ncols, n + 1)
            plt.ylim((ymin - tol, ymax + tol))
            plt.plot(self.L[n, :] + self.S[n, :], 'r')
            plt.plot(self.L[n, :], 'b')
            if not axis_on:
                plt.axis('off')