def fit(self, lambda_user=10, lambda_item=25):
self.lambda_user = lambda_user
self.lambda_item = lambda_item
self.n_items = self.URM_train.shape[1]
# convert to csc matrix for faster column-wise sum
self.URM_train = check_matrix(self.URM_train, 'csc', dtype=np.float32)
# 1) global average
self.mu = self.URM_train.data.sum(
dtype=np.float32) / self.URM_train.data.shape[0]
# 2) item average bias
# compute the number of non-zero elements for each column
col_nnz = np.diff(self.URM_train.indptr)
# it is equivalent to:
# col_nnz = X.indptr[1:] - X.indptr[:-1]
# and it is **much faster** than
# col_nnz = (X != 0).sum(axis=0)
URM_train_unbiased = self.URM_train.copy()
URM_train_unbiased.data -= self.mu
self.item_bias = URM_train_unbiased.sum(axis=0) / (col_nnz +
self.lambda_item)
self.item_bias = np.asarray(self.item_bias).ravel(
) # converts 2-d matrix to 1-d array without anycopy
# 3) user average bias
# NOTE: the user bias is *useless* for the sake of ranking items. We just show it here for educational purposes.
# first subtract the item biases from each column
# then repeat each element of the item bias vector a number of times equal to col_nnz
# and subtract it from the data vector
URM_train_unbiased.data -= np.repeat(self.item_bias, col_nnz)
# now convert the csc matrix to csr for efficient row-wise computation
URM_train_unbiased_csr = URM_train_unbiased.tocsr()
row_nnz = np.diff(URM_train_unbiased_csr.indptr)
# finally, let's compute the bias
self.user_bias = URM_train_unbiased_csr.sum(
axis=1).ravel() / (row_nnz + self.lambda_user)
# 4) precompute the item ranking by using the item bias only
# the global average and user bias won't change the ranking, so there is no need to use them
#self.item_ranking = np.argsort(self.bi)[::-1]
self.URM_train = check_matrix(self.URM_train, 'csr', dtype=np.float32)
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 remove_empty_rows_and_cols(URM, ICM=None):
URM = check_matrix(URM, "csr")
rows = URM.indptr
numRatings = np.ediff1d(rows)
user_mask = numRatings >= 1
URM = URM[user_mask, :]
cols = URM.tocsc().indptr
numRatings = np.ediff1d(cols)
item_mask = numRatings >= 1
URM = URM[:, item_mask]
removedUsers = np.arange(0, len(user_mask))[np.logical_not(user_mask)]
removedItems = np.arange(0, len(item_mask))[np.logical_not(item_mask)]
if ICM is not None:
ICM = ICM[item_mask, :]
return URM.tocsr(), ICM.tocsr(), removedUsers, removedItems
return URM.tocsr(), removedUsers, removedItems
def __init__(self, URM_train, verbose=True):
super(BaseRecommender, self).__init__()
self.URM_train = check_matrix(URM_train.copy(),
'csr',
dtype=np.float32)
self.URM_train.eliminate_zeros()
self.n_users, self.n_items = self.URM_train.shape
self.verbose = verbose
self.filterTopPop = False
self.filterTopPop_ItemsID = np.array([], dtype=np.int)
self.items_to_ignore_flag = False
self.items_to_ignore_ID = np.array([], dtype=np.int)
self._cold_user_mask = np.ediff1d(self.URM_train.indptr) == 0
if self._cold_user_mask.any():
self._print("URM Detected {} ({:.2f} %) cold users.".format(
self._cold_user_mask.sum(),
self._cold_user_mask.sum() / self.n_users * 100))
self._cold_item_mask = np.ediff1d(self.URM_train.tocsc().indptr) == 0
if self._cold_item_mask.any():
self._print("URM Detected {} ({:.2f} %) cold items.".format(
self._cold_item_mask.sum(),
self._cold_item_mask.sum() / self.n_items * 100))
def __init__(self, URM_recommendations_items):
super(PredefinedListRecommender, self).__init__()
# convert to csc matrix for faster column-wise sum
self.URM_recommendations = check_matrix(URM_recommendations_items,
'csr',
dtype=np.int)
self.URM_train = sps.csr_matrix((self.URM_recommendations.shape))
def remove_features(ICM,
min_occurrence=5,
max_percentage_occurrence=0.30,
reconcile_mapper=None):
"""
The function eliminates the values associated to feature occurring in less than the minimal percentage of items
or more then the max. Shape of ICM is reduced deleting features.
:param ICM:
:param minPercOccurrence:
:param max_percentage_occurrence:
:param reconcile_mapper: DICT mapper [token] -> index
:return: ICM
:return: deletedFeatures
:return: DICT mapper [token] -> index
"""
ICM = check_matrix(ICM, 'csc')
n_items = ICM.shape[0]
cols = ICM.indptr
numOccurrences = np.ediff1d(cols)
feature_mask = np.logical_and(
numOccurrences >= min_occurrence,
numOccurrences <= n_items * max_percentage_occurrence)
ICM = ICM[:, feature_mask]
deletedFeatures = np.arange(
0, len(feature_mask))[np.logical_not(feature_mask)]
print(
"RemoveFeatures: removed {} features with less then {} occurrences, removed {} features with more than {} occurrencies"
.format(sum(numOccurrences < min_occurrence), min_occurrence,
sum(numOccurrences > n_items * max_percentage_occurrence),
int(n_items * max_percentage_occurrence)))
if reconcile_mapper is not None:
reconcile_mapper = reconcile_mapper_with_removed_tokens(
reconcile_mapper, deletedFeatures)
return ICM, deletedFeatures, reconcile_mapper
return ICM, deletedFeatures
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 = np.power(sumOfSquared, 2 * (1 - self.asymmetric_alpha))
sumOfSquared_to_alpha = np.power(sumOfSquared, 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:
end_col_block = min(start_col_block + block_size, end_col_local)
this_block_size = end_col_block-start_col_block
# All data points for a given item
item_data = self.dataMatrix[:, start_col_block:end_col_block]
item_data = item_data.toarray().squeeze()
# If only 1 feature avoid last dimension to disappear
if item_data.ndim == 1:
item_data = np.atleast_2d(item_data)
if self.use_row_weights:
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()
# 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)
# Add previous block size
processedItems += this_block_size
if time.time() - start_time_print_batch >= 30 or end_col_block==end_col_local:
columnPerSec = processedItems / (time.time() - start_time + 1e-9)
#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()
start_col_block += block_size
# End while on columns
W_sparse = sps.csr_matrix((values, (rows, cols)),
shape=(self.n_columns, self.n_columns),
dtype=np.float32)
return W_sparse
