1131 lines
39 KiB
Python
1131 lines
39 KiB
Python
""" Dictionary learning
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"""
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# Author: Vlad Niculae, Gael Varoquaux, Alexandre Gramfort
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# License: BSD
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import time
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import sys
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import itertools
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from math import sqrt, floor, ceil
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import numpy as np
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from scipy import linalg
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from numpy.lib.stride_tricks import as_strided
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from ..base import BaseEstimator, TransformerMixin
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from ..externals.joblib import Parallel, delayed, cpu_count
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from ..utils import array2d, check_random_state, gen_even_slices
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from ..utils.extmath import randomized_svd
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from ..linear_model import Lasso, orthogonal_mp_gram, LassoLars, Lars
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def _sparse_encode(X, dictionary, gram, cov=None, algorithm='lasso_lars',
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regularization=None, copy_cov=True,
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init=None, max_iter=1000):
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"""Generic sparse coding
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Each column of the result is the solution to a Lasso problem.
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Parameters
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----------
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X: array of shape (n_samples, n_features)
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Data matrix.
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dictionary: array of shape (n_atoms, n_features)
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The dictionary matrix against which to solve the sparse coding of
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the data. Some of the algorithms assume normalized rows.
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gram: None | array, shape=(n_atoms, n_atoms)
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Precomputed Gram matrix, dictionary * dictionary'
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gram can be None if method is 'threshold'.
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cov: array, shape=(n_atoms, n_samples)
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Precomputed covariance, dictionary * X'
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algorithm: {'lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'}
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lars: uses the least angle regression method (linear_model.lars_path)
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lasso_lars: uses Lars to compute the Lasso solution
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lasso_cd: uses the coordinate descent method to compute the
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Lasso solution (linear_model.Lasso). lasso_lars will be faster if
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the estimated components are sparse.
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omp: uses orthogonal matching pursuit to estimate the sparse solution
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threshold: squashes to zero all coefficients less than regularization
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from the projection dictionary * data'
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regularization : int | float
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The regularization parameter. It corresponds to alpha when
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algorithm is 'lasso_lars', 'lasso_cd' or 'threshold'.
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Otherwise it corresponds to n_nonzero_coefs.
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init: array of shape (n_samples, n_atoms)
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Initialization value of the sparse code. Only used if
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`algorithm='lasso_cd'`.
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max_iter: int, 1000 by default
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Maximum number of iterations to perform if `algorithm='lasso_cd'`.
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copy_cov: boolean, optional
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Whether to copy the precomputed covariance matrix; if False, it may be
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overwritten.
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Returns
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-------
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code: array of shape (n_components, n_features)
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The sparse codes
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See also
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--------
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sklearn.linear_model.lars_path
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sklearn.linear_model.orthogonal_mp
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sklearn.linear_model.Lasso
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SparseCoder
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"""
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if X.ndim == 1:
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X = X[:, np.newaxis]
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n_samples, n_features = X.shape
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if cov is None and algorithm != 'lasso_cd':
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# overwriting cov is safe
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copy_cov = False
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cov = np.dot(dictionary, X.T)
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if algorithm == 'lasso_lars':
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alpha = float(regularization) / n_features # account for scaling
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try:
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err_mgt = np.seterr(all='ignore')
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lasso_lars = LassoLars(alpha=alpha, fit_intercept=False,
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verbose=False, normalize=False, precompute=gram,
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fit_path=False)
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lasso_lars.fit(dictionary.T, X.T, Xy=cov)
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new_code = lasso_lars.coef_
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finally:
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np.seterr(**err_mgt)
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elif algorithm == 'lasso_cd':
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alpha = float(regularization) / n_features # account for scaling
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clf = Lasso(alpha=alpha, fit_intercept=False, precompute=gram,
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max_iter=max_iter)
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clf.fit(dictionary.T, X.T, Xy=cov, coef_init=init)
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new_code = clf.coef_
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elif algorithm == 'lars':
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try:
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err_mgt = np.seterr(all='ignore')
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lars = Lars(fit_intercept=False, verbose=False, normalize=False,
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precompute=gram, n_nonzero_coefs=int(regularization),
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fit_path=False)
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lars.fit(dictionary.T, X.T, Xy=cov)
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new_code = lars.coef_
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finally:
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np.seterr(**err_mgt)
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elif algorithm == 'threshold':
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new_code = ((np.sign(cov) *
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np.maximum(np.abs(cov) - regularization, 0)).T)
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elif algorithm == 'omp':
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norms_squared = np.sum((X ** 2), axis=1)
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new_code = orthogonal_mp_gram(gram, cov, regularization, None,
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norms_squared, copy_Xy=copy_cov).T
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else:
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raise NotImplemented('Sparse coding method %s not implemented' %
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algorithm)
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return new_code
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# XXX : could be moved to the linear_model module
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def sparse_encode(X, dictionary, gram=None, cov=None, algorithm='lasso_lars',
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n_nonzero_coefs=None, alpha=None, copy_cov=True, init=None,
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max_iter=1000, n_jobs=1):
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"""Sparse coding
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Each row of the result is the solution to a sparse coding problem.
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The goal is to find a sparse array `code` such that::
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X ~= code * dictionary
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Parameters
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----------
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X: array of shape (n_samples, n_features)
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Data matrix
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dictionary: array of shape (n_atoms, n_features)
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The dictionary matrix against which to solve the sparse coding of
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the data. Some of the algorithms assume normalized rows for meaningful
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output.
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gram: array, shape=(n_atoms, n_atoms)
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Precomputed Gram matrix, dictionary * dictionary'
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cov: array, shape=(n_atoms, n_samples)
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Precomputed covariance, dictionary' * X
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algorithm: {'lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'}
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lars: uses the least angle regression method (linear_model.lars_path)
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lasso_lars: uses Lars to compute the Lasso solution
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lasso_cd: uses the coordinate descent method to compute the
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Lasso solution (linear_model.Lasso). lasso_lars will be faster if
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the estimated components are sparse.
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omp: uses orthogonal matching pursuit to estimate the sparse solution
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threshold: squashes to zero all coefficients less than alpha from
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the projection dictionary * X'
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n_nonzero_coefs: int, 0.1 * n_features by default
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Number of nonzero coefficients to target in each column of the
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solution. This is only used by `algorithm='lars'` and `algorithm='omp'`
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and is overridden by `alpha` in the `omp` case.
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alpha: float, 1. by default
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If `algorithm='lasso_lars'` or `algorithm='lasso_cd'`, `alpha` is the
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penalty applied to the L1 norm.
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If `algorithm='threhold'`, `alpha` is the absolute value of the
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threshold below which coefficients will be squashed to zero.
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If `algorithm='omp'`, `alpha` is the tolerance parameter: the value of
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the reconstruction error targeted. In this case, it overrides
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`n_nonzero_coefs`.
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init: array of shape (n_samples, n_atoms)
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Initialization value of the sparse codes. Only used if
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`algorithm='lasso_cd'`.
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max_iter: int, 1000 by default
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Maximum number of iterations to perform if `algorithm='lasso_cd'`.
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copy_cov: boolean, optional
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Whether to copy the precomputed covariance matrix; if False, it may be
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overwritten.
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n_jobs: int, optional
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Number of parallel jobs to run.
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Returns
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-------
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code: array of shape (n_samples, n_atoms)
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The sparse codes
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See also
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--------
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sklearn.linear_model.lars_path
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sklearn.linear_model.orthogonal_mp
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sklearn.linear_model.Lasso
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SparseCoder
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"""
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dictionary = array2d(dictionary)
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X = array2d(X)
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n_samples, n_features = X.shape
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n_atoms = dictionary.shape[0]
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if gram is None and algorithm != 'threshold':
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gram = np.dot(dictionary, dictionary.T)
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if cov is None:
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copy_cov = False
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cov = np.dot(dictionary, X.T)
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if algorithm in ('lars', 'omp'):
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regularization = n_nonzero_coefs
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if regularization is None:
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regularization = max(n_features / 10, 1)
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else:
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regularization = alpha
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if regularization is None:
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regularization = 1.
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if n_jobs == 1 or algorithm == 'threshold':
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return _sparse_encode(X, dictionary, gram, cov=cov,
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algorithm=algorithm, regularization=regularization,
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copy_cov=copy_cov, init=init, max_iter=max_iter)
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# Enter parallel code block
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code = np.empty((n_samples, n_atoms))
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slices = list(gen_even_slices(n_samples, n_jobs))
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if cov is None:
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# We cannot keep cov to None: it needs to be slicable
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class StupidSliceable(object):
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def __getitem__(self, anything):
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return None
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cov = StupidSliceable()
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code_views = Parallel(n_jobs=n_jobs)(
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delayed(_sparse_encode)(X[this_slice], dictionary, gram,
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cov[:, this_slice], algorithm,
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regularization=regularization, copy_cov=copy_cov,
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init=init[this_slice] if init is not None else None,
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max_iter=max_iter)
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for this_slice in slices)
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for this_slice, this_view in zip(slices, code_views):
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code[this_slice] = this_view
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return code
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def _update_dict(dictionary, Y, code, verbose=False, return_r2=False,
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random_state=None):
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"""Update the dense dictionary factor in place.
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Parameters
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----------
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dictionary: array of shape (n_features, n_atoms)
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Value of the dictionary at the previous iteration.
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Y: array of shape (n_features, n_samples)
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Data matrix.
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code: array of shape (n_atoms, n_samples)
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Sparse coding of the data against which to optimize the dictionary.
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verbose:
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Degree of output the procedure will print.
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return_r2: bool
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Whether to compute and return the residual sum of squares corresponding
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to the computed solution.
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random_state: int or RandomState
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Pseudo number generator state used for random sampling.
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Returns
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-------
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dictionary: array of shape (n_features, n_atoms)
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Updated dictionary.
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"""
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n_atoms = len(code)
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n_samples = Y.shape[0]
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random_state = check_random_state(random_state)
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# Residuals, computed 'in-place' for efficiency
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R = -np.dot(dictionary, code)
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R += Y
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R = np.asfortranarray(R)
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ger, = linalg.get_blas_funcs(('ger',), (dictionary, code))
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for k in xrange(n_atoms):
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# R <- 1.0 * U_k * V_k^T + R
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R = ger(1.0, dictionary[:, k], code[k, :], a=R, overwrite_a=True)
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dictionary[:, k] = np.dot(R, code[k, :].T)
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# Scale k'th atom
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atom_norm_square = np.dot(dictionary[:, k], dictionary[:, k])
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if atom_norm_square < 1e-20:
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if verbose == 1:
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sys.stdout.write("+")
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sys.stdout.flush()
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elif verbose:
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print "Adding new random atom"
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dictionary[:, k] = random_state.randn(n_samples)
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# Setting corresponding coefs to 0
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code[k, :] = 0.0
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dictionary[:, k] /= sqrt(np.dot(dictionary[:, k],
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dictionary[:, k]))
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else:
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dictionary[:, k] /= sqrt(atom_norm_square)
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# R <- -1.0 * U_k * V_k^T + R
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R = ger(-1.0, dictionary[:, k], code[k, :], a=R, overwrite_a=True)
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if return_r2:
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R **= 2
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# R is fortran-ordered. For numpy version < 1.6, sum does not
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# follow the quick striding first, and is thus inefficient on
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# fortran ordered data. We take a flat view of the data with no
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# striding
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R = as_strided(R, shape=(R.size, ), strides=(R.dtype.itemsize,))
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R = np.sum(R)
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return dictionary, R
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return dictionary
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def dict_learning(X, n_atoms, alpha, max_iter=100, tol=1e-8,
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method='lars', n_jobs=1, dict_init=None, code_init=None,
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callback=None, verbose=False, random_state=None):
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"""Solves a dictionary learning matrix factorization problem.
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Finds the best dictionary and the corresponding sparse code for
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approximating the data matrix X by solving::
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(U^*, V^*) = argmin 0.5 || X - U V ||_2^2 + alpha * || U ||_1
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(U,V)
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with || V_k ||_2 = 1 for all 0 <= k < n_atoms
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where V is the dictionary and U is the sparse code.
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Parameters
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----------
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X: array of shape (n_samples, n_features)
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Data matrix.
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n_atoms: int,
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Number of dictionary atoms to extract.
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alpha: int,
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Sparsity controlling parameter.
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max_iter: int,
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Maximum number of iterations to perform.
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tol: float,
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Tolerance for the stopping condition.
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method: {'lars', 'cd'}
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lars: uses the least angle regression method to solve the lasso problem
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(linear_model.lars_path)
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cd: uses the coordinate descent method to compute the
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Lasso solution (linear_model.Lasso). Lars will be faster if
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the estimated components are sparse.
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n_jobs: int,
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Number of parallel jobs to run, or -1 to autodetect.
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dict_init: array of shape (n_atoms, n_features),
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Initial value for the dictionary for warm restart scenarios.
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code_init: array of shape (n_samples, n_atoms),
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Initial value for the sparse code for warm restart scenarios.
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callback:
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Callable that gets invoked every five iterations.
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verbose:
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Degree of output the procedure will print.
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random_state: int or RandomState
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Pseudo number generator state used for random sampling.
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Returns
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-------
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code: array of shape (n_samples, n_atoms)
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The sparse code factor in the matrix factorization.
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dictionary: array of shape (n_atoms, n_features),
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The dictionary factor in the matrix factorization.
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errors: array
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Vector of errors at each iteration.
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See also
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--------
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dict_learning_online
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DictionaryLearning
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MiniBatchDictionaryLearning
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SparsePCA
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MiniBatchSparsePCA
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"""
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if method not in ('lars', 'cd'):
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raise ValueError('Coding method not supported as a fit algorithm.')
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method = 'lasso_' + method
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t0 = time.time()
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# Avoid integer division problems
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alpha = float(alpha)
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random_state = check_random_state(random_state)
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if n_jobs == -1:
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n_jobs = cpu_count()
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# Init the code and the dictionary with SVD of Y
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if code_init is not None and dict_init is not None:
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code = np.array(code_init, order='F')
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# Don't copy V, it will happen below
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dictionary = dict_init
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else:
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code, S, dictionary = linalg.svd(X, full_matrices=False)
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dictionary = S[:, np.newaxis] * dictionary
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r = len(dictionary)
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if n_atoms <= r: # True even if n_atoms=None
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code = code[:, :n_atoms]
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dictionary = dictionary[:n_atoms, :]
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else:
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code = np.c_[code, np.zeros((len(code), n_atoms - r))]
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dictionary = np.r_[dictionary,
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np.zeros((n_atoms - r, dictionary.shape[1]))]
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# Fortran-order dict, as we are going to access its row vectors
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dictionary = np.array(dictionary, order='F')
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residuals = 0
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errors = []
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current_cost = np.nan
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if verbose == 1:
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print '[dict_learning]',
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for ii in xrange(max_iter):
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dt = (time.time() - t0)
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if verbose == 1:
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sys.stdout.write(".")
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sys.stdout.flush()
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elif verbose:
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print ("Iteration % 3i "
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"(elapsed time: % 3is, % 4.1fmn, current cost % 7.3f)" %
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(ii, dt, dt / 60, current_cost))
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# Update code
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code = sparse_encode(X, dictionary, algorithm=method, alpha=alpha,
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init=code, n_jobs=n_jobs)
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# Update dictionary
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dictionary, residuals = _update_dict(dictionary.T, X.T, code.T,
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verbose=verbose, return_r2=True,
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random_state=random_state)
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dictionary = dictionary.T
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# Cost function
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current_cost = 0.5 * residuals + alpha * np.sum(np.abs(code))
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errors.append(current_cost)
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if ii > 0:
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dE = errors[-2] - errors[-1]
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# assert(dE >= -tol * errors[-1])
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if dE < tol * errors[-1]:
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if verbose == 1:
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# A line return
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print ""
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elif verbose:
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print "--- Convergence reached after %d iterations" % ii
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break
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if ii % 5 == 0 and callback is not None:
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callback(locals())
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return code, dictionary, errors
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def dict_learning_online(X, n_atoms, alpha, n_iter=100, return_code=True,
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dict_init=None, callback=None, chunk_size=3,
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verbose=False, shuffle=True, n_jobs=1,
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method='lars', iter_offset=0, random_state=None):
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"""Solves a dictionary learning matrix factorization problem online.
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Finds the best dictionary and the corresponding sparse code for
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approximating the data matrix X by solving::
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(U^*, V^*) = argmin 0.5 || X - U V ||_2^2 + alpha * || U ||_1
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(U,V)
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with || V_k ||_2 = 1 for all 0 <= k < n_atoms
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where V is the dictionary and U is the sparse code. This is
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accomplished by repeatedly iterating over mini-batches by slicing
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the input data.
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Parameters
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----------
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X: array of shape (n_samples, n_features)
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data matrix
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n_atoms: int,
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number of dictionary atoms to extract
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alpha: int,
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sparsity controlling parameter
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n_iter: int,
|
|
number of iterations to perform
|
|
|
|
return_code: boolean,
|
|
whether to also return the code U or just the dictionary V
|
|
|
|
dict_init: array of shape (n_atoms, n_features),
|
|
initial value for the dictionary for warm restart scenarios
|
|
|
|
callback:
|
|
callable that gets invoked every five iterations
|
|
|
|
chunk_size: int,
|
|
the number of samples to take in each batch
|
|
|
|
verbose:
|
|
degree of output the procedure will print
|
|
|
|
shuffle: boolean,
|
|
whether to shuffle the data before splitting it in batches
|
|
|
|
n_jobs: int,
|
|
number of parallel jobs to run, or -1 to autodetect.
|
|
|
|
method: {'lars', 'cd'}
|
|
lars: uses the least angle regression method to solve the lasso problem
|
|
(linear_model.lars_path)
|
|
cd: uses the coordinate descent method to compute the
|
|
Lasso solution (linear_model.Lasso). Lars will be faster if
|
|
the estimated components are sparse.
|
|
|
|
iter_offset: int, default 0
|
|
number of previous iterations completed on the dictionary used for
|
|
initialization
|
|
|
|
random_state: int or RandomState
|
|
Pseudo number generator state used for random sampling.
|
|
|
|
Returns
|
|
-------
|
|
code: array of shape (n_samples, n_atoms),
|
|
the sparse code (only returned if `return_code=True`)
|
|
|
|
dictionary: array of shape (n_atoms, n_features),
|
|
the solutions to the dictionary learning problem
|
|
|
|
See also
|
|
--------
|
|
dict_learning
|
|
DictionaryLearning
|
|
MiniBatchDictionaryLearning
|
|
SparsePCA
|
|
MiniBatchSparsePCA
|
|
|
|
"""
|
|
if method not in ('lars', 'cd'):
|
|
raise ValueError('Coding method not supported as a fit algorithm.')
|
|
method = 'lasso_' + method
|
|
|
|
t0 = time.time()
|
|
n_samples, n_features = X.shape
|
|
# Avoid integer division problems
|
|
alpha = float(alpha)
|
|
random_state = check_random_state(random_state)
|
|
|
|
if n_jobs == -1:
|
|
n_jobs = cpu_count()
|
|
|
|
# Init V with SVD of X
|
|
if dict_init is not None:
|
|
dictionary = dict_init
|
|
else:
|
|
_, S, dictionary = randomized_svd(X, n_atoms)
|
|
dictionary = S[:, np.newaxis] * dictionary
|
|
r = len(dictionary)
|
|
if n_atoms <= r:
|
|
dictionary = dictionary[:n_atoms, :]
|
|
else:
|
|
dictionary = np.r_[dictionary,
|
|
np.zeros((n_atoms - r, dictionary.shape[1]))]
|
|
dictionary = np.ascontiguousarray(dictionary.T)
|
|
|
|
if verbose == 1:
|
|
print '[dict_learning]',
|
|
|
|
n_batches = floor(float(len(X)) / chunk_size)
|
|
if shuffle:
|
|
X_train = X.copy()
|
|
random_state.shuffle(X_train)
|
|
else:
|
|
X_train = X
|
|
batches = np.array_split(X_train, n_batches)
|
|
batches = itertools.cycle(batches)
|
|
|
|
# The covariance of the dictionary
|
|
A = np.zeros((n_atoms, n_atoms))
|
|
# The data approximation
|
|
B = np.zeros((n_features, n_atoms))
|
|
|
|
for ii, this_X in itertools.izip(xrange(iter_offset, iter_offset + n_iter),
|
|
batches):
|
|
dt = (time.time() - t0)
|
|
if verbose == 1:
|
|
sys.stdout.write(".")
|
|
sys.stdout.flush()
|
|
elif verbose:
|
|
if verbose > 10 or ii % ceil(100. / verbose) == 0:
|
|
print ("Iteration % 3i (elapsed time: % 3is, % 4.1fmn)" %
|
|
(ii, dt, dt / 60))
|
|
|
|
this_code = sparse_encode(this_X, dictionary.T, algorithm=method,
|
|
alpha=alpha).T
|
|
|
|
# Update the auxiliary variables
|
|
if ii < chunk_size - 1:
|
|
theta = float((ii + 1) * chunk_size)
|
|
else:
|
|
theta = float(chunk_size ** 2 + ii + 1 - chunk_size)
|
|
beta = (theta + 1 - chunk_size) / (theta + 1)
|
|
|
|
A *= beta
|
|
A += np.dot(this_code, this_code.T)
|
|
B *= beta
|
|
B += np.dot(this_X.T, this_code.T)
|
|
|
|
# Update dictionary
|
|
dictionary = _update_dict(dictionary, B, A, verbose=verbose,
|
|
random_state=random_state)
|
|
# XXX: Can the residuals be of any use?
|
|
|
|
# Maybe we need a stopping criteria based on the amount of
|
|
# modification in the dictionary
|
|
if callback is not None:
|
|
callback(locals())
|
|
|
|
if return_code:
|
|
if verbose > 1:
|
|
print 'Learning code...',
|
|
elif verbose == 1:
|
|
print '|',
|
|
code = sparse_encode(X, dictionary.T, algorithm=method, alpha=alpha,
|
|
n_jobs=n_jobs)
|
|
if verbose > 1:
|
|
dt = (time.time() - t0)
|
|
print 'done (total time: % 3is, % 4.1fmn)' % (dt, dt / 60)
|
|
return code, dictionary.T
|
|
|
|
return dictionary.T
|
|
|
|
|
|
class SparseCodingMixin(TransformerMixin):
|
|
"""Sparse coding mixin"""
|
|
|
|
def _set_sparse_coding_params(self, n_atoms, transform_algorithm='omp',
|
|
transform_n_nonzero_coefs=None,
|
|
transform_alpha=None, split_sign=False,
|
|
n_jobs=1):
|
|
self.n_atoms = n_atoms
|
|
self.transform_algorithm = transform_algorithm
|
|
self.transform_n_nonzero_coefs = transform_n_nonzero_coefs
|
|
self.transform_alpha = transform_alpha
|
|
self.split_sign = split_sign
|
|
self.n_jobs = n_jobs
|
|
|
|
def transform(self, X, y=None):
|
|
"""Encode the data as a sparse combination of the dictionary atoms.
|
|
|
|
Coding method is determined by the object parameter
|
|
`transform_algorithm`.
|
|
|
|
Parameters
|
|
----------
|
|
X : array of shape (n_samples, n_features)
|
|
Test data to be transformed, must have the same number of
|
|
features as the data used to train the model.
|
|
|
|
Returns
|
|
-------
|
|
X_new : array, shape (n_samples, n_components)
|
|
Transformed data
|
|
|
|
"""
|
|
# XXX : kwargs is not documented
|
|
X = array2d(X)
|
|
n_samples, n_features = X.shape
|
|
|
|
code = sparse_encode(
|
|
X, self.components_, algorithm=self.transform_algorithm,
|
|
n_nonzero_coefs=self.transform_n_nonzero_coefs,
|
|
alpha=self.transform_alpha, n_jobs=self.n_jobs)
|
|
|
|
if self.split_sign:
|
|
# feature vector is split into a positive and negative side
|
|
n_samples, n_features = code.shape
|
|
split_code = np.empty((n_samples, 2 * n_features))
|
|
split_code[:, :n_features] = np.maximum(code, 0)
|
|
split_code[:, n_features:] = -np.minimum(code, 0)
|
|
code = split_code
|
|
|
|
return code
|
|
|
|
|
|
class SparseCoder(BaseEstimator, SparseCodingMixin):
|
|
"""Sparse coding
|
|
|
|
Finds a sparse representation of data against a fixed, precomputed
|
|
dictionary.
|
|
|
|
Each row of the result is the solution to a sparse coding problem.
|
|
The goal is to find a sparse array `code` such that::
|
|
|
|
X ~= code * dictionary
|
|
|
|
Parameters
|
|
----------
|
|
dictionary : array, [n_atoms, n_features]
|
|
The dictionary atoms used for sparse coding. Lines are assumed to be
|
|
normalized to unit norm.
|
|
|
|
transform_algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', \
|
|
'threshold'}
|
|
Algorithm used to transform the data:
|
|
lars: uses the least angle regression method (linear_model.lars_path)
|
|
lasso_lars: uses Lars to compute the Lasso solution
|
|
lasso_cd: uses the coordinate descent method to compute the
|
|
Lasso solution (linear_model.Lasso). lasso_lars will be faster if
|
|
the estimated components are sparse.
|
|
omp: uses orthogonal matching pursuit to estimate the sparse solution
|
|
threshold: squashes to zero all coefficients less than alpha from
|
|
the projection ``dictionary * X'``
|
|
|
|
transform_n_nonzero_coefs : int, ``0.1 * n_features`` by default
|
|
Number of nonzero coefficients to target in each column of the
|
|
solution. This is only used by `algorithm='lars'` and `algorithm='omp'`
|
|
and is overridden by `alpha` in the `omp` case.
|
|
|
|
transform_alpha : float, 1. by default
|
|
If `algorithm='lasso_lars'` or `algorithm='lasso_cd'`, `alpha` is the
|
|
penalty applied to the L1 norm.
|
|
If `algorithm='threshold'`, `alpha` is the absolute value of the
|
|
threshold below which coefficients will be squashed to zero.
|
|
If `algorithm='omp'`, `alpha` is the tolerance parameter: the value of
|
|
the reconstruction error targeted. In this case, it overrides
|
|
`n_nonzero_coefs`.
|
|
|
|
split_sign : bool, False by default
|
|
Whether to split the sparse feature vector into the concatenation of
|
|
its negative part and its positive part. This can improve the
|
|
performance of downstream classifiers.
|
|
|
|
n_jobs : int,
|
|
number of parallel jobs to run
|
|
|
|
Attributes
|
|
----------
|
|
`components_` : array, [n_atoms, n_features]
|
|
The unchanged dictionary atoms
|
|
|
|
See also
|
|
--------
|
|
DictionaryLearning
|
|
MiniBatchDictionaryLearning
|
|
SparsePCA
|
|
MiniBatchSparsePCA
|
|
sparse_encode
|
|
"""
|
|
|
|
def __init__(self, dictionary, transform_algorithm='omp',
|
|
transform_n_nonzero_coefs=None, transform_alpha=None,
|
|
split_sign=False, n_jobs=1):
|
|
self._set_sparse_coding_params(dictionary.shape[0],
|
|
transform_algorithm,
|
|
transform_n_nonzero_coefs,
|
|
transform_alpha, split_sign, n_jobs)
|
|
self.components_ = dictionary
|
|
|
|
def fit(self, X, y=None):
|
|
"""Do nothing and return the estimator unchanged
|
|
|
|
This method is just there to implement the usual API and hence
|
|
work in pipelines.
|
|
"""
|
|
return self
|
|
|
|
|
|
class DictionaryLearning(BaseEstimator, SparseCodingMixin):
|
|
"""Dictionary learning
|
|
|
|
Finds a dictionary (a set of atoms) that can best be used to represent data
|
|
using a sparse code.
|
|
|
|
Solves the optimization problem::
|
|
|
|
(U^*,V^*) = argmin 0.5 || Y - U V ||_2^2 + alpha * || U ||_1
|
|
(U,V)
|
|
with || V_k ||_2 = 1 for all 0 <= k < n_atoms
|
|
|
|
Parameters
|
|
----------
|
|
n_atoms : int,
|
|
number of dictionary elements to extract
|
|
|
|
alpha : int,
|
|
sparsity controlling parameter
|
|
|
|
max_iter : int,
|
|
maximum number of iterations to perform
|
|
|
|
tol : float,
|
|
tolerance for numerical error
|
|
|
|
fit_algorithm : {'lars', 'cd'}
|
|
lars: uses the least angle regression method to solve the lasso problem
|
|
(linear_model.lars_path)
|
|
cd: uses the coordinate descent method to compute the
|
|
Lasso solution (linear_model.Lasso). Lars will be faster if
|
|
the estimated components are sparse.
|
|
|
|
transform_algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', \
|
|
'threshold'}
|
|
Algorithm used to transform the data
|
|
lars: uses the least angle regression method (linear_model.lars_path)
|
|
lasso_lars: uses Lars to compute the Lasso solution
|
|
lasso_cd: uses the coordinate descent method to compute the
|
|
Lasso solution (linear_model.Lasso). lasso_lars will be faster if
|
|
the estimated components are sparse.
|
|
omp: uses orthogonal matching pursuit to estimate the sparse solution
|
|
threshold: squashes to zero all coefficients less than alpha from
|
|
the projection ``dictionary * X'``
|
|
|
|
transform_n_nonzero_coefs : int, ``0.1 * n_features`` by default
|
|
Number of nonzero coefficients to target in each column of the
|
|
solution. This is only used by `algorithm='lars'` and `algorithm='omp'`
|
|
and is overridden by `alpha` in the `omp` case.
|
|
|
|
transform_alpha : float, 1. by default
|
|
If `algorithm='lasso_lars'` or `algorithm='lasso_cd'`, `alpha` is the
|
|
penalty applied to the L1 norm.
|
|
If `algorithm='threshold'`, `alpha` is the absolute value of the
|
|
threshold below which coefficients will be squashed to zero.
|
|
If `algorithm='omp'`, `alpha` is the tolerance parameter: the value of
|
|
the reconstruction error targeted. In this case, it overrides
|
|
`n_nonzero_coefs`.
|
|
|
|
split_sign : bool, False by default
|
|
Whether to split the sparse feature vector into the concatenation of
|
|
its negative part and its positive part. This can improve the
|
|
performance of downstream classifiers.
|
|
|
|
n_jobs : int,
|
|
number of parallel jobs to run
|
|
|
|
code_init : array of shape (n_samples, n_atoms),
|
|
initial value for the code, for warm restart
|
|
|
|
dict_init : array of shape (n_atoms, n_features),
|
|
initial values for the dictionary, for warm restart
|
|
|
|
verbose :
|
|
degree of verbosity of the printed output
|
|
|
|
random_state : int or RandomState
|
|
Pseudo number generator state used for random sampling.
|
|
|
|
Attributes
|
|
----------
|
|
`components_` : array, [n_atoms, n_features]
|
|
dictionary atoms extracted from the data
|
|
|
|
`error_` : array
|
|
vector of errors at each iteration
|
|
|
|
Notes
|
|
-----
|
|
**References:**
|
|
|
|
J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning
|
|
for sparse coding (http://www.di.ens.fr/sierra/pdfs/icml09.pdf)
|
|
|
|
See also
|
|
--------
|
|
SparseCoder
|
|
MiniBatchDictionaryLearning
|
|
SparsePCA
|
|
MiniBatchSparsePCA
|
|
"""
|
|
def __init__(self, n_atoms=None, alpha=1, max_iter=1000, tol=1e-8,
|
|
fit_algorithm='lars', transform_algorithm='omp',
|
|
transform_n_nonzero_coefs=None, transform_alpha=None,
|
|
n_jobs=1, code_init=None, dict_init=None, verbose=False,
|
|
split_sign=False, random_state=None):
|
|
self._set_sparse_coding_params(n_atoms, transform_algorithm,
|
|
transform_n_nonzero_coefs,
|
|
transform_alpha, split_sign, n_jobs)
|
|
self.alpha = alpha
|
|
self.max_iter = max_iter
|
|
self.tol = tol
|
|
self.fit_algorithm = fit_algorithm
|
|
self.code_init = code_init
|
|
self.dict_init = dict_init
|
|
self.verbose = verbose
|
|
self.random_state = random_state
|
|
|
|
def fit(self, X, y=None):
|
|
"""Fit the model from data in X.
|
|
|
|
Parameters
|
|
----------
|
|
X: array-like, shape (n_samples, n_features)
|
|
Training vector, where n_samples in the number of samples
|
|
and n_features is the number of features.
|
|
|
|
Returns
|
|
-------
|
|
self: object
|
|
Returns the object itself
|
|
"""
|
|
self.random_state = check_random_state(self.random_state)
|
|
X = array2d(X)
|
|
if self.n_atoms is None:
|
|
n_atoms = X.shape[1]
|
|
else:
|
|
n_atoms = self.n_atoms
|
|
|
|
V, U, E = dict_learning(X, n_atoms, self.alpha,
|
|
tol=self.tol, max_iter=self.max_iter,
|
|
method=self.fit_algorithm,
|
|
n_jobs=self.n_jobs,
|
|
code_init=self.code_init,
|
|
dict_init=self.dict_init,
|
|
verbose=self.verbose,
|
|
random_state=self.random_state)
|
|
self.components_ = U
|
|
self.error_ = E
|
|
return self
|
|
|
|
|
|
class MiniBatchDictionaryLearning(BaseEstimator, SparseCodingMixin):
|
|
"""Mini-batch dictionary learning
|
|
|
|
Finds a dictionary (a set of atoms) that can best be used to represent data
|
|
using a sparse code.
|
|
|
|
Solves the optimization problem::
|
|
|
|
(U^*,V^*) = argmin 0.5 || Y - U V ||_2^2 + alpha * || U ||_1
|
|
(U,V)
|
|
with || V_k ||_2 = 1 for all 0 <= k < n_atoms
|
|
|
|
Parameters
|
|
----------
|
|
n_atoms : int,
|
|
number of dictionary elements to extract
|
|
|
|
alpha : int,
|
|
sparsity controlling parameter
|
|
|
|
n_iter : int,
|
|
total number of iterations to perform
|
|
|
|
fit_algorithm : {'lars', 'cd'}
|
|
lars: uses the least angle regression method to solve the lasso problem
|
|
(linear_model.lars_path)
|
|
cd: uses the coordinate descent method to compute the
|
|
Lasso solution (linear_model.Lasso). Lars will be faster if
|
|
the estimated components are sparse.
|
|
|
|
transform_algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', \
|
|
'threshold'}
|
|
Algorithm used to transform the data.
|
|
lars: uses the least angle regression method (linear_model.lars_path)
|
|
lasso_lars: uses Lars to compute the Lasso solution
|
|
lasso_cd: uses the coordinate descent method to compute the
|
|
Lasso solution (linear_model.Lasso). lasso_lars will be faster if
|
|
the estimated components are sparse.
|
|
omp: uses orthogonal matching pursuit to estimate the sparse solution
|
|
threshold: squashes to zero all coefficients less than alpha from
|
|
the projection dictionary * X'
|
|
|
|
transform_n_nonzero_coefs : int, ``0.1 * n_features`` by default
|
|
Number of nonzero coefficients to target in each column of the
|
|
solution. This is only used by `algorithm='lars'` and `algorithm='omp'`
|
|
and is overridden by `alpha` in the `omp` case.
|
|
|
|
transform_alpha : float, 1. by default
|
|
If `algorithm='lasso_lars'` or `algorithm='lasso_cd'`, `alpha` is the
|
|
penalty applied to the L1 norm.
|
|
If `algorithm='threshold'`, `alpha` is the absolute value of the
|
|
threshold below which coefficients will be squashed to zero.
|
|
If `algorithm='omp'`, `alpha` is the tolerance parameter: the value of
|
|
the reconstruction error targeted. In this case, it overrides
|
|
`n_nonzero_coefs`.
|
|
|
|
split_sign : bool, False by default
|
|
Whether to split the sparse feature vector into the concatenation of
|
|
its negative part and its positive part. This can improve the
|
|
performance of downstream classifiers.
|
|
|
|
n_jobs : int,
|
|
number of parallel jobs to run
|
|
|
|
dict_init : array of shape (n_atoms, n_features),
|
|
initial value of the dictionary for warm restart scenarios
|
|
|
|
verbose :
|
|
degree of verbosity of the printed output
|
|
|
|
chunk_size : int,
|
|
number of samples in each mini-batch
|
|
|
|
shuffle : bool,
|
|
whether to shuffle the samples before forming batches
|
|
|
|
random_state : int or RandomState
|
|
Pseudo number generator state used for random sampling.
|
|
|
|
Attributes
|
|
----------
|
|
`components_` : array, [n_atoms, n_features]
|
|
components extracted from the data
|
|
|
|
Notes
|
|
-----
|
|
**References:**
|
|
|
|
J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning
|
|
for sparse coding (http://www.di.ens.fr/sierra/pdfs/icml09.pdf)
|
|
|
|
See also
|
|
--------
|
|
SparseCoder
|
|
DictionaryLearning
|
|
SparsePCA
|
|
MiniBatchSparsePCA
|
|
|
|
"""
|
|
def __init__(self, n_atoms=None, alpha=1, n_iter=1000,
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fit_algorithm='lars', n_jobs=1, chunk_size=3,
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shuffle=True, dict_init=None, transform_algorithm='omp',
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transform_n_nonzero_coefs=None, transform_alpha=None,
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verbose=False, split_sign=False, random_state=None):
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self._set_sparse_coding_params(n_atoms, transform_algorithm,
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transform_n_nonzero_coefs,
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transform_alpha, split_sign, n_jobs)
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self.alpha = alpha
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self.n_iter = n_iter
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self.fit_algorithm = fit_algorithm
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self.dict_init = dict_init
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self.verbose = verbose
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self.shuffle = shuffle
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self.chunk_size = chunk_size
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self.split_sign = split_sign
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self.random_state = random_state
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def fit(self, X, y=None):
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"""Fit the model from data in X.
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Parameters
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----------
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X: array-like, shape (n_samples, n_features)
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Training vector, where n_samples in the number of samples
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and n_features is the number of features.
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Returns
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-------
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self : object
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Returns the instance itself.
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"""
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self.random_state = check_random_state(self.random_state)
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X = array2d(X)
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if self.n_atoms is None:
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n_atoms = X.shape[1]
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else:
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n_atoms = self.n_atoms
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U = dict_learning_online(X, n_atoms, self.alpha,
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n_iter=self.n_iter, return_code=False,
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method=self.fit_algorithm,
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n_jobs=self.n_jobs,
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dict_init=self.dict_init,
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chunk_size=self.chunk_size,
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shuffle=self.shuffle, verbose=self.verbose,
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random_state=self.random_state)
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self.components_ = U
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return self
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def partial_fit(self, X, y=None, iter_offset=0):
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"""Updates the model using the data in X as a mini-batch.
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Parameters
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----------
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X: array-like, shape (n_samples, n_features)
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|
Training vector, where n_samples in the number of samples
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|
and n_features is the number of features.
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|
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Returns
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-------
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self : object
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|
Returns the instance itself.
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"""
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self.random_state = check_random_state(self.random_state)
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X = array2d(X)
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if hasattr(self, 'components_'):
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dict_init = self.components_
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else:
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dict_init = self.dict_init
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U = dict_learning_online(X, self.n_atoms, self.alpha,
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n_iter=self.n_iter,
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method=self.fit_algorithm,
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n_jobs=self.n_jobs, dict_init=dict_init,
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chunk_size=len(X), shuffle=False,
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verbose=self.verbose, return_code=False,
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iter_offset=iter_offset,
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random_state=self.random_state)
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self.components_ = U
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return self
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