""" Dictionary learning. """ # Author: Vlad Niculae, Gael Varoquaux, Alexandre Gramfort # License: BSD 3 clause import time import sys import itertools from math import ceil import numpy as np from scipy import linalg from joblib import Parallel, effective_n_jobs from ..base import BaseEstimator, TransformerMixin from ..utils import deprecated from ..utils import (check_array, check_random_state, gen_even_slices, gen_batches) from ..utils.extmath import randomized_svd, row_norms from ..utils.validation import check_is_fitted, _deprecate_positional_args from ..utils.fixes import delayed from ..linear_model import Lasso, orthogonal_mp_gram, LassoLars, Lars def _check_positive_coding(method, positive): if positive and method in ["omp", "lars"]: raise ValueError( "Positive constraint not supported for '{}' " "coding method.".format(method) ) 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, positive=False): """Generic sparse coding. Each column of the result is the solution to a Lasso problem. Parameters ---------- X : ndarray of shape (n_samples, n_features) Data matrix. dictionary : ndarray 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 : ndarray of shape (n_components, n_components) or None Precomputed Gram matrix, `dictionary * dictionary'` gram can be `None` if method is 'threshold'. cov : ndarray of shape (n_components, n_samples), default=None Precomputed covariance, `dictionary * X'`. algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'}, \ default='lasso_lars' The algorithm used: * `'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 or float, default=None The regularization parameter. It corresponds to alpha when algorithm is `'lasso_lars'`, `'lasso_cd'` or `'threshold'`. Otherwise it corresponds to `n_nonzero_coefs`. init : ndarray of shape (n_samples, n_components), default=None Initialization value of the sparse code. Only used if `algorithm='lasso_cd'`. max_iter : int, default=1000 Maximum number of iterations to perform if `algorithm='lasso_cd'` or `'lasso_lars'`. copy_cov : bool, default=True Whether to copy the precomputed covariance matrix; if `False`, it may be overwritten. check_input : bool, default=True If `False`, the input arrays `X` and dictionary will not be checked. verbose : int, default=0 Controls the verbosity; the higher, the more messages. positive: bool, default=False Whether to enforce a positivity constraint on the sparse code. .. versionadded:: 0.20 Returns ------- code : ndarray 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) _check_positive_coding(algorithm, positive) 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, positive=positive, max_iter=max_iter) 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, positive=positive) 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) if positive: np.clip(new_code, 0, None, out=new_code) elif algorithm == 'omp': 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 @_deprecate_positional_args 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=None, check_input=True, verbose=0, positive=False): """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 : ndarray of shape (n_samples, n_features) Data matrix. dictionary : ndarray 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 : ndarray of shape (n_components, n_components), default=None Precomputed Gram matrix, `dictionary * dictionary'`. cov : ndarray of shape (n_components, n_samples), default=None Precomputed covariance, `dictionary' * X`. algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'}, \ default='lasso_lars' The algorithm used: * `'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'`. n_nonzero_coefs : int, default=None 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. If `None`, then `n_nonzero_coefs=int(n_features / 10)`. alpha : float, default=None 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`. If `None`, default to 1. copy_cov : bool, default=True Whether to copy the precomputed covariance matrix; if `False`, it may be overwritten. init : ndarray of shape (n_samples, n_components), default=None Initialization value of the sparse codes. Only used if `algorithm='lasso_cd'`. max_iter : int, default=1000 Maximum number of iterations to perform if `algorithm='lasso_cd'` or `'lasso_lars'`. n_jobs : int, default=None Number of parallel jobs to run. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. check_input : bool, default=True If `False`, the input arrays X and dictionary will not be checked. verbose : int, default=0 Controls the verbosity; the higher, the more messages. positive : bool, default=False Whether to enforce positivity when finding the encoding. .. versionadded:: 0.20 Returns ------- code : ndarray 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 effective_n_jobs(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, positive=positive) return code # Enter parallel code block code = np.empty((n_samples, n_components)) slices = list(gen_even_slices(n_samples, effective_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, verbose=verbose, positive=positive) 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, positive=False): """Update the dense dictionary factor in place. Parameters ---------- dictionary : ndarray of shape (n_features, n_components) Value of the dictionary at the previous iteration. Y : ndarray of shape (n_features, n_samples) Data matrix. code : ndarray of shape (n_components, n_samples) Sparse coding of the data against which to optimize the dictionary. verbose: bool, default=False Degree of output the procedure will print. return_r2 : bool, default=False Whether to compute and return the residual sum of squares corresponding to the computed solution. random_state : int, RandomState instance or None, default=None Used for randomly initializing the dictionary. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. positive : bool, default=False Whether to enforce positivity when finding the dictionary. .. versionadded:: 0.20 Returns ------- dictionary : ndarray of shape (n_features, n_components) Updated dictionary. """ n_components = len(code) n_features = Y.shape[0] random_state = check_random_state(random_state) # Get BLAS functions gemm, = linalg.get_blas_funcs(('gemm',), (dictionary, code, Y)) ger, = linalg.get_blas_funcs(('ger',), (dictionary, code)) nrm2, = linalg.get_blas_funcs(('nrm2',), (dictionary,)) # Residuals, computed with BLAS for speed and efficiency # R <- -1.0 * U * V^T + 1.0 * Y # Outputs R as Fortran array for efficiency R = gemm(-1.0, dictionary, code, 1.0, Y) 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, :]) if positive: np.clip(dictionary[:, k], 0, None, out=dictionary[:, k]) # Scale k'th atom # (U_k * U_k) ** 0.5 atom_norm = nrm2(dictionary[:, k]) if atom_norm < 1e-10: if verbose == 1: sys.stdout.write("+") sys.stdout.flush() elif verbose: print("Adding new random atom") dictionary[:, k] = random_state.randn(n_features) if positive: np.clip(dictionary[:, k], 0, None, out=dictionary[:, k]) # Setting corresponding coefs to 0 code[k, :] = 0.0 # (U_k * U_k) ** 0.5 atom_norm = nrm2(dictionary[:, k]) dictionary[:, k] /= atom_norm else: dictionary[:, k] /= atom_norm # 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 = nrm2(R) ** 2.0 return dictionary, R return dictionary @_deprecate_positional_args def dict_learning(X, n_components, *, alpha, max_iter=100, tol=1e-8, method='lars', n_jobs=None, dict_init=None, code_init=None, callback=None, verbose=False, random_state=None, return_n_iter=False, positive_dict=False, positive_code=False, method_max_iter=1000): """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 : ndarray 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, default=100 Maximum number of iterations to perform. tol : float, default=1e-8 Tolerance for the stopping condition. method : {'lars', 'cd'}, default='lars' The method used: * `'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, default=None Number of parallel jobs to run. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. dict_init : ndarray of shape (n_components, n_features), default=None Initial value for the dictionary for warm restart scenarios. code_init : ndarray of shape (n_samples, n_components), default=None Initial value for the sparse code for warm restart scenarios. callback : callable, default=None Callable that gets invoked every five iterations verbose : bool, default=False To control the verbosity of the procedure. random_state : int, RandomState instance or None, default=None Used for randomly initializing the dictionary. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. return_n_iter : bool, default=False Whether or not to return the number of iterations. positive_dict : bool, default=False Whether to enforce positivity when finding the dictionary. .. versionadded:: 0.20 positive_code : bool, default=False Whether to enforce positivity when finding the code. .. versionadded:: 0.20 method_max_iter : int, default=1000 Maximum number of iterations to perform. .. versionadded:: 0.22 Returns ------- code : ndarray of shape (n_samples, n_components) The sparse code factor in the matrix factorization. dictionary : ndarray 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) _check_positive_coding(method, positive_code) method = 'lasso_' + method t0 = time.time() # Avoid integer division problems alpha = float(alpha) random_state = check_random_state(random_state) # 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, positive=positive_code, max_iter=method_max_iter, verbose=verbose) # Update dictionary dictionary, residuals = _update_dict(dictionary.T, X.T, code.T, verbose=verbose, return_r2=True, random_state=random_state, positive=positive_dict) 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 @_deprecate_positional_args 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=None, method='lars', iter_offset=0, random_state=None, return_inner_stats=False, inner_stats=None, return_n_iter=False, positive_dict=False, positive_code=False, method_max_iter=1000): """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 : ndarray of shape (n_samples, n_features) Data matrix. n_components : int, default=2 Number of dictionary atoms to extract. alpha : float, default=1 Sparsity controlling parameter. n_iter : int, default=100 Number of mini-batch iterations to perform. return_code : bool, default=True Whether to also return the code U or just the dictionary `V`. dict_init : ndarray of shape (n_components, n_features), default=None Initial value for the dictionary for warm restart scenarios. callback : callable, default=None callable that gets invoked every five iterations. batch_size : int, default=3 The number of samples to take in each batch. verbose : bool, default=False To control the verbosity of the procedure. shuffle : bool, default=True Whether to shuffle the data before splitting it in batches. n_jobs : int, default=None Number of parallel jobs to run. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. method : {'lars', 'cd'}, default='lars' * `'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, default=None Used for initializing the dictionary when ``dict_init`` is not specified, randomly shuffling the data when ``shuffle`` is set to ``True``, and updating the dictionary. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. return_inner_stats : bool, default=False 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, default=None Inner sufficient statistics that are kept by the algorithm. Passing them at initialization is useful in online settings, to avoid losing 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, default=False Whether or not to return the number of iterations. positive_dict : bool, default=False Whether to enforce positivity when finding the dictionary. .. versionadded:: 0.20 positive_code : bool, default=False Whether to enforce positivity when finding the code. .. versionadded:: 0.20 method_max_iter : int, default=1000 Maximum number of iterations to perform when solving the lasso problem. .. versionadded:: 0.22 Returns ------- code : ndarray of shape (n_samples, n_components), The sparse code (only returned if `return_code=True`). dictionary : ndarray 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.') _check_positive_coding(method, positive_code) 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) # 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) dictionary = np.require(dictionary, requirements='W') 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, check_input=False, positive=positive_code, max_iter=method_max_iter, verbose=verbose).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, positive=positive_dict) # 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, positive=positive_code, max_iter=method_max_iter, verbose=verbose) 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 _BaseSparseCoding(TransformerMixin): """Base class from SparseCoder and DictionaryLearning algorithms.""" def __init__(self, transform_algorithm, transform_n_nonzero_coefs, transform_alpha, split_sign, n_jobs, positive_code, transform_max_iter): self.transform_algorithm = transform_algorithm self.transform_n_nonzero_coefs = transform_n_nonzero_coefs self.transform_alpha = transform_alpha self.transform_max_iter = transform_max_iter self.split_sign = split_sign self.n_jobs = n_jobs self.positive_code = positive_code def _transform(self, X, dictionary): """Private method allowing to accomodate both DictionaryLearning and SparseCoder.""" X = self._validate_data(X, reset=False) code = sparse_encode( X, dictionary, algorithm=self.transform_algorithm, n_nonzero_coefs=self.transform_n_nonzero_coefs, alpha=self.transform_alpha, max_iter=self.transform_max_iter, n_jobs=self.n_jobs, positive=self.positive_code) 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 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 : ndarray 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 : ndarray of shape (n_samples, n_components) Transformed data. """ check_is_fitted(self) return self._transform(X, self.components_) class SparseCoder(_BaseSparseCoding, BaseEstimator): """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 : ndarray of shape (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'}, default='omp' 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, default=None 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. If `None`, then `transform_n_nonzero_coefs=int(n_features / 10)`. transform_alpha : float, default=None 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`. If `None`, default to 1. split_sign : bool, default=False 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, default=None Number of parallel jobs to run. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. positive_code : bool, default=False Whether to enforce positivity when finding the code. .. versionadded:: 0.20 transform_max_iter : int, default=1000 Maximum number of iterations to perform if `algorithm='lasso_cd'` or `lasso_lars`. .. versionadded:: 0.22 Attributes ---------- components_ : ndarray of shape (n_components, n_features) The unchanged dictionary atoms. .. deprecated:: 0.24 This attribute is deprecated in 0.24 and will be removed in 1.1 (renaming of 0.26). Use `dictionary` instead. Examples -------- >>> import numpy as np >>> from sklearn.decomposition import SparseCoder >>> X = np.array([[-1, -1, -1], [0, 0, 3]]) >>> dictionary = np.array( ... [[0, 1, 0], ... [-1, -1, 2], ... [1, 1, 1], ... [0, 1, 1], ... [0, 2, 1]], ... dtype=np.float64 ... ) >>> coder = SparseCoder( ... dictionary=dictionary, transform_algorithm='lasso_lars', ... transform_alpha=1e-10, ... ) >>> coder.transform(X) array([[ 0., 0., -1., 0., 0.], [ 0., 1., 1., 0., 0.]]) See Also -------- DictionaryLearning MiniBatchDictionaryLearning SparsePCA MiniBatchSparsePCA sparse_encode """ _required_parameters = ["dictionary"] @_deprecate_positional_args def __init__(self, dictionary, *, transform_algorithm='omp', transform_n_nonzero_coefs=None, transform_alpha=None, split_sign=False, n_jobs=None, positive_code=False, transform_max_iter=1000): super().__init__( transform_algorithm, transform_n_nonzero_coefs, transform_alpha, split_sign, n_jobs, positive_code, transform_max_iter ) self.dictionary = 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 """ return self @deprecated("The attribute 'components_' is deprecated " # type: ignore "in 0.24 and will be removed in 1.1 (renaming of 0.26). Use " "the 'dictionary' instead.") @property def components_(self): return self.dictionary 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 : ndarray 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 : ndarray of shape (n_samples, n_components) Transformed data. """ return super()._transform(X, self.dictionary) def _more_tags(self): return {"requires_fit": False} @property def n_components_(self): return self.dictionary.shape[0] @property def n_features_in_(self): return self.dictionary.shape[1] class DictionaryLearning(_BaseSparseCoding, BaseEstimator): """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 || X - 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, default=n_features Number of dictionary elements to extract. alpha : float, default=1.0 Sparsity controlling parameter. max_iter : int, default=1000 Maximum number of iterations to perform. tol : float, default=1e-8 Tolerance for numerical error. fit_algorithm : {'lars', 'cd'}, default='lars' * `'lars'`: uses the least angle regression method to solve the lasso problem (:func:`~sklearn.linear_model.lars_path`); * `'cd'`: uses the coordinate descent method to compute the Lasso solution (:class:`~sklearn.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'}, default='omp' Algorithm used to transform the data: - `'lars'`: uses the least angle regression method (:func:`~sklearn.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 (:class:`~sklearn.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, default=None 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. If `None`, then `transform_n_nonzero_coefs=int(n_features / 10)`. transform_alpha : float, default=None 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`. If `None`, default to 1.0 n_jobs : int or None, default=None Number of parallel jobs to run. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. code_init : ndarray of shape (n_samples, n_components), default=None Initial value for the code, for warm restart. dict_init : ndarray of shape (n_components, n_features), default=None Initial values for the dictionary, for warm restart. verbose : bool, default=False To control the verbosity of the procedure. split_sign : bool, default=False 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, default=None Used for initializing the dictionary when ``dict_init`` is not specified, randomly shuffling the data when ``shuffle`` is set to ``True``, and updating the dictionary. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. positive_code : bool, default=False Whether to enforce positivity when finding the code. .. versionadded:: 0.20 positive_dict : bool, default=False Whether to enforce positivity when finding the dictionary .. versionadded:: 0.20 transform_max_iter : int, default=1000 Maximum number of iterations to perform if `algorithm='lasso_cd'` or `'lasso_lars'`. .. versionadded:: 0.22 Attributes ---------- components_ : ndarray of shape (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. Examples -------- >>> import numpy as np >>> from sklearn.datasets import make_sparse_coded_signal >>> from sklearn.decomposition import DictionaryLearning >>> X, dictionary, code = make_sparse_coded_signal( ... n_samples=100, n_components=15, n_features=20, n_nonzero_coefs=10, ... random_state=42, ... ) >>> dict_learner = DictionaryLearning( ... n_components=15, transform_algorithm='lasso_lars', random_state=42, ... ) >>> X_transformed = dict_learner.fit_transform(X) We can check the level of sparsity of `X_transformed`: >>> np.mean(X_transformed == 0) 0.88... We can compare the average squared euclidean norm of the reconstruction error of the sparse coded signal relative to the squared euclidean norm of the original signal: >>> X_hat = X_transformed @ dict_learner.components_ >>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1)) 0.07... Notes ----- **References:** J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning for sparse coding (https://www.di.ens.fr/sierra/pdfs/icml09.pdf) See Also -------- SparseCoder MiniBatchDictionaryLearning SparsePCA MiniBatchSparsePCA """ @_deprecate_positional_args 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=None, code_init=None, dict_init=None, verbose=False, split_sign=False, random_state=None, positive_code=False, positive_dict=False, transform_max_iter=1000): super().__init__( transform_algorithm, transform_n_nonzero_coefs, transform_alpha, split_sign, n_jobs, positive_code, transform_max_iter ) self.n_components = n_components 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 self.positive_dict = positive_dict def fit(self, X, y=None): """Fit the model from data in X. Parameters ---------- X : array-like of 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 = self._validate_data(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, alpha=self.alpha, tol=self.tol, max_iter=self.max_iter, method=self.fit_algorithm, method_max_iter=self.transform_max_iter, 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, positive_dict=self.positive_dict, positive_code=self.positive_code) self.components_ = U self.error_ = E return self class MiniBatchDictionaryLearning(_BaseSparseCoding, BaseEstimator): """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 || X - 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, default=None Number of dictionary elements to extract. alpha : float, default=1 Sparsity controlling parameter. n_iter : int, default=1000 Total number of iterations to perform. fit_algorithm : {'lars', 'cd'}, default='lars' The algorithm used: - `'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, default=None Number of parallel jobs to run. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. batch_size : int, default=3 Number of samples in each mini-batch. shuffle : bool, default=True Whether to shuffle the samples before forming batches. dict_init : ndarray of shape (n_components, n_features), default=None initial value of the dictionary for warm restart scenarios transform_algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', \ 'threshold'}, default='omp' 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, default=None 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. If `None`, then `transform_n_nonzero_coefs=int(n_features / 10)`. transform_alpha : float, default=None 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`. If `None`, default to 1. verbose : bool, default=False To control the verbosity of the procedure. split_sign : bool, default=False 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, default=None Used for initializing the dictionary when ``dict_init`` is not specified, randomly shuffling the data when ``shuffle`` is set to ``True``, and updating the dictionary. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. positive_code : bool, default=False Whether to enforce positivity when finding the code. .. versionadded:: 0.20 positive_dict : bool, default=False Whether to enforce positivity when finding the dictionary. .. versionadded:: 0.20 transform_max_iter : int, default=1000 Maximum number of iterations to perform if `algorithm='lasso_cd'` or `'lasso_lars'`. .. versionadded:: 0.22 Attributes ---------- components_ : ndarray of shape (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 losing 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. iter_offset_ : int The number of iteration on data batches that has been performed before. random_state_ : RandomState instance RandomState instance that is generated either from a seed, the random number generattor or by `np.random`. Examples -------- >>> import numpy as np >>> from sklearn.datasets import make_sparse_coded_signal >>> from sklearn.decomposition import MiniBatchDictionaryLearning >>> X, dictionary, code = make_sparse_coded_signal( ... n_samples=100, n_components=15, n_features=20, n_nonzero_coefs=10, ... random_state=42) >>> dict_learner = MiniBatchDictionaryLearning( ... n_components=15, transform_algorithm='lasso_lars', random_state=42, ... ) >>> X_transformed = dict_learner.fit_transform(X) We can check the level of sparsity of `X_transformed`: >>> np.mean(X_transformed == 0) 0.87... We can compare the average squared euclidean norm of the reconstruction error of the sparse coded signal relative to the squared euclidean norm of the original signal: >>> X_hat = X_transformed @ dict_learner.components_ >>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1)) 0.10... Notes ----- **References:** J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning for sparse coding (https://www.di.ens.fr/sierra/pdfs/icml09.pdf) See Also -------- SparseCoder DictionaryLearning SparsePCA MiniBatchSparsePCA """ @_deprecate_positional_args def __init__(self, n_components=None, *, alpha=1, n_iter=1000, fit_algorithm='lars', n_jobs=None, 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, positive_code=False, positive_dict=False, transform_max_iter=1000): super().__init__( transform_algorithm, transform_n_nonzero_coefs, transform_alpha, split_sign, n_jobs, positive_code, transform_max_iter ) self.n_components = n_components 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 self.positive_dict = positive_dict def fit(self, X, y=None): """Fit the model from data in X. Parameters ---------- X : array-like of 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 = self._validate_data(X) U, (A, B), self.n_iter_ = dict_learning_online( X, self.n_components, alpha=self.alpha, n_iter=self.n_iter, return_code=False, method=self.fit_algorithm, method_max_iter=self.transform_max_iter, 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, positive_dict=self.positive_dict, positive_code=self.positive_code) 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 self.random_state_ = random_state 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 of 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 : int, default=None 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) 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) X = self._validate_data(X, reset=(iter_offset == 0)) U, (A, B) = dict_learning_online( X, self.n_components, alpha=self.alpha, n_iter=1, method=self.fit_algorithm, method_max_iter=self.transform_max_iter, 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, positive_dict=self.positive_dict, positive_code=self.positive_code) 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 + 1 return self