"""Approximate nearest neighbor search""" # Author: Maheshakya Wijewardena # Joel Nothman import numpy as np import warnings from scipy import sparse from .base import KNeighborsMixin, RadiusNeighborsMixin from ..base import BaseEstimator from ..utils.validation import check_array from ..utils import check_random_state from ..metrics.pairwise import pairwise_distances from ..random_projection import GaussianRandomProjection __all__ = ["LSHForest"] HASH_DTYPE = '>u4' MAX_HASH_SIZE = np.dtype(HASH_DTYPE).itemsize * 8 def _find_matching_indices(tree, bin_X, left_mask, right_mask): """Finds indices in sorted array of integers. Most significant h bits in the binary representations of the integers are matched with the items' most significant h bits. """ left_index = np.searchsorted(tree, bin_X & left_mask) right_index = np.searchsorted(tree, bin_X | right_mask, side='right') return left_index, right_index def _find_longest_prefix_match(tree, bin_X, hash_size, left_masks, right_masks): """Find the longest prefix match in tree for each query in bin_X Most significant bits are considered as the prefix. """ hi = np.empty_like(bin_X, dtype=np.intp) hi.fill(hash_size) lo = np.zeros_like(bin_X, dtype=np.intp) res = np.empty_like(bin_X, dtype=np.intp) left_idx, right_idx = _find_matching_indices(tree, bin_X, left_masks[hi], right_masks[hi]) found = right_idx > left_idx res[found] = lo[found] = hash_size r = np.arange(bin_X.shape[0]) kept = r[lo < hi] # indices remaining in bin_X mask while kept.shape[0]: mid = (lo.take(kept) + hi.take(kept)) // 2 left_idx, right_idx = _find_matching_indices(tree, bin_X.take(kept), left_masks[mid], right_masks[mid]) found = right_idx > left_idx mid_found = mid[found] lo[kept[found]] = mid_found + 1 res[kept[found]] = mid_found hi[kept[~found]] = mid[~found] kept = r[lo < hi] return res class ProjectionToHashMixin(object): """Turn a transformed real-valued array into a hash""" @staticmethod def _to_hash(projected): if projected.shape[1] % 8 != 0: raise ValueError('Require reduced dimensionality to be a multiple ' 'of 8 for hashing') # XXX: perhaps non-copying operation better out = np.packbits((projected > 0).astype(int)).view(dtype=HASH_DTYPE) return out.reshape(projected.shape[0], -1) def fit_transform(self, X, y=None): self.fit(X) return self.transform(X) def transform(self, X, y=None): return self._to_hash(super(ProjectionToHashMixin, self).transform(X)) class GaussianRandomProjectionHash(ProjectionToHashMixin, GaussianRandomProjection): """Use GaussianRandomProjection to produce a cosine LSH fingerprint""" def __init__(self, n_components=8, random_state=None): super(GaussianRandomProjectionHash, self).__init__( n_components=n_components, random_state=random_state) def _array_of_arrays(list_of_arrays): """Creates an array of array from list of arrays.""" out = np.empty(len(list_of_arrays), dtype=object) out[:] = list_of_arrays return out class LSHForest(BaseEstimator, KNeighborsMixin, RadiusNeighborsMixin): """Performs approximate nearest neighbor search using LSH forest. LSH Forest: Locality Sensitive Hashing forest [1] is an alternative method for vanilla approximate nearest neighbor search methods. LSH forest data structure has been implemented using sorted arrays and binary search and 32 bit fixed-length hashes. Random projection is used as the hash family which approximates cosine distance. The cosine distance is defined as ``1 - cosine_similarity``: the lowest value is 0 (identical point) but it is bounded above by 2 for the farthest points. Its value does not depend on the norm of the vector points but only on their relative angles. Read more in the :ref:`User Guide `. Parameters ---------- n_estimators : int (default = 10) Number of trees in the LSH Forest. min_hash_match : int (default = 4) lowest hash length to be searched when candidate selection is performed for nearest neighbors. n_candidates : int (default = 10) Minimum number of candidates evaluated per estimator, assuming enough items meet the `min_hash_match` constraint. n_neighbors : int (default = 5) Number of neighbors to be returned from query function when it is not provided to the :meth:`kneighbors` method. radius : float, optinal (default = 1.0) Radius from the data point to its neighbors. This is the parameter space to use by default for the :meth`radius_neighbors` queries. radius_cutoff_ratio : float, optional (default = 0.9) A value ranges from 0 to 1. Radius neighbors will be searched until the ratio between total neighbors within the radius and the total candidates becomes less than this value unless it is terminated by hash length reaching `min_hash_match`. random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Attributes ---------- hash_functions_ : list of GaussianRandomProjectionHash objects Hash function g(p,x) for a tree is an array of 32 randomly generated float arrays with the same dimension as the data set. This array is stored in GaussianRandomProjectionHash object and can be obtained from ``components_`` attribute. trees_ : array, shape (n_estimators, n_samples) Each tree (corresponding to a hash function) contains an array of sorted hashed values. The array representation may change in future versions. original_indices_ : array, shape (n_estimators, n_samples) Original indices of sorted hashed values in the fitted index. References ---------- .. [1] M. Bawa, T. Condie and P. Ganesan, "LSH Forest: Self-Tuning Indexes for Similarity Search", WWW '05 Proceedings of the 14th international conference on World Wide Web, 651-660, 2005. Examples -------- >>> from sklearn.neighbors import LSHForest >>> X_train = [[5, 5, 2], [21, 5, 5], [1, 1, 1], [8, 9, 1], [6, 10, 2]] >>> X_test = [[9, 1, 6], [3, 1, 10], [7, 10, 3]] >>> lshf = LSHForest(random_state=42) >>> lshf.fit(X_train) # doctest: +NORMALIZE_WHITESPACE LSHForest(min_hash_match=4, n_candidates=50, n_estimators=10, n_neighbors=5, radius=1.0, radius_cutoff_ratio=0.9, random_state=42) >>> distances, indices = lshf.kneighbors(X_test, n_neighbors=2) >>> distances # doctest: +ELLIPSIS array([[ 0.069..., 0.149...], [ 0.229..., 0.481...], [ 0.004..., 0.014...]]) >>> indices array([[1, 2], [2, 0], [4, 0]]) """ def __init__(self, n_estimators=10, radius=1.0, n_candidates=50, n_neighbors=5, min_hash_match=4, radius_cutoff_ratio=.9, random_state=None): self.n_estimators = n_estimators self.radius = radius self.random_state = random_state self.n_candidates = n_candidates self.n_neighbors = n_neighbors self.min_hash_match = min_hash_match self.radius_cutoff_ratio = radius_cutoff_ratio def _compute_distances(self, query, candidates): """Computes the cosine distance. Distance is from the query to points in the candidates array. Returns argsort of distances in the candidates array and sorted distances. """ if candidates.shape == (0,): # needed since _fit_X[np.array([])] doesn't work if _fit_X sparse return np.empty(0, dtype=np.int), np.empty(0, dtype=float) if sparse.issparse(self._fit_X): candidate_X = self._fit_X[candidates] else: candidate_X = self._fit_X.take(candidates, axis=0, mode='clip') distances = pairwise_distances(query, candidate_X, metric='cosine')[0] distance_positions = np.argsort(distances) distances = distances.take(distance_positions, mode='clip', axis=0) return distance_positions, distances def _generate_masks(self): """Creates left and right masks for all hash lengths.""" tri_size = MAX_HASH_SIZE + 1 # Called once on fitting, output is independent of hashes left_mask = np.tril(np.ones((tri_size, tri_size), dtype=int))[:, 1:] right_mask = left_mask[::-1, ::-1] self._left_mask = np.packbits(left_mask).view(dtype=HASH_DTYPE) self._right_mask = np.packbits(right_mask).view(dtype=HASH_DTYPE) def _get_candidates(self, query, max_depth, bin_queries, n_neighbors): """Performs the Synchronous ascending phase. Returns an array of candidates, their distance ranks and distances. """ index_size = self._fit_X.shape[0] # Number of candidates considered including duplicates # XXX: not sure whether this is being calculated correctly wrt # duplicates from different iterations through a single tree n_candidates = 0 candidate_set = set() min_candidates = self.n_candidates * self.n_estimators while (max_depth > self.min_hash_match and (n_candidates < min_candidates or len(candidate_set) < n_neighbors)): left_mask = self._left_mask[max_depth] right_mask = self._right_mask[max_depth] for i in range(self.n_estimators): start, stop = _find_matching_indices(self.trees_[i], bin_queries[i], left_mask, right_mask) n_candidates += stop - start candidate_set.update( self.original_indices_[i][start:stop].tolist()) max_depth -= 1 candidates = np.fromiter(candidate_set, count=len(candidate_set), dtype=np.intp) # For insufficient candidates, candidates are filled. # Candidates are filled from unselected indices uniformly. if candidates.shape[0] < n_neighbors: warnings.warn( "Number of candidates is not sufficient to retrieve" " %i neighbors with" " min_hash_match = %i. Candidates are filled up" " uniformly from unselected" " indices." % (n_neighbors, self.min_hash_match)) remaining = np.setdiff1d(np.arange(0, index_size), candidates) to_fill = n_neighbors - candidates.shape[0] candidates = np.concatenate((candidates, remaining[:to_fill])) ranks, distances = self._compute_distances(query, candidates.astype(int)) return (candidates[ranks[:n_neighbors]], distances[:n_neighbors]) def _get_radius_neighbors(self, query, max_depth, bin_queries, radius): """Finds radius neighbors from the candidates obtained. Their distances from query are smaller than radius. Returns radius neighbors and distances. """ ratio_within_radius = 1 threshold = 1 - self.radius_cutoff_ratio total_candidates = np.array([], dtype=int) total_neighbors = np.array([], dtype=int) total_distances = np.array([], dtype=float) while (max_depth > self.min_hash_match and ratio_within_radius > threshold): left_mask = self._left_mask[max_depth] right_mask = self._right_mask[max_depth] candidates = [] for i in range(self.n_estimators): start, stop = _find_matching_indices(self.trees_[i], bin_queries[i], left_mask, right_mask) candidates.extend( self.original_indices_[i][start:stop].tolist()) candidates = np.setdiff1d(candidates, total_candidates) total_candidates = np.append(total_candidates, candidates) ranks, distances = self._compute_distances(query, candidates) m = np.searchsorted(distances, radius, side='right') positions = np.searchsorted(total_distances, distances[:m]) total_neighbors = np.insert(total_neighbors, positions, candidates[ranks[:m]]) total_distances = np.insert(total_distances, positions, distances[:m]) ratio_within_radius = (total_neighbors.shape[0] / float(total_candidates.shape[0])) max_depth = max_depth - 1 return total_neighbors, total_distances def fit(self, X, y=None): """Fit the LSH forest on the data. This creates binary hashes of input data points by getting the dot product of input points and hash_function then transforming the projection into a binary string array based on the sign (positive/negative) of the projection. A sorted array of binary hashes is created. Parameters ---------- X : array_like or sparse (CSR) matrix, shape (n_samples, n_features) List of n_features-dimensional data points. Each row corresponds to a single data point. Returns ------- self : object Returns self. """ self._fit_X = check_array(X, accept_sparse='csr') # Creates a g(p,x) for each tree self.hash_functions_ = [] self.trees_ = [] self.original_indices_ = [] rng = check_random_state(self.random_state) int_max = np.iinfo(np.int32).max for i in range(self.n_estimators): # This is g(p,x) for a particular tree. # Builds a single tree. Hashing is done on an array of data points. # `GaussianRandomProjection` is used for hashing. # `n_components=hash size and n_features=n_dim. hasher = GaussianRandomProjectionHash(MAX_HASH_SIZE, rng.randint(0, int_max)) hashes = hasher.fit_transform(self._fit_X)[:, 0] original_index = np.argsort(hashes) bin_hashes = hashes[original_index] self.original_indices_.append(original_index) self.trees_.append(bin_hashes) self.hash_functions_.append(hasher) self._generate_masks() return self def _query(self, X): """Performs descending phase to find maximum depth.""" # Calculate hashes of shape (n_samples, n_estimators, [hash_size]) bin_queries = np.asarray([hasher.transform(X)[:, 0] for hasher in self.hash_functions_]) bin_queries = np.rollaxis(bin_queries, 1) # descend phase depths = [_find_longest_prefix_match(tree, tree_queries, MAX_HASH_SIZE, self._left_mask, self._right_mask) for tree, tree_queries in zip(self.trees_, np.rollaxis(bin_queries, 1))] return bin_queries, np.max(depths, axis=0) def kneighbors(self, X, n_neighbors=None, return_distance=True): """Returns n_neighbors of approximate nearest neighbors. Parameters ---------- X : array_like or sparse (CSR) matrix, shape (n_samples, n_features) List of n_features-dimensional data points. Each row corresponds to a single query. n_neighbors : int, opitonal (default = None) Number of neighbors required. If not provided, this will return the number specified at the initialization. return_distance : boolean, optional (default = True) Returns the distances of neighbors if set to True. Returns ------- dist : array, shape (n_samples, n_neighbors) Array representing the cosine distances to each point, only present if return_distance=True. ind : array, shape (n_samples, n_neighbors) Indices of the approximate nearest points in the population matrix. """ if not hasattr(self, 'hash_functions_'): raise ValueError("estimator should be fitted.") if n_neighbors is None: n_neighbors = self.n_neighbors X = check_array(X, accept_sparse='csr') neighbors, distances = [], [] bin_queries, max_depth = self._query(X) for i in range(X.shape[0]): neighs, dists = self._get_candidates(X[[i]], max_depth[i], bin_queries[i], n_neighbors) neighbors.append(neighs) distances.append(dists) if return_distance: return np.array(distances), np.array(neighbors) else: return np.array(neighbors) def radius_neighbors(self, X, radius=None, return_distance=True): """Finds the neighbors within a given radius of a point or points. Return the indices and distances of some points from the dataset lying in a ball with size ``radius`` around the points of the query array. Points lying on the boundary are included in the results. The result points are *not* necessarily sorted by distance to their query point. LSH Forest being an approximate method, some true neighbors from the indexed dataset might be missing from the results. Parameters ---------- X : array_like or sparse (CSR) matrix, shape (n_samples, n_features) List of n_features-dimensional data points. Each row corresponds to a single query. radius : float Limiting distance of neighbors to return. (default is the value passed to the constructor). return_distance : boolean, optional (default = False) Returns the distances of neighbors if set to True. Returns ------- dist : array, shape (n_samples,) of arrays Each element is an array representing the cosine distances to some points found within ``radius`` of the respective query. Only present if ``return_distance=True``. ind : array, shape (n_samples,) of arrays Each element is an array of indices for neighbors within ``radius`` of the respective query. """ if not hasattr(self, 'hash_functions_'): raise ValueError("estimator should be fitted.") if radius is None: radius = self.radius X = check_array(X, accept_sparse='csr') neighbors, distances = [], [] bin_queries, max_depth = self._query(X) for i in range(X.shape[0]): neighs, dists = self._get_radius_neighbors(X[[i]], max_depth[i], bin_queries[i], radius) neighbors.append(neighs) distances.append(dists) if return_distance: return _array_of_arrays(distances), _array_of_arrays(neighbors) else: return _array_of_arrays(neighbors) def partial_fit(self, X, y=None): """ Inserts new data into the already fitted LSH Forest. Cost is proportional to new total size, so additions should be batched. Parameters ---------- X : array_like or sparse (CSR) matrix, shape (n_samples, n_features) New data point to be inserted into the LSH Forest. """ X = check_array(X, accept_sparse='csr') if not hasattr(self, 'hash_functions_'): return self.fit(X) if X.shape[1] != self._fit_X.shape[1]: raise ValueError("Number of features in X and" " fitted array does not match.") n_samples = X.shape[0] n_indexed = self._fit_X.shape[0] for i in range(self.n_estimators): bin_X = self.hash_functions_[i].transform(X)[:, 0] # gets the position to be added in the tree. positions = self.trees_[i].searchsorted(bin_X) # adds the hashed value into the tree. self.trees_[i] = np.insert(self.trees_[i], positions, bin_X) # add the entry into the original_indices_. self.original_indices_[i] = np.insert(self.original_indices_[i], positions, np.arange(n_indexed, n_indexed + n_samples)) # adds the entry into the input_array. if sparse.issparse(X) or sparse.issparse(self._fit_X): self._fit_X = sparse.vstack((self._fit_X, X)) else: self._fit_X = np.row_stack((self._fit_X, X)) return self