"""Dictionary learning.""" # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause import itertools import sys import time from numbers import Integral, Real import numpy as np from joblib import effective_n_jobs from scipy import linalg from ..base import ( BaseEstimator, ClassNamePrefixFeaturesOutMixin, TransformerMixin, _fit_context, ) from ..linear_model import Lars, Lasso, LassoLars, orthogonal_mp_gram from ..utils import check_array, check_random_state, gen_batches, gen_even_slices from ..utils._param_validation import Interval, StrOptions, validate_params from ..utils.extmath import randomized_svd, row_norms, svd_flip from ..utils.parallel import Parallel, delayed from ..utils.validation import check_is_fitted, validate_data 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_precomputed( X, dictionary, *, gram=None, cov=None, algorithm="lasso_lars", regularization=None, copy_cov=True, init=None, max_iter=1000, verbose=0, positive=False, ): """Generic sparse coding with precomputed Gram and/or covariance matrices. Each row 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), default=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. 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. """ n_samples, n_features = X.shape n_components = dictionary.shape[0] 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, 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, precompute=gram, max_iter=max_iter, warm_start=True, positive=positive, ) if init is not None: # In some workflows using coordinate descent algorithms: # - users might provide NumPy arrays with read-only buffers # - `joblib` might memmap arrays making their buffer read-only # TODO: move this handling (which is currently too broad) # closer to the actual private function which need buffers to be writable. if not init.flags["WRITEABLE"]: init = np.array(init) clf.coef_ = init clf.fit(dictionary.T, X.T, check_input=False) 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, 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 return new_code.reshape(n_samples, n_components) @validate_params( { "X": ["array-like"], "dictionary": ["array-like"], "gram": ["array-like", None], "cov": ["array-like", None], "algorithm": [ StrOptions({"lasso_lars", "lasso_cd", "lars", "omp", "threshold"}) ], "n_nonzero_coefs": [Interval(Integral, 1, None, closed="left"), None], "alpha": [Interval(Real, 0, None, closed="left"), None], "copy_cov": ["boolean"], "init": ["array-like", None], "max_iter": [Interval(Integral, 0, None, closed="left")], "n_jobs": [Integral, None], "check_input": ["boolean"], "verbose": ["verbose"], "positive": ["boolean"], }, prefer_skip_nested_validation=True, ) # 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=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 : array-like of shape (n_samples, n_features) Data matrix. dictionary : array-like 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-like of shape (n_components, n_components), default=None Precomputed Gram matrix, `dictionary * dictionary'`. cov : array-like 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 : Compute Least Angle Regression or Lasso path using LARS algorithm. sklearn.linear_model.orthogonal_mp : Solves Orthogonal Matching Pursuit problems. sklearn.linear_model.Lasso : Train Linear Model with L1 prior as regularizer. SparseCoder : Find a sparse representation of data from a fixed precomputed dictionary. Examples -------- >>> import numpy as np >>> from sklearn.decomposition import sparse_encode >>> 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 ... ) >>> sparse_encode(X, dictionary, alpha=1e-10) array([[ 0., 0., -1., 0., 0.], [ 0., 1., 1., 0., 0.]]) """ if check_input: if algorithm == "lasso_cd": dictionary = check_array( dictionary, order="C", dtype=[np.float64, np.float32] ) X = check_array(X, order="C", dtype=[np.float64, np.float32]) else: dictionary = check_array(dictionary) X = check_array(X) 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) ) _check_positive_coding(algorithm, positive) return _sparse_encode( X, dictionary, gram=gram, cov=cov, algorithm=algorithm, n_nonzero_coefs=n_nonzero_coefs, alpha=alpha, copy_cov=copy_cov, init=init, max_iter=max_iter, n_jobs=n_jobs, verbose=verbose, positive=positive, ) 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, verbose=0, positive=False, ): """Sparse coding without input/parameter validation.""" n_samples, n_features = X.shape n_components = dictionary.shape[0] 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 = 1.0 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 effective_n_jobs(n_jobs) == 1 or algorithm == "threshold": code = _sparse_encode_precomputed( X, dictionary, gram=gram, cov=cov, algorithm=algorithm, regularization=regularization, copy_cov=copy_cov, init=init, max_iter=max_iter, verbose=verbose, positive=positive, ) return code # Enter parallel code block n_samples = X.shape[0] n_components = dictionary.shape[0] 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_precomputed)( X[this_slice], dictionary, gram=gram, cov=cov[:, this_slice] if cov is not None else None, algorithm=algorithm, regularization=regularization, copy_cov=copy_cov, init=init[this_slice] if init is not None else None, max_iter=max_iter, 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, A=None, B=None, verbose=False, random_state=None, positive=False, ): """Update the dense dictionary factor in place. Parameters ---------- dictionary : ndarray of shape (n_components, n_features) Value of the dictionary at the previous iteration. Y : ndarray of shape (n_samples, n_features) Data matrix. code : ndarray of shape (n_samples, n_components) Sparse coding of the data against which to optimize the dictionary. A : ndarray of shape (n_components, n_components), default=None Together with `B`, sufficient stats of the online model to update the dictionary. B : ndarray of shape (n_features, n_components), default=None Together with `A`, sufficient stats of the online model to update the dictionary. verbose: bool, default=False Degree of output the procedure will print. 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 """ n_samples, n_components = code.shape random_state = check_random_state(random_state) if A is None: A = code.T @ code if B is None: B = Y.T @ code n_unused = 0 for k in range(n_components): if A[k, k] > 1e-6: # 1e-6 is arbitrary but consistent with the spams implementation dictionary[k] += (B[:, k] - A[k] @ dictionary) / A[k, k] else: # kth atom is almost never used -> sample a new one from the data newd = Y[random_state.choice(n_samples)] # add small noise to avoid making the sparse coding ill conditioned noise_level = 0.01 * (newd.std() or 1) # avoid 0 std noise = random_state.normal(0, noise_level, size=len(newd)) dictionary[k] = newd + noise code[:, k] = 0 n_unused += 1 if positive: np.clip(dictionary[k], 0, None, out=dictionary[k]) # Projection on the constraint set ||V_k|| <= 1 dictionary[k] /= max(linalg.norm(dictionary[k]), 1) if verbose and n_unused > 0: print(f"{n_unused} unused atoms resampled.") def _dict_learning( X, n_components, *, alpha, max_iter, tol, method, n_jobs, dict_init, code_init, callback, verbose, random_state, return_n_iter, positive_dict, positive_code, method_max_iter, ): """Main dictionary learning algorithm""" t0 = time.time() # 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) # flip the initial code's sign to enforce deterministic output code, dictionary = svd_flip(code, dictionary) 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 better suited for the sparse coding which is the # bottleneck of this algorithm. dictionary = np.asfortranarray(dictionary) 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 in place _update_dict( dictionary, X, code, verbose=verbose, random_state=random_state, positive=positive_dict, ) # Cost function current_cost = 0.5 * np.sum((X - code @ dictionary) ** 2) + 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 @validate_params( { "X": ["array-like"], "return_code": ["boolean"], "method": [StrOptions({"cd", "lars"})], "method_max_iter": [Interval(Integral, 0, None, closed="left")], }, prefer_skip_nested_validation=False, ) def dict_learning_online( X, n_components=2, *, alpha=1, max_iter=100, return_code=True, dict_init=None, callback=None, batch_size=256, verbose=False, shuffle=True, n_jobs=None, method="lars", random_state=None, positive_dict=False, positive_code=False, method_max_iter=1000, tol=1e-3, max_no_improvement=10, ): """Solve 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 ||_Fro^2 + alpha * || U ||_1,1 (U,V) with || V_k ||_2 = 1 for all 0 <= k < n_components where V is the dictionary and U is the sparse code. ||.||_Fro stands for the Frobenius norm and ||.||_1,1 stands for the entry-wise matrix norm which is the sum of the absolute values of all the entries in the matrix. This is accomplished by repeatedly iterating over mini-batches by slicing the input data. Read more in the :ref:`User Guide `. Parameters ---------- X : array-like of shape (n_samples, n_features) Data matrix. n_components : int or None, default=2 Number of dictionary atoms to extract. If None, then ``n_components`` is set to ``n_features``. alpha : float, default=1 Sparsity controlling parameter. max_iter : int, default=100 Maximum number of iterations over the complete dataset before stopping independently of any early stopping criterion heuristics. .. versionadded:: 1.1 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 values for the dictionary for warm restart scenarios. If `None`, the initial values for the dictionary are created with an SVD decomposition of the data via :func:`~sklearn.utils.extmath.randomized_svd`. callback : callable, default=None A callable that gets invoked at the end of each iteration. batch_size : int, default=256 The number of samples to take in each batch. .. versionchanged:: 1.3 The default value of `batch_size` changed from 3 to 256 in version 1.3. 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. 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_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 tol : float, default=1e-3 Control early stopping based on the norm of the differences in the dictionary between 2 steps. To disable early stopping based on changes in the dictionary, set `tol` to 0.0. .. versionadded:: 1.1 max_no_improvement : int, default=10 Control early stopping based on the consecutive number of mini batches that does not yield an improvement on the smoothed cost function. To disable convergence detection based on cost function, set `max_no_improvement` to None. .. versionadded:: 1.1 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 : Solve a dictionary learning matrix factorization problem. DictionaryLearning : Find a dictionary that sparsely encodes data. MiniBatchDictionaryLearning : A faster, less accurate, version of the dictionary learning algorithm. SparsePCA : Sparse Principal Components Analysis. MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis. Examples -------- >>> import numpy as np >>> from sklearn.datasets import make_sparse_coded_signal >>> from sklearn.decomposition import dict_learning_online >>> X, _, _ = make_sparse_coded_signal( ... n_samples=30, n_components=15, n_features=20, n_nonzero_coefs=10, ... random_state=42, ... ) >>> U, V = dict_learning_online( ... X, n_components=15, alpha=0.2, max_iter=20, batch_size=3, random_state=42 ... ) We can check the level of sparsity of `U`: >>> np.mean(U == 0) np.float64(0.53...) 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 = U @ V >>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1)) np.float64(0.05...) """ transform_algorithm = "lasso_" + method est = MiniBatchDictionaryLearning( n_components=n_components, alpha=alpha, max_iter=max_iter, n_jobs=n_jobs, fit_algorithm=method, batch_size=batch_size, shuffle=shuffle, dict_init=dict_init, random_state=random_state, transform_algorithm=transform_algorithm, transform_alpha=alpha, positive_code=positive_code, positive_dict=positive_dict, transform_max_iter=method_max_iter, verbose=verbose, callback=callback, tol=tol, max_no_improvement=max_no_improvement, ).fit(X) if not return_code: return est.components_ else: code = est.transform(X) return code, est.components_ @validate_params( { "X": ["array-like"], "method": [StrOptions({"lars", "cd"})], "return_n_iter": ["boolean"], "method_max_iter": [Interval(Integral, 0, None, closed="left")], }, prefer_skip_nested_validation=False, ) 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, ): """Solve 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 ||_Fro^2 + alpha * || U ||_1,1 (U,V) with || V_k ||_2 = 1 for all 0 <= k < n_components where V is the dictionary and U is the sparse code. ||.||_Fro stands for the Frobenius norm and ||.||_1,1 stands for the entry-wise matrix norm which is the sum of the absolute values of all the entries in the matrix. Read more in the :ref:`User Guide `. Parameters ---------- X : array-like of shape (n_samples, n_features) Data matrix. n_components : int Number of dictionary atoms to extract. alpha : int or float 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. Only used if `code_init` and `dict_init` are not None. code_init : ndarray of shape (n_samples, n_components), default=None Initial value for the sparse code for warm restart scenarios. Only used if `code_init` and `dict_init` are not None. 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 : Solve a dictionary learning matrix factorization problem online. DictionaryLearning : Find a dictionary that sparsely encodes data. MiniBatchDictionaryLearning : A faster, less accurate version of the dictionary learning algorithm. SparsePCA : Sparse Principal Components Analysis. MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis. Examples -------- >>> import numpy as np >>> from sklearn.datasets import make_sparse_coded_signal >>> from sklearn.decomposition import dict_learning >>> X, _, _ = make_sparse_coded_signal( ... n_samples=30, n_components=15, n_features=20, n_nonzero_coefs=10, ... random_state=42, ... ) >>> U, V, errors = dict_learning(X, n_components=15, alpha=0.1, random_state=42) We can check the level of sparsity of `U`: >>> np.mean(U == 0) np.float64(0.6...) 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 = U @ V >>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1)) np.float64(0.01...) """ estimator = DictionaryLearning( n_components=n_components, alpha=alpha, max_iter=max_iter, tol=tol, fit_algorithm=method, n_jobs=n_jobs, dict_init=dict_init, callback=callback, code_init=code_init, verbose=verbose, random_state=random_state, positive_code=positive_code, positive_dict=positive_dict, transform_max_iter=method_max_iter, ).set_output(transform="default") code = estimator.fit_transform(X) if return_n_iter: return ( code, estimator.components_, estimator.error_, estimator.n_iter_, ) return code, estimator.components_, estimator.error_ class _BaseSparseCoding(ClassNamePrefixFeaturesOutMixin, 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 accommodate both DictionaryLearning and SparseCoder.""" X = validate_data(self, X, reset=False) if hasattr(self, "alpha") and self.transform_alpha is None: transform_alpha = self.alpha else: transform_alpha = self.transform_alpha code = sparse_encode( X, dictionary, algorithm=self.transform_algorithm, n_nonzero_coefs=self.transform_n_nonzero_coefs, alpha=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 ---------- n_components_ : int Number of atoms. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- DictionaryLearning : Find a dictionary that sparsely encodes data. MiniBatchDictionaryLearning : A faster, less accurate, version of the dictionary learning algorithm. MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis. SparsePCA : Sparse Principal Components Analysis. sparse_encode : Sparse coding where each row of the result is the solution to a sparse coding problem. 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.]]) """ 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 Not used, present for API consistency by convention. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Returns the instance itself. """ return self 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) Training vector, where `n_samples` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. Returns ------- X_new : ndarray of shape (n_samples, n_components) Transformed data. """ return super()._transform(X, self.dictionary) def __sklearn_tags__(self): tags = super().__sklearn_tags__() tags.requires_fit = False tags.transformer_tags.preserves_dtype = ["float64", "float32"] return tags @property def n_components_(self): """Number of atoms.""" return self.dictionary.shape[0] @property def n_features_in_(self): """Number of features seen during `fit`.""" return self.dictionary.shape[1] @property def _n_features_out(self): """Number of transformed output features.""" return self.n_components_ class DictionaryLearning(_BaseSparseCoding, BaseEstimator): """Dictionary learning. Finds a dictionary (a set of atoms) that performs well at sparsely encoding the fitted data. Solves the optimization problem:: (U^*,V^*) = argmin 0.5 || X - U V ||_Fro^2 + alpha * || U ||_1,1 (U,V) with || V_k ||_2 <= 1 for all 0 <= k < n_components ||.||_Fro stands for the Frobenius norm and ||.||_1,1 stands for the entry-wise matrix norm which is the sum of the absolute values of all the entries in the matrix. Read more in the :ref:`User Guide `. Parameters ---------- n_components : int, default=None Number of dictionary elements to extract. If None, then ``n_components`` is set to ``n_features``. 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'`. 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 `None`, defaults to `alpha`. .. versionchanged:: 1.2 When None, default value changed from 1.0 to `alpha`. 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. Only used if `code_init` and `dict_init` are not None. dict_init : ndarray of shape (n_components, n_features), default=None Initial values for the dictionary, for warm restart. Only used if `code_init` and `dict_init` are not None. callback : callable, default=None Callable that gets invoked every five iterations. .. versionadded:: 1.3 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_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 n_iter_ : int Number of iterations run. See Also -------- MiniBatchDictionaryLearning: A faster, less accurate, version of the dictionary learning algorithm. MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis. SparseCoder : Find a sparse representation of data from a fixed, precomputed dictionary. SparsePCA : Sparse Principal Components Analysis. References ---------- J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning for sparse coding (https://www.di.ens.fr/~fbach/mairal_icml09.pdf) 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=30, n_components=15, n_features=20, n_nonzero_coefs=10, ... random_state=42, ... ) >>> dict_learner = DictionaryLearning( ... n_components=15, transform_algorithm='lasso_lars', transform_alpha=0.1, ... random_state=42, ... ) >>> X_transformed = dict_learner.fit(X).transform(X) We can check the level of sparsity of `X_transformed`: >>> np.mean(X_transformed == 0) np.float64(0.52...) 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)) np.float64(0.05...) """ _parameter_constraints: dict = { "n_components": [Interval(Integral, 1, None, closed="left"), None], "alpha": [Interval(Real, 0, None, closed="left")], "max_iter": [Interval(Integral, 0, None, closed="left")], "tol": [Interval(Real, 0, None, closed="left")], "fit_algorithm": [StrOptions({"lars", "cd"})], "transform_algorithm": [ StrOptions({"lasso_lars", "lasso_cd", "lars", "omp", "threshold"}) ], "transform_n_nonzero_coefs": [Interval(Integral, 1, None, closed="left"), None], "transform_alpha": [Interval(Real, 0, None, closed="left"), None], "n_jobs": [Integral, None], "code_init": [np.ndarray, None], "dict_init": [np.ndarray, None], "callback": [callable, None], "verbose": ["verbose"], "split_sign": ["boolean"], "random_state": ["random_state"], "positive_code": ["boolean"], "positive_dict": ["boolean"], "transform_max_iter": [Interval(Integral, 0, None, closed="left")], } 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, callback=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.callback = callback 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` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Returns the instance itself. """ self.fit_transform(X) return self @_fit_context(prefer_skip_nested_validation=True) def fit_transform(self, X, y=None): """Fit the model from data in X and return the transformed data. Parameters ---------- X : array-like of shape (n_samples, n_features) Training vector, where `n_samples` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. Returns ------- V : ndarray of shape (n_samples, n_components) Transformed data. """ _check_positive_coding(method=self.fit_algorithm, positive=self.positive_code) method = "lasso_" + self.fit_algorithm random_state = check_random_state(self.random_state) X = validate_data(self, 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=method, method_max_iter=self.transform_max_iter, n_jobs=self.n_jobs, code_init=self.code_init, dict_init=self.dict_init, callback=self.callback, 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 V @property def _n_features_out(self): """Number of transformed output features.""" return self.components_.shape[0] def __sklearn_tags__(self): tags = super().__sklearn_tags__() tags.transformer_tags.preserves_dtype = ["float64", "float32"] return tags class MiniBatchDictionaryLearning(_BaseSparseCoding, BaseEstimator): """Mini-batch dictionary learning. Finds a dictionary (a set of atoms) that performs well at sparsely encoding the fitted data. Solves the optimization problem:: (U^*,V^*) = argmin 0.5 || X - U V ||_Fro^2 + alpha * || U ||_1,1 (U,V) with || V_k ||_2 <= 1 for all 0 <= k < n_components ||.||_Fro stands for the Frobenius norm and ||.||_1,1 stands for the entry-wise matrix norm which is the sum of the absolute values of all the entries in the matrix. 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. max_iter : int, default=1_000 Maximum number of iterations over the complete dataset before stopping independently of any early stopping criterion heuristics. .. versionadded:: 1.1 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=256 Number of samples in each mini-batch. .. versionchanged:: 1.3 The default value of `batch_size` changed from 3 to 256 in version 1.3. 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'`. 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 `None`, defaults to `alpha`. .. versionchanged:: 1.2 When None, default value changed from 1.0 to `alpha`. verbose : bool or int, 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 callback : callable, default=None A callable that gets invoked at the end of each iteration. .. versionadded:: 1.1 tol : float, default=1e-3 Control early stopping based on the norm of the differences in the dictionary between 2 steps. To disable early stopping based on changes in the dictionary, set `tol` to 0.0. .. versionadded:: 1.1 max_no_improvement : int, default=10 Control early stopping based on the consecutive number of mini batches that does not yield an improvement on the smoothed cost function. To disable convergence detection based on cost function, set `max_no_improvement` to None. .. versionadded:: 1.1 Attributes ---------- components_ : ndarray of shape (n_components, n_features) Components extracted from the data. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 n_iter_ : int Number of iterations over the full dataset. n_steps_ : int Number of mini-batches processed. .. versionadded:: 1.1 See Also -------- DictionaryLearning : Find a dictionary that sparsely encodes data. MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis. SparseCoder : Find a sparse representation of data from a fixed, precomputed dictionary. SparsePCA : Sparse Principal Components Analysis. References ---------- J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning for sparse coding (https://www.di.ens.fr/~fbach/mairal_icml09.pdf) 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=30, n_components=15, n_features=20, n_nonzero_coefs=10, ... random_state=42) >>> dict_learner = MiniBatchDictionaryLearning( ... n_components=15, batch_size=3, transform_algorithm='lasso_lars', ... transform_alpha=0.1, max_iter=20, 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) > 0.5 np.True_ 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)) np.float64(0.052...) """ _parameter_constraints: dict = { "n_components": [Interval(Integral, 1, None, closed="left"), None], "alpha": [Interval(Real, 0, None, closed="left")], "max_iter": [Interval(Integral, 0, None, closed="left")], "fit_algorithm": [StrOptions({"cd", "lars"})], "n_jobs": [None, Integral], "batch_size": [Interval(Integral, 1, None, closed="left")], "shuffle": ["boolean"], "dict_init": [None, np.ndarray], "transform_algorithm": [ StrOptions({"lasso_lars", "lasso_cd", "lars", "omp", "threshold"}) ], "transform_n_nonzero_coefs": [Interval(Integral, 1, None, closed="left"), None], "transform_alpha": [Interval(Real, 0, None, closed="left"), None], "verbose": ["verbose"], "split_sign": ["boolean"], "random_state": ["random_state"], "positive_code": ["boolean"], "positive_dict": ["boolean"], "transform_max_iter": [Interval(Integral, 0, None, closed="left")], "callback": [None, callable], "tol": [Interval(Real, 0, None, closed="left")], "max_no_improvement": [Interval(Integral, 0, None, closed="left"), None], } def __init__( self, n_components=None, *, alpha=1, max_iter=1_000, fit_algorithm="lars", n_jobs=None, batch_size=256, 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, callback=None, tol=1e-3, max_no_improvement=10, ): 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.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 self.callback = callback self.max_no_improvement = max_no_improvement self.tol = tol def _check_params(self, X): # n_components self._n_components = self.n_components if self._n_components is None: self._n_components = X.shape[1] # fit_algorithm _check_positive_coding(self.fit_algorithm, self.positive_code) self._fit_algorithm = "lasso_" + self.fit_algorithm # batch_size self._batch_size = min(self.batch_size, X.shape[0]) def _initialize_dict(self, X, random_state): """Initialization of the dictionary.""" if self.dict_init is not None: dictionary = self.dict_init else: # Init V with SVD of X _, S, dictionary = randomized_svd( X, self._n_components, random_state=random_state ) dictionary = S[:, np.newaxis] * dictionary if self._n_components <= len(dictionary): dictionary = dictionary[: self._n_components, :] else: dictionary = np.concatenate( ( dictionary, np.zeros( (self._n_components - len(dictionary), dictionary.shape[1]), dtype=dictionary.dtype, ), ) ) dictionary = check_array(dictionary, order="F", dtype=X.dtype, copy=False) dictionary = np.require(dictionary, requirements="W") return dictionary def _update_inner_stats(self, X, code, batch_size, step): """Update the inner stats inplace.""" if step < batch_size - 1: theta = (step + 1) * batch_size else: theta = batch_size**2 + step + 1 - batch_size beta = (theta + 1 - batch_size) / (theta + 1) self._A *= beta self._A += code.T @ code / batch_size self._B *= beta self._B += X.T @ code / batch_size def _minibatch_step(self, X, dictionary, random_state, step): """Perform the update on the dictionary for one minibatch.""" batch_size = X.shape[0] # Compute code for this batch code = _sparse_encode( X, dictionary, algorithm=self._fit_algorithm, alpha=self.alpha, n_jobs=self.n_jobs, positive=self.positive_code, max_iter=self.transform_max_iter, verbose=self.verbose, ) batch_cost = ( 0.5 * ((X - code @ dictionary) ** 2).sum() + self.alpha * np.sum(np.abs(code)) ) / batch_size # Update inner stats self._update_inner_stats(X, code, batch_size, step) # Update dictionary _update_dict( dictionary, X, code, self._A, self._B, verbose=self.verbose, random_state=random_state, positive=self.positive_dict, ) return batch_cost def _check_convergence( self, X, batch_cost, new_dict, old_dict, n_samples, step, n_steps ): """Helper function to encapsulate the early stopping logic. Early stopping is based on two factors: - A small change of the dictionary between two minibatch updates. This is controlled by the tol parameter. - No more improvement on a smoothed estimate of the objective function for a a certain number of consecutive minibatch updates. This is controlled by the max_no_improvement parameter. """ batch_size = X.shape[0] # counts steps starting from 1 for user friendly verbose mode. step = step + 1 # Ignore 100 first steps or 1 epoch to avoid initializing the ewa_cost with a # too bad value if step <= min(100, n_samples / batch_size): if self.verbose: print(f"Minibatch step {step}/{n_steps}: mean batch cost: {batch_cost}") return False # Compute an Exponentially Weighted Average of the cost function to # monitor the convergence while discarding minibatch-local stochastic # variability: https://en.wikipedia.org/wiki/Moving_average if self._ewa_cost is None: self._ewa_cost = batch_cost else: alpha = batch_size / (n_samples + 1) alpha = min(alpha, 1) self._ewa_cost = self._ewa_cost * (1 - alpha) + batch_cost * alpha if self.verbose: print( f"Minibatch step {step}/{n_steps}: mean batch cost: " f"{batch_cost}, ewa cost: {self._ewa_cost}" ) # Early stopping based on change of dictionary dict_diff = linalg.norm(new_dict - old_dict) / self._n_components if self.tol > 0 and dict_diff <= self.tol: if self.verbose: print(f"Converged (small dictionary change) at step {step}/{n_steps}") return True # Early stopping heuristic due to lack of improvement on smoothed # cost function if self._ewa_cost_min is None or self._ewa_cost < self._ewa_cost_min: self._no_improvement = 0 self._ewa_cost_min = self._ewa_cost else: self._no_improvement += 1 if ( self.max_no_improvement is not None and self._no_improvement >= self.max_no_improvement ): if self.verbose: print( "Converged (lack of improvement in objective function) " f"at step {step}/{n_steps}" ) return True return False @_fit_context(prefer_skip_nested_validation=True) 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` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Returns the instance itself. """ X = validate_data( self, X, dtype=[np.float64, np.float32], order="C", copy=False ) self._check_params(X) self._random_state = check_random_state(self.random_state) dictionary = self._initialize_dict(X, self._random_state) old_dict = dictionary.copy() if self.shuffle: X_train = X.copy() self._random_state.shuffle(X_train) else: X_train = X n_samples, n_features = X_train.shape if self.verbose: print("[dict_learning]") # Inner stats self._A = np.zeros( (self._n_components, self._n_components), dtype=X_train.dtype ) self._B = np.zeros((n_features, self._n_components), dtype=X_train.dtype) # Attributes to monitor the convergence self._ewa_cost = None self._ewa_cost_min = None self._no_improvement = 0 batches = gen_batches(n_samples, self._batch_size) batches = itertools.cycle(batches) n_steps_per_iter = int(np.ceil(n_samples / self._batch_size)) n_steps = self.max_iter * n_steps_per_iter i = -1 # to allow max_iter = 0 for i, batch in zip(range(n_steps), batches): X_batch = X_train[batch] batch_cost = self._minibatch_step( X_batch, dictionary, self._random_state, i ) if self._check_convergence( X_batch, batch_cost, dictionary, old_dict, n_samples, i, n_steps ): break # XXX callback param added for backward compat in #18975 but a common # unified callback API should be preferred if self.callback is not None: self.callback(locals()) old_dict[:] = dictionary self.n_steps_ = i + 1 self.n_iter_ = np.ceil(self.n_steps_ / n_steps_per_iter) self.components_ = dictionary return self @_fit_context(prefer_skip_nested_validation=True) def partial_fit(self, X, y=None): """Update 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` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Return the instance itself. """ has_components = hasattr(self, "components_") X = validate_data( self, X, dtype=[np.float64, np.float32], order="C", reset=not has_components ) if not has_components: # This instance has not been fitted yet (fit or partial_fit) self._check_params(X) self._random_state = check_random_state(self.random_state) dictionary = self._initialize_dict(X, self._random_state) self.n_steps_ = 0 self._A = np.zeros((self._n_components, self._n_components), dtype=X.dtype) self._B = np.zeros((X.shape[1], self._n_components), dtype=X.dtype) else: dictionary = self.components_ self._minibatch_step(X, dictionary, self._random_state, self.n_steps_) self.components_ = dictionary self.n_steps_ += 1 return self @property def _n_features_out(self): """Number of transformed output features.""" return self.components_.shape[0] def __sklearn_tags__(self): tags = super().__sklearn_tags__() tags.transformer_tags.preserves_dtype = ["float64", "float32"] return tags