""" Dictionary learning """ from __future__ import print_function # Author: Vlad Niculae, Gael Varoquaux, Alexandre Gramfort # License: BSD 3 clause import time import sys import itertools from math import sqrt, ceil import numpy as np from scipy import linalg from numpy.lib.stride_tricks import as_strided from ..base import BaseEstimator, TransformerMixin from ..externals.joblib import Parallel, delayed, cpu_count from ..externals.six.moves import zip from ..utils import (check_array, check_random_state, gen_even_slices, gen_batches, _get_n_jobs) from ..utils.extmath import randomized_svd, row_norms from ..utils.validation import check_is_fitted from ..linear_model import Lasso, orthogonal_mp_gram, LassoLars, Lars def _sparse_encode(X, dictionary, gram, cov=None, algorithm='lasso_lars', regularization=None, copy_cov=True, init=None, max_iter=1000, check_input=True, verbose=0): """Generic sparse coding Each column of the result is the solution to a Lasso problem. Parameters ---------- X : array of shape (n_samples, n_features) Data matrix. dictionary : array of shape (n_components, n_features) The dictionary matrix against which to solve the sparse coding of the data. Some of the algorithms assume normalized rows. gram : None | array, shape=(n_components, n_components) Precomputed Gram matrix, dictionary * dictionary' gram can be None if method is 'threshold'. cov : array, shape=(n_components, n_samples) Precomputed covariance, dictionary * X' algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'} 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 regularization from the projection dictionary * data' regularization : int | float The regularization parameter. It corresponds to alpha when algorithm is 'lasso_lars', 'lasso_cd' or 'threshold'. Otherwise it corresponds to n_nonzero_coefs. init : array of shape (n_samples, n_components) Initialization value of the sparse code. Only used if `algorithm='lasso_cd'`. max_iter : int, 1000 by default Maximum number of iterations to perform if `algorithm='lasso_cd'`. copy_cov : boolean, optional Whether to copy the precomputed covariance matrix; if False, it may be overwritten. check_input : boolean, optional If False, the input arrays X and dictionary will not be checked. verbose : int Controls the verbosity; the higher, the more messages. Defaults to 0. Returns ------- code : array of shape (n_components, n_features) The sparse codes See also -------- sklearn.linear_model.lars_path sklearn.linear_model.orthogonal_mp sklearn.linear_model.Lasso SparseCoder """ if X.ndim == 1: X = X[:, np.newaxis] n_samples, n_features = X.shape n_components = dictionary.shape[0] if dictionary.shape[1] != X.shape[1]: raise ValueError("Dictionary and X have different numbers of features:" "dictionary.shape: {} X.shape{}".format( dictionary.shape, X.shape)) if cov is None and algorithm != 'lasso_cd': # overwriting cov is safe copy_cov = False cov = np.dot(dictionary, X.T) if algorithm == 'lasso_lars': alpha = float(regularization) / n_features # account for scaling try: err_mgt = np.seterr(all='ignore') # Not passing in verbose=max(0, verbose-1) because Lars.fit already # corrects the verbosity level. lasso_lars = LassoLars(alpha=alpha, fit_intercept=False, verbose=verbose, normalize=False, precompute=gram, fit_path=False) lasso_lars.fit(dictionary.T, X.T, Xy=cov) new_code = lasso_lars.coef_ finally: np.seterr(**err_mgt) elif algorithm == 'lasso_cd': alpha = float(regularization) / n_features # account for scaling # TODO: Make verbosity argument for Lasso? # sklearn.linear_model.coordinate_descent.enet_path has a verbosity # argument that we could pass in from Lasso. clf = Lasso(alpha=alpha, fit_intercept=False, normalize=False, precompute=gram, max_iter=max_iter, warm_start=True) if init is not None: clf.coef_ = init clf.fit(dictionary.T, X.T, check_input=check_input) new_code = clf.coef_ elif algorithm == 'lars': try: err_mgt = np.seterr(all='ignore') # Not passing in verbose=max(0, verbose-1) because Lars.fit already # corrects the verbosity level. lars = Lars(fit_intercept=False, verbose=verbose, normalize=False, precompute=gram, n_nonzero_coefs=int(regularization), fit_path=False) lars.fit(dictionary.T, X.T, Xy=cov) new_code = lars.coef_ finally: np.seterr(**err_mgt) elif algorithm == 'threshold': new_code = ((np.sign(cov) * np.maximum(np.abs(cov) - regularization, 0)).T) elif algorithm == 'omp': # TODO: Should verbose argument be passed to this? new_code = orthogonal_mp_gram( Gram=gram, Xy=cov, n_nonzero_coefs=int(regularization), tol=None, norms_squared=row_norms(X, squared=True), copy_Xy=copy_cov).T else: raise ValueError('Sparse coding method must be "lasso_lars" ' '"lasso_cd", "lasso", "threshold" or "omp", got %s.' % algorithm) if new_code.ndim != 2: return new_code.reshape(n_samples, n_components) return new_code # XXX : could be moved to the linear_model module def sparse_encode(X, dictionary, gram=None, cov=None, algorithm='lasso_lars', n_nonzero_coefs=None, alpha=None, copy_cov=True, init=None, max_iter=1000, n_jobs=1, check_input=True, verbose=0): """Sparse coding 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 Read more in the :ref:`User Guide `. Parameters ---------- X : array of shape (n_samples, n_features) Data matrix dictionary : array of shape (n_components, n_features) The dictionary matrix against which to solve the sparse coding of the data. Some of the algorithms assume normalized rows for meaningful output. gram : array, shape=(n_components, n_components) Precomputed Gram matrix, dictionary * dictionary' cov : array, shape=(n_components, n_samples) Precomputed covariance, dictionary' * X algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'} 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' 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. 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`. copy_cov : boolean, optional Whether to copy the precomputed covariance matrix; if False, it may be overwritten. init : array of shape (n_samples, n_components) Initialization value of the sparse codes. Only used if `algorithm='lasso_cd'`. max_iter : int, 1000 by default Maximum number of iterations to perform if `algorithm='lasso_cd'`. n_jobs : int, optional Number of parallel jobs to run. check_input : boolean, optional If False, the input arrays X and dictionary will not be checked. verbose : int, optional Controls the verbosity; the higher, the more messages. Defaults to 0. Returns ------- code : array of shape (n_samples, n_components) The sparse codes See also -------- sklearn.linear_model.lars_path sklearn.linear_model.orthogonal_mp sklearn.linear_model.Lasso SparseCoder """ if check_input: if algorithm == 'lasso_cd': dictionary = check_array(dictionary, order='C', dtype='float64') X = check_array(X, order='C', dtype='float64') else: dictionary = check_array(dictionary) X = check_array(X) n_samples, n_features = X.shape n_components = dictionary.shape[0] if gram is None and algorithm != 'threshold': gram = np.dot(dictionary, dictionary.T) if cov is None and algorithm != 'lasso_cd': copy_cov = False cov = np.dot(dictionary, X.T) if algorithm in ('lars', 'omp'): regularization = n_nonzero_coefs if regularization is None: regularization = min(max(n_features / 10, 1), n_components) else: regularization = alpha if regularization is None: regularization = 1. if n_jobs == 1 or algorithm == 'threshold': code = _sparse_encode(X, dictionary, gram, cov=cov, algorithm=algorithm, regularization=regularization, copy_cov=copy_cov, init=init, max_iter=max_iter, check_input=False, verbose=verbose) return code # Enter parallel code block code = np.empty((n_samples, n_components)) slices = list(gen_even_slices(n_samples, _get_n_jobs(n_jobs))) code_views = Parallel(n_jobs=n_jobs, verbose=verbose)( delayed(_sparse_encode)( X[this_slice], dictionary, gram, cov[:, this_slice] if cov is not None else None, algorithm, regularization=regularization, copy_cov=copy_cov, init=init[this_slice] if init is not None else None, max_iter=max_iter, check_input=False) for this_slice in slices) for this_slice, this_view in zip(slices, code_views): code[this_slice] = this_view return code def _update_dict(dictionary, Y, code, verbose=False, return_r2=False, random_state=None): """Update the dense dictionary factor in place. Parameters ---------- dictionary : array of shape (n_features, n_components) Value of the dictionary at the previous iteration. Y : array of shape (n_features, n_samples) Data matrix. code : array of shape (n_components, n_samples) Sparse coding of the data against which to optimize the dictionary. verbose: Degree of output the procedure will print. return_r2 : bool Whether to compute and return the residual sum of squares corresponding to the computed solution. random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Returns ------- dictionary : array of shape (n_features, n_components) Updated dictionary. """ n_components = len(code) n_samples = Y.shape[0] random_state = check_random_state(random_state) # Residuals, computed 'in-place' for efficiency R = -np.dot(dictionary, code) R += Y R = np.asfortranarray(R) ger, = linalg.get_blas_funcs(('ger',), (dictionary, code)) for k in range(n_components): # R <- 1.0 * U_k * V_k^T + R R = ger(1.0, dictionary[:, k], code[k, :], a=R, overwrite_a=True) dictionary[:, k] = np.dot(R, code[k, :].T) # Scale k'th atom atom_norm_square = np.dot(dictionary[:, k], dictionary[:, k]) if atom_norm_square < 1e-20: if verbose == 1: sys.stdout.write("+") sys.stdout.flush() elif verbose: print("Adding new random atom") dictionary[:, k] = random_state.randn(n_samples) # Setting corresponding coefs to 0 code[k, :] = 0.0 dictionary[:, k] /= sqrt(np.dot(dictionary[:, k], dictionary[:, k])) else: dictionary[:, k] /= sqrt(atom_norm_square) # R <- -1.0 * U_k * V_k^T + R R = ger(-1.0, dictionary[:, k], code[k, :], a=R, overwrite_a=True) if return_r2: R **= 2 # R is fortran-ordered. For numpy version < 1.6, sum does not # follow the quick striding first, and is thus inefficient on # fortran ordered data. We take a flat view of the data with no # striding R = as_strided(R, shape=(R.size, ), strides=(R.dtype.itemsize,)) R = np.sum(R) return dictionary, R return dictionary def dict_learning(X, n_components, alpha, max_iter=100, tol=1e-8, method='lars', n_jobs=1, dict_init=None, code_init=None, callback=None, verbose=False, random_state=None, return_n_iter=False): """Solves a dictionary learning matrix factorization problem. Finds the best dictionary and the corresponding sparse code for approximating the data matrix X by solving:: (U^*, V^*) = argmin 0.5 || X - U V ||_2^2 + alpha * || U ||_1 (U,V) with || V_k ||_2 = 1 for all 0 <= k < n_components where V is the dictionary and U is the sparse code. Read more in the :ref:`User Guide `. Parameters ---------- X : array of shape (n_samples, n_features) Data matrix. n_components : int, Number of dictionary atoms to extract. alpha : int, Sparsity controlling parameter. max_iter : int, Maximum number of iterations to perform. tol : float, Tolerance for the stopping condition. 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. n_jobs : int, Number of parallel jobs to run, or -1 to autodetect. dict_init : array of shape (n_components, n_features), Initial value for the dictionary for warm restart scenarios. code_init : array of shape (n_samples, n_components), Initial value for the sparse code for warm restart scenarios. callback : callable or None, optional (default: None) Callable that gets invoked every five iterations verbose : bool, optional (default: False) To control the verbosity of the procedure. random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. return_n_iter : bool Whether or not to return the number of iterations. Returns ------- code : array of shape (n_samples, n_components) The sparse code factor in the matrix factorization. dictionary : array of shape (n_components, n_features), The dictionary factor in the matrix factorization. errors : array Vector of errors at each iteration. n_iter : int Number of iterations run. Returned only if `return_n_iter` is set to True. See also -------- dict_learning_online DictionaryLearning MiniBatchDictionaryLearning SparsePCA MiniBatchSparsePCA """ if method not in ('lars', 'cd'): raise ValueError('Coding method %r not supported as a fit algorithm.' % method) method = 'lasso_' + method t0 = time.time() # Avoid integer division problems alpha = float(alpha) random_state = check_random_state(random_state) if n_jobs == -1: n_jobs = cpu_count() # Init the code and the dictionary with SVD of Y if code_init is not None and dict_init is not None: code = np.array(code_init, order='F') # Don't copy V, it will happen below dictionary = dict_init else: code, S, dictionary = linalg.svd(X, full_matrices=False) dictionary = S[:, np.newaxis] * dictionary r = len(dictionary) if n_components <= r: # True even if n_components=None code = code[:, :n_components] dictionary = dictionary[:n_components, :] else: code = np.c_[code, np.zeros((len(code), n_components - r))] dictionary = np.r_[dictionary, np.zeros((n_components - r, dictionary.shape[1]))] # Fortran-order dict, as we are going to access its row vectors dictionary = np.array(dictionary, order='F') residuals = 0 errors = [] current_cost = np.nan if verbose == 1: print('[dict_learning]', end=' ') # If max_iter is 0, number of iterations returned should be zero ii = -1 for ii in range(max_iter): dt = (time.time() - t0) if verbose == 1: sys.stdout.write(".") sys.stdout.flush() elif verbose: print("Iteration % 3i " "(elapsed time: % 3is, % 4.1fmn, current cost % 7.3f)" % (ii, dt, dt / 60, current_cost)) # Update code code = sparse_encode(X, dictionary, algorithm=method, alpha=alpha, init=code, n_jobs=n_jobs) # Update dictionary dictionary, residuals = _update_dict(dictionary.T, X.T, code.T, verbose=verbose, return_r2=True, random_state=random_state) dictionary = dictionary.T # Cost function current_cost = 0.5 * residuals + alpha * np.sum(np.abs(code)) errors.append(current_cost) if ii > 0: dE = errors[-2] - errors[-1] # assert(dE >= -tol * errors[-1]) if dE < tol * errors[-1]: if verbose == 1: # A line return print("") elif verbose: print("--- Convergence reached after %d iterations" % ii) break if ii % 5 == 0 and callback is not None: callback(locals()) if return_n_iter: return code, dictionary, errors, ii + 1 else: return code, dictionary, errors def dict_learning_online(X, n_components=2, alpha=1, n_iter=100, return_code=True, dict_init=None, callback=None, batch_size=3, verbose=False, shuffle=True, n_jobs=1, method='lars', iter_offset=0, random_state=None, return_inner_stats=False, inner_stats=None, return_n_iter=False): """Solves a dictionary learning matrix factorization problem online. Finds the best dictionary and the corresponding sparse code for approximating the data matrix X by solving:: (U^*, V^*) = argmin 0.5 || X - U V ||_2^2 + alpha * || U ||_1 (U,V) with || V_k ||_2 = 1 for all 0 <= k < n_components where V is the dictionary and U is the sparse code. This is accomplished by repeatedly iterating over mini-batches by slicing the input data. Read more in the :ref:`User Guide `. Parameters ---------- X : array of shape (n_samples, n_features) Data matrix. n_components : int, Number of dictionary atoms to extract. alpha : float, Sparsity controlling parameter. 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_components, n_features), Initial value for the dictionary for warm restart scenarios. callback : callable or None, optional (default: None) callable that gets invoked every five iterations batch_size : int, The number of samples to take in each batch. verbose : bool, optional (default: False) To control the verbosity of the procedure. 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, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. return_inner_stats : boolean, optional Return the inner statistics A (dictionary covariance) and B (data approximation). Useful to restart the algorithm in an online setting. If return_inner_stats is True, return_code is ignored inner_stats : tuple of (A, B) ndarrays Inner sufficient statistics that are kept by the algorithm. Passing them at initialization is useful in online settings, to avoid loosing the history of the evolution. A (n_components, n_components) is the dictionary covariance matrix. B (n_features, n_components) is the data approximation matrix return_n_iter : bool Whether or not to return the number of iterations. Returns ------- code : array of shape (n_samples, n_components), the sparse code (only returned if `return_code=True`) dictionary : array of shape (n_components, n_features), the solutions to the dictionary learning problem n_iter : int Number of iterations run. Returned only if `return_n_iter` is set to `True`. See also -------- dict_learning DictionaryLearning MiniBatchDictionaryLearning SparsePCA MiniBatchSparsePCA """ if n_components is None: n_components = X.shape[1] 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_components, random_state=random_state) dictionary = S[:, np.newaxis] * dictionary r = len(dictionary) if n_components <= r: dictionary = dictionary[:n_components, :] else: dictionary = np.r_[dictionary, np.zeros((n_components - r, dictionary.shape[1]))] if verbose == 1: print('[dict_learning]', end=' ') if shuffle: X_train = X.copy() random_state.shuffle(X_train) else: X_train = X dictionary = check_array(dictionary.T, order='F', dtype=np.float64, copy=False) X_train = check_array(X_train, order='C', dtype=np.float64, copy=False) batches = gen_batches(n_samples, batch_size) batches = itertools.cycle(batches) # The covariance of the dictionary if inner_stats is None: A = np.zeros((n_components, n_components)) # The data approximation B = np.zeros((n_features, n_components)) else: A = inner_stats[0].copy() B = inner_stats[1].copy() # If n_iter is zero, we need to return zero. ii = iter_offset - 1 for ii, batch in zip(range(iter_offset, iter_offset + n_iter), batches): this_X = X_train[batch] 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, n_jobs=n_jobs).T # Update the auxiliary variables if ii < batch_size - 1: theta = float((ii + 1) * batch_size) else: theta = float(batch_size ** 2 + ii + 1 - batch_size) beta = (theta + 1 - batch_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_inner_stats: if return_n_iter: return dictionary.T, (A, B), ii - iter_offset + 1 else: return dictionary.T, (A, B) if return_code: if verbose > 1: print('Learning code...', end=' ') elif verbose == 1: print('|', end=' ') code = sparse_encode(X, dictionary.T, algorithm=method, alpha=alpha, n_jobs=n_jobs, check_input=False) if verbose > 1: dt = (time.time() - t0) print('done (total time: % 3is, % 4.1fmn)' % (dt, dt / 60)) if return_n_iter: return code, dictionary.T, ii - iter_offset + 1 else: return code, dictionary.T if return_n_iter: return dictionary.T, ii - iter_offset + 1 else: return dictionary.T class SparseCodingMixin(TransformerMixin): """Sparse coding mixin""" def _set_sparse_coding_params(self, n_components, transform_algorithm='omp', transform_n_nonzero_coefs=None, transform_alpha=None, split_sign=False, n_jobs=1): self.n_components = n_components 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): """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 """ check_is_fitted(self, 'components_') X = check_array(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 Read more in the :ref:`User Guide `. Parameters ---------- dictionary : array, [n_components, 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_components, n_features] The unchanged dictionary atoms See also -------- DictionaryLearning MiniBatchDictionaryLearning SparsePCA MiniBatchSparsePCA sparse_encode """ _required_parameters = ["dictionary"] 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. Parameters ---------- X : Ignored. y : Ignored. Returns ------- self : object Returns the object itself """ 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_components Read more in the :ref:`User Guide `. Parameters ---------- n_components : int, number of dictionary elements to extract alpha : float, 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. .. versionadded:: 0.17 *cd* coordinate descent method to improve speed. 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'`` .. versionadded:: 0.17 *lasso_cd* coordinate descent method to improve speed. 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`. n_jobs : int, number of parallel jobs to run code_init : array of shape (n_samples, n_components), initial value for the code, for warm restart dict_init : array of shape (n_components, n_features), initial values for the dictionary, for warm restart verbose : bool, optional (default: False) To control the verbosity of the procedure. 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. random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Attributes ---------- components_ : array, [n_components, n_features] dictionary atoms extracted from the data error_ : array vector of errors at each iteration n_iter_ : int Number of iterations run. 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_components=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_components, 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. y : Ignored. Returns ------- self : object Returns the object itself """ random_state = check_random_state(self.random_state) X = check_array(X) if self.n_components is None: n_components = X.shape[1] else: n_components = self.n_components V, U, E, self.n_iter_ = dict_learning( X, n_components, 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=random_state, return_n_iter=True) 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_components Read more in the :ref:`User Guide `. Parameters ---------- n_components : int, number of dictionary elements to extract alpha : float, 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. n_jobs : int, number of parallel jobs to run batch_size : int, number of samples in each mini-batch shuffle : bool, whether to shuffle the samples before forming batches dict_init : array of shape (n_components, n_features), initial value of the dictionary for warm restart scenarios 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`. verbose : bool, optional (default: False) To control the verbosity of the procedure. 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. random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Attributes ---------- components_ : array, [n_components, n_features] components extracted from the data inner_stats_ : tuple of (A, B) ndarrays Internal sufficient statistics that are kept by the algorithm. Keeping them is useful in online settings, to avoid loosing the history of the evolution, but they shouldn't have any use for the end user. A (n_components, n_components) is the dictionary covariance matrix. B (n_features, n_components) is the data approximation matrix n_iter_ : int Number of iterations run. 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_components=None, alpha=1, n_iter=1000, fit_algorithm='lars', n_jobs=1, batch_size=3, shuffle=True, dict_init=None, transform_algorithm='omp', transform_n_nonzero_coefs=None, transform_alpha=None, verbose=False, split_sign=False, random_state=None): self._set_sparse_coding_params(n_components, transform_algorithm, transform_n_nonzero_coefs, transform_alpha, split_sign, n_jobs) self.alpha = alpha self.n_iter = n_iter self.fit_algorithm = fit_algorithm self.dict_init = dict_init self.verbose = verbose self.shuffle = shuffle self.batch_size = batch_size self.split_sign = split_sign 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. y : Ignored. Returns ------- self : object Returns the instance itself. """ random_state = check_random_state(self.random_state) X = check_array(X) U, (A, B), self.n_iter_ = dict_learning_online( X, self.n_components, self.alpha, n_iter=self.n_iter, return_code=False, method=self.fit_algorithm, n_jobs=self.n_jobs, dict_init=self.dict_init, batch_size=self.batch_size, shuffle=self.shuffle, verbose=self.verbose, random_state=random_state, return_inner_stats=True, return_n_iter=True) self.components_ = U # Keep track of the state of the algorithm to be able to do # some online fitting (partial_fit) self.inner_stats_ = (A, B) self.iter_offset_ = self.n_iter return self def partial_fit(self, X, y=None, iter_offset=None): """Updates the model using the data in X as a mini-batch. 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. y : Ignored. iter_offset : integer, optional The number of iteration on data batches that has been performed before this call to partial_fit. This is optional: if no number is passed, the memory of the object is used. Returns ------- self : object Returns the instance itself. """ if not hasattr(self, 'random_state_'): self.random_state_ = check_random_state(self.random_state) X = check_array(X) if hasattr(self, 'components_'): dict_init = self.components_ else: dict_init = self.dict_init inner_stats = getattr(self, 'inner_stats_', None) if iter_offset is None: iter_offset = getattr(self, 'iter_offset_', 0) U, (A, B) = dict_learning_online( X, self.n_components, self.alpha, n_iter=self.n_iter, method=self.fit_algorithm, n_jobs=self.n_jobs, dict_init=dict_init, batch_size=len(X), shuffle=False, verbose=self.verbose, return_code=False, iter_offset=iter_offset, random_state=self.random_state_, return_inner_stats=True, inner_stats=inner_stats) self.components_ = U # Keep track of the state of the algorithm to be able to do # some online fitting (partial_fit) self.inner_stats_ = (A, B) self.iter_offset_ = iter_offset + self.n_iter return self