def applyPearsonCorrelation(self): """ Remove from every data point the average for the corresponding column :return: """ self.dataMatrix = check_matrix(self.dataMatrix, 'csc') interactionsPerCol = np.diff(self.dataMatrix.indptr) nonzeroCols = interactionsPerCol > 0 sumPerCol = np.asarray(self.dataMatrix.sum(axis=0)).ravel() colAverage = np.zeros_like(sumPerCol) colAverage[nonzeroCols] = sumPerCol[nonzeroCols] / interactionsPerCol[ nonzeroCols] # Split in blocks to avoid duplicating the whole data structure start_col = 0 end_col = 0 blockSize = 1000 while end_col < self.n_columns: end_col = min(self.n_columns, end_col + blockSize) self.dataMatrix.data[self.dataMatrix.indptr[start_col]:self.dataMatrix.indptr[end_col]] -= \ np.repeat(colAverage[start_col:end_col], interactionsPerCol[start_col:end_col]) start_col += blockSize
def applyAdjustedCosine(self): """ Remove from every data point the average for the corresponding row :return: """ self.dataMatrix = check_matrix(self.dataMatrix, 'csr') interactionsPerRow = np.diff(self.dataMatrix.indptr) nonzeroRows = interactionsPerRow > 0 sumPerRow = np.asarray(self.dataMatrix.sum(axis=1)).ravel() rowAverage = np.zeros_like(sumPerRow) rowAverage[nonzeroRows] = sumPerRow[nonzeroRows] / interactionsPerRow[ nonzeroRows] # Split in blocks to avoid duplicating the whole data structure start_row = 0 end_row = 0 blockSize = 1000 while end_row < self.n_rows: end_row = min(self.n_rows, end_row + blockSize) self.dataMatrix.data[self.dataMatrix.indptr[start_row]:self.dataMatrix.indptr[end_row]] -= \ np.repeat(rowAverage[start_row:end_row], interactionsPerRow[start_row:end_row]) start_row += blockSize
def fit(self, l1_ratio=1e-06, positive_only=True, topK=50): assert l1_ratio >= 0 and l1_ratio <= 1, "SLIM_ElasticNet: l1_ratio must be between 0 and 1, provided value was {}".format( l1_ratio) self.l1_ratio = l1_ratio self.positive_only = positive_only self.topK = topK # initialize the ElasticNet model self.model = ElasticNet(alpha=1.0, l1_ratio=self.l1_ratio, positive=self.positive_only, fit_intercept=False, copy_X=False, precompute=True, selection='random', max_iter=100, tol=1e-4) URM = check_matrix(self.URM, 'csc', dtype=np.float32) n_items = URM.shape[1] # Use array as it reduces memory requirements compared to lists dataBlock = 10000000 rows = np.zeros(dataBlock, dtype=np.int32) cols = np.zeros(dataBlock, dtype=np.int32) values = np.zeros(dataBlock, dtype=np.float32) numCells = 0 start_time = time.time() start_time_printBatch = start_time # fit each item's factors sequentially (not in parallel) for currentItem in range(n_items): # get the target column y = URM[:, currentItem].toarray() # set the j-th column of X to zero start_pos = URM.indptr[currentItem] end_pos = URM.indptr[currentItem + 1] current_item_data_backup = URM.data[start_pos:end_pos].copy() URM.data[start_pos:end_pos] = 0.0 # fit one ElasticNet model per column self.model.fit(URM, y) # self.model.coef_ contains the coefficient of the ElasticNet model # let's keep only the non-zero values # Select topK values # Sorting is done in three steps. Faster then plain np.argsort for higher number of items # - Partition the data to extract the set of relevant items # - Sort only the relevant items # - Get the original item index # nonzero_model_coef_index = self.model.coef_.nonzero()[0] # nonzero_model_coef_value = self.model.coef_[nonzero_model_coef_index] nonzero_model_coef_index = self.model.sparse_coef_.indices nonzero_model_coef_value = self.model.sparse_coef_.data local_topK = min(len(nonzero_model_coef_value) - 1, self.topK) relevant_items_partition = ( -nonzero_model_coef_value ).argpartition(local_topK)[0:local_topK] relevant_items_partition_sorting = np.argsort( -nonzero_model_coef_value[relevant_items_partition]) ranking = relevant_items_partition[ relevant_items_partition_sorting] for index in range(len(ranking)): if numCells == len(rows): rows = np.concatenate( (rows, np.zeros(dataBlock, dtype=np.int32))) cols = np.concatenate( (cols, np.zeros(dataBlock, dtype=np.int32))) values = np.concatenate( (values, np.zeros(dataBlock, dtype=np.float32))) rows[numCells] = nonzero_model_coef_index[ranking[index]] cols[numCells] = currentItem values[numCells] = nonzero_model_coef_value[ranking[index]] numCells += 1 # finally, replace the original values of the j-th column URM.data[start_pos:end_pos] = current_item_data_backup if time.time( ) - start_time_printBatch > 300 or currentItem == n_items - 1: print( "Processed {} ( {:.2f}% ) in {:.2f} minutes. Items per second: {:.0f}" .format(currentItem + 1, 100.0 * float(currentItem + 1) / n_items, (time.time() - start_time) / 60, float(currentItem) / (time.time() - start_time))) sys.stdout.flush() sys.stderr.flush() start_time_printBatch = time.time() # generate the sparse weight matrix self.W_sparse = sps.csr_matrix( (values[:numCells], (rows[:numCells], cols[:numCells])), shape=(n_items, n_items), dtype=np.float32)
def __init__(self, URM): self.URM = check_matrix(URM, format='csr', dtype=np.float32)
def similarityMatrixTopK(self, item_weights, forceSparseOutput=True, k=150, verbose=False, inplace=True): """ The function selects the TopK most similar elements, column-wise :param item_weights: :param forceSparseOutput: :param k: :param verbose: :param inplace: Default True, WARNING matrix will be modified :return: """ assert (item_weights.shape[0] == item_weights.shape[1] ), "selectTopK: ItemWeights is not a square matrix" start_time = time.time() if verbose: print("Generating topK matrix") nitems = item_weights.shape[1] k = min(k, nitems) # for each column, keep only the top-k scored items sparse_weights = not isinstance(item_weights, np.ndarray) if not sparse_weights: idx_sorted = np.argsort(item_weights, axis=0) # sort data inside each column if inplace: W = item_weights else: W = item_weights.copy() # index of the items that don't belong to the top-k similar items of each column not_top_k = idx_sorted[:-k, :] # use numpy fancy indexing to zero-out the values in sim without using a for loop W[not_top_k, np.arange(nitems)] = 0.0 if forceSparseOutput: W_sparse = sps.csr_matrix(W, shape=(nitems, nitems)) if verbose: print("Sparse TopK matrix generated in {:.2f} seconds". format(time.time() - start_time)) return W_sparse if verbose: print("Dense TopK matrix generated in {:.2f} seconds".format( time.time() - start_time)) return W else: # iterate over each column and keep only the top-k similar items data, rows_indices, cols_indptr = [], [], [] item_weights = check_matrix(item_weights, format='csc', dtype=np.float32) for item_idx in range(nitems): cols_indptr.append(len(data)) start_position = item_weights.indptr[item_idx] end_position = item_weights.indptr[item_idx + 1] column_data = item_weights.data[start_position:end_position] column_row_index = item_weights.indices[ start_position:end_position] non_zero_data = column_data != 0 idx_sorted = np.argsort( column_data[non_zero_data]) # sort by column top_k_idx = idx_sorted[-k:] data.extend(column_data[non_zero_data][top_k_idx]) rows_indices.extend(column_row_index[non_zero_data][top_k_idx]) cols_indptr.append(len(data)) # During testing CSR is faster W_sparse = sps.csc_matrix((data, rows_indices, cols_indptr), shape=(nitems, nitems), dtype=np.float32) W_sparse = W_sparse.tocsr() if verbose: print("Sparse TopK matrix generated in {:.2f} seconds".format( time.time() - start_time)) return W_sparse
def compute_similarity(self, start_col=None, end_col=None, block_size=100): """ Compute the similarity for the given dataset :param self: :param start_col: column to begin with :param end_col: column to stop before, end_col is excluded :return: """ values = [] rows = [] cols = [] start_time = time.time() start_time_print_batch = start_time processedItems = 0 if self.adjusted_cosine: self.applyAdjustedCosine() elif self.pearson_correlation: self.applyPearsonCorrelation() elif self.tanimoto_coefficient or self.dice_coefficient or self.tversky_coefficient: self.useOnlyBooleanInteractions() # We explore the matrix column-wise self.dataMatrix = check_matrix(self.dataMatrix, 'csc') # Compute sum of squared values to be used in normalization sumOfSquared = np.array(self.dataMatrix.power(2).sum(axis=0)).ravel() # Tanimoto does not require the square root to be applied if not (self.tanimoto_coefficient or self.dice_coefficient or self.tversky_coefficient): sumOfSquared = np.sqrt(sumOfSquared) if self.asymmetric_cosine: sumOfSquared_to_1_minus_alpha = sumOfSquared.power( 2 * (1 - self.asymmetric_alpha)) sumOfSquared_to_alpha = sumOfSquared.power(2 * self.asymmetric_alpha) self.dataMatrix = check_matrix(self.dataMatrix, 'csc') start_col_local = 0 end_col_local = self.n_columns if start_col is not None and start_col > 0 and start_col < self.n_columns: start_col_local = start_col if end_col is not None and end_col > start_col_local and end_col < self.n_columns: end_col_local = end_col start_col_block = start_col_local this_block_size = 0 # Compute all similarities for each item using vectorization while start_col_block < end_col_local: # Add previous block size processedItems += this_block_size end_col_block = min(start_col_block + block_size, end_col_local) this_block_size = end_col_block - start_col_block if time.time( ) - start_time_print_batch >= 30 or end_col_block == end_col_local: columnPerSec = processedItems / (time.time() - start_time + 0.0000001) print( "Similarity column {} ( {:2.0f} % ), {:.2f} column/sec, elapsed time {:.2f} min" .format( processedItems, processedItems / (end_col_local - start_col_local) * 100, columnPerSec, (time.time() - start_time) / 60)) sys.stdout.flush() sys.stderr.flush() start_time_print_batch = time.time() # All data points for a given item item_data = self.dataMatrix[:, start_col_block:end_col_block] item_data = item_data.toarray().squeeze() if self.use_row_weights: # item_data = np.multiply(item_data, self.row_weights) # item_data = item_data.T.dot(self.row_weights_diag).T this_block_weights = self.dataMatrix_weighted.T.dot(item_data) else: # Compute item similarities this_block_weights = self.dataMatrix.T.dot(item_data) for col_index_in_block in range(this_block_size): if this_block_size == 1: this_column_weights = this_block_weights else: this_column_weights = this_block_weights[:, col_index_in_block] columnIndex = col_index_in_block + start_col_block this_column_weights[columnIndex] = 0.0 # Apply normalization and shrinkage, ensure denominator != 0 if self.normalize: if self.asymmetric_cosine: denominator = sumOfSquared_to_alpha[ columnIndex] * sumOfSquared_to_1_minus_alpha + self.shrink + 1e-6 else: denominator = sumOfSquared[ columnIndex] * sumOfSquared + self.shrink + 1e-6 this_column_weights = np.multiply(this_column_weights, 1 / denominator) # Apply the specific denominator for Tanimoto elif self.tanimoto_coefficient: denominator = sumOfSquared[ columnIndex] + sumOfSquared - this_column_weights + self.shrink + 1e-6 this_column_weights = np.multiply(this_column_weights, 1 / denominator) elif self.dice_coefficient: denominator = sumOfSquared[ columnIndex] + sumOfSquared + self.shrink + 1e-6 this_column_weights = np.multiply(this_column_weights, 1 / denominator) elif self.tversky_coefficient: denominator = this_column_weights + \ (sumOfSquared[columnIndex] - this_column_weights) * self.tversky_alpha + \ (sumOfSquared - this_column_weights) * self.tversky_beta + self.shrink + 1e-6 this_column_weights = np.multiply(this_column_weights, 1 / denominator) # If no normalization or tanimoto is selected, apply only shrink elif self.shrink != 0: this_column_weights = this_column_weights / self.shrink # this_column_weights = this_column_weights.toarray().ravel() if self.TopK == 0: self.W_dense[:, columnIndex] = this_column_weights else: # Sort indices and select TopK # Sorting is done in three steps. Faster then plain np.argsort for higher number of items # - Partition the data to extract the set of relevant items # - Sort only the relevant items # - Get the original item index relevant_items_partition = ( -this_column_weights).argpartition(self.TopK - 1)[0:self.TopK] relevant_items_partition_sorting = np.argsort( -this_column_weights[relevant_items_partition]) top_k_idx = relevant_items_partition[ relevant_items_partition_sorting] # Incrementally build sparse matrix, do not add zeros notZerosMask = this_column_weights[top_k_idx] != 0.0 numNotZeros = np.sum(notZerosMask) values.extend(this_column_weights[top_k_idx][notZerosMask]) rows.extend(top_k_idx[notZerosMask]) cols.extend(np.ones(numNotZeros) * columnIndex) start_col_block += block_size # End while on columns if self.TopK == 0: return self.W_dense else: W_sparse = sps.csr_matrix((values, (rows, cols)), shape=(self.n_columns, self.n_columns), dtype=np.float32) return W_sparse