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