def fit(self,
X: sp.csr_matrix,
n_samples: int,
multiplier: np.ndarray = None):
"""Learn the idf vector (global term weights).
Arguments:
X: A matrix of term/token counts.
n_samples: Number of total documents
"""
X = check_array(X, accept_sparse=('csr', 'csc'))
if not sp.issparse(X):
X = sp.csr_matrix(X)
dtype = np.float64
if self.use_idf:
_, n_features = X.shape
df = np.squeeze(np.asarray(X.sum(axis=0)))
avg_nr_samples = int(X.sum(axis=1).mean())
idf = np.log(avg_nr_samples / df)
if multiplier is not None:
idf = idf * multiplier
self._idf_diag = sp.diags(idf,
offsets=0,
shape=(n_features, n_features),
format='csr',
dtype=dtype)
return self
def fit(self, X: sp.csr_matrix, n_samples: int):
"""Learn the idf vector (global term weights)
Parameters
----------
X : sparse matrix of shape n_samples, n_features)
A matrix of term/token counts.
"""
# Prepare input
X = check_array(X, accept_sparse=('csr', 'csc'))
if not sp.issparse(X):
X = sp.csr_matrix(X)
dtype = X.dtype if X.dtype in FLOAT_DTYPES else np.float64
# Calculate IDF scores
_, n_features = X.shape
df = np.squeeze(np.asarray(X.sum(axis=0)))
avg_nr_samples = int(X.sum(axis=1).mean())
idf = np.log(avg_nr_samples / df)
self._idf_diag = sp.diags(idf,
offsets=0,
shape=(n_features, n_features),
format='csr',
dtype=dtype)
return self
def normalize_adj(adj : sp.csr_matrix):
"""Normalize adjacency matrix and convert it to a sparse tensor."""
if sp.isspmatrix(adj):
adj = adj.tolil()
adj.setdiag(1)
adj = adj.tocsr()
deg = np.ravel(adj.sum(1))
deg_sqrt_inv = 1 / np.sqrt(deg)
adj_norm = adj.multiply(deg_sqrt_inv[:, None]).multiply(deg_sqrt_inv[None, :])
elif torch.is_tensor(adj):
deg = adj.sum(1)
deg_sqrt_inv = 1 / torch.sqrt(deg)
adj_norm = adj * deg_sqrt_inv[:, None] * deg_sqrt_inv[None, :]
return to_sparse_tensor(adj_norm)
def evaluate_item(train:ss.csr_matrix, test:ss.csr_matrix, user:np.ndarray, item:np.ndarray, topk:int=200, cutoff:int=200):
train = train.tocsr()
test = test.tocsr()
idx = np.squeeze((test.sum(axis=1) > 0).A)
train = train[idx, :]
test = test[idx, :]
user = user[idx, :]
N = train.shape[1]
cand_count = N - train.sum(axis=1)
if topk <0:
mat_rank = Eval.predict(train, test, user, item)
else:
mat_rank = Eval.topk_search_(train, test, user, item, topk)
return Eval.compute_item_metric(test, mat_rank, cand_count, cutoff)
def test_rp3(X: sps.csr_matrix, alpha: float, beta: float) -> None:
rec = RP3betaRecommender(X, alpha=alpha, beta=beta, n_threads=4)
rec.learn()
W = rec.W.toarray()
W_sum = W.sum(axis=1)
W_sum = W_sum[W_sum >= 0]
popularity = X.sum(axis=0).A1.ravel() ** beta
def zero_or_1(X: np.ndarray) -> np.ndarray:
X = X.copy()
X[X == 0] = 1
return X
P_ui = np.power(X.toarray(), alpha)
P_iu = np.power(X.T.toarray(), alpha)
P_ui /= zero_or_1(P_ui.sum(axis=1))[:, None]
P_iu /= zero_or_1(P_iu.sum(axis=1))[:, None]
W_man = P_iu.dot(P_ui)
# p_{ui} ^{RP3} = p_{ui} ^{P3} / popularity_i ^ beta
W_man = W_man / zero_or_1(popularity)[None, :]
np.testing.assert_allclose(W, W_man)
rec_norm = RP3betaRecommender(
X, alpha=alpha, n_threads=4, top_k=2, normalize_weight=True
)
rec_norm.learn()
# rec
W_sum = rec_norm.W.sum(axis=1).A1
for w in W_sum:
assert w == pytest.approx(1.0)
def _normalise_adjacency(adjacency: csr_matrix) -> csr_matrix:
""" A_tidle = D^(-0.5) A D^(-0.5) """
# Create D^(-0.5)
degree_inv_sqrt = np.power(np.array(adjacency.sum(1)), -0.5).flatten()
degree_inv_sqrt[np.isinf(degree_inv_sqrt)] = 0.0
degree_inv_sqrt = diags(degree_inv_sqrt, format="coo")
# Compute D^(-0.5) A D^(-0.5)
return degree_inv_sqrt.dot(adjacency).dot(degree_inv_sqrt)
def normalize_sparse_matrix(matrix: sparse.csr_matrix) -> sparse.csr_matrix:
"""Normalizes each row to one.
Norms of rows aren't exactly because before division 0.1 is added
just to make sure that 0 doesn't appear in the nominator.
"""
sums_for_strings = matrix.sum(axis=1).A.flatten()
normalization_matrix = create_sparce_from_diagonal(1 / (sums_for_strings + 0.1))
return normalization_matrix.dot(matrix)
def __call__(self, matrix: csr_matrix):
SUM = matrix.sum()
row_sum = matrix.sum(axis=1)
col_sum = matrix.sum(axis=0)
# do: 1 / each cell
row_sum = _safe_divide(1, row_sum)
col_sum = _safe_divide(1, col_sum)
row_sum *= SUM
if self.smooth:
row_sum = np.power(row_sum, SMOOTH_POWER)
res = matrix.multiply(row_sum).multiply(col_sum).tocsr()
res.data = np.log(res.data)
res.eliminate_zeros()
return res
def calcDInv(K: sparse.csr_matrix):
"""Calculates a scaling diagonal matrix D to rescale eigen vectors
Parameters
----------
K the sparse matrix K for the pairwise affinity
Returns
-------
a sparse matrix with type csr, and D's diagonal values
"""
dim = K.shape[0]
D_diag_inv = 1 / (K.sum(axis=1) + .000000001
) # add small epsilon to each row in K.sum()
# D_diag = 1 / K.sum(axis=1)
# print("D_diag",D_diag)
D_sparse = sparse.dia_matrix((np.reshape(D_diag_inv, [1, -1]), [0]),
(dim, dim))
return sparse.csr_matrix(D_sparse), (K.sum(axis=1) + .000000001)
def calculate_normalized_affinity(
W: csr_matrix
) -> Tuple[csr_matrix, np.array, np.array]:
diag = W.sum(axis=1).A1
diag_half = np.sqrt(diag)
W_norm = W.tocoo(copy=True)
W_norm.data /= diag_half[W_norm.row]
W_norm.data /= diag_half[W_norm.col]
W_norm = W_norm.tocsr()
return W_norm, diag, diag_half
def sparse_mat_decompose(user_preference: ss.csr_matrix, latent_factor_num: int = 1) -> (ss.csr_matrix, ss.csr_matrix):
"""
分解稀疏的用户偏好矩阵至两个初始化矩阵 U 和 V，U 的列数和 V 的行数为 latent_factor_num
:param user_preference: 分解用户偏好矩阵
:param latent_factor_num: U 的列数和 V 的行数
:return: U, V
"""
rows_num, column_num = user_preference.shape
not_nan_elements_num = user_preference.count_nonzero()
avg = user_preference.sum() / not_nan_elements_num
init_element = np.sqrt(avg / latent_factor_num)
u_init, v_init = np.full((rows_num, latent_factor_num), init_element), \
np.full((latent_factor_num, column_num), init_element)
return ss.csr_matrix(u_init), ss.csr_matrix(v_init)
def evaluate_item(train: ss.csr_matrix,
test: ss.csr_matrix,
user: np.ndarray,
item: np.ndarray,
topk: int = -1,
cutoff: int = 100):
train = train.tocsr()
test = test.tocsr()
N = train.shape[1]
cand_count = N - train.sum(axis=1)
if topk < 0:
mat_rank = Eval.predict(train, test, user, item)
else:
mat_rank = Eval.topk_search_(train, test, user, item, topk)
return Eval.compute_item_metric(test, mat_rank, cand_count, cutoff)
def fit(self, X: sp.csr_matrix, multiplier: np.ndarray = None):
"""Learn the idf vector (global term weights).
Arguments:
X: A matrix of term/token counts.
multiplier: A multiplier for increasing/decreasing certain IDF scores
"""
X = check_array(X, accept_sparse=('csr', 'csc'))
if not sp.issparse(X):
X = sp.csr_matrix(X)
dtype = np.float64
if self.use_idf:
_, n_features = X.shape
# Calculate the frequency of words across all classes
df = np.squeeze(np.asarray(X.sum(axis=0)))
# Calculate the average number of samples as regularization
avg_nr_samples = int(X.sum(axis=1).mean())
# Divide the average number of samples by the word frequency
# +1 is added to force values to be positive
idf = np.log((avg_nr_samples / df) + 1)
# Multiplier to increase/decrease certain idf scores
if multiplier is not None:
idf = idf * multiplier
self._idf_diag = sp.diags(idf,
offsets=0,
shape=(n_features, n_features),
format='csr',
dtype=dtype)
return self
def evaluate_topk(train:ss.csr_matrix, test:ss.csr_matrix, topk_item:np.ndarray, cutoff:int=200):
train = train.tocsr()
test = test.tocsr()
result = topk_item
N = train.shape[1]
cand_count = N - train.sum(axis=1)
M = test.shape[0]
uir = []
for i in range(M):
R = set(test.indices[test.indptr[i]:test.indptr[i+1]])
for k in range(result.shape[1]):
if result[i,k] in R:
uir.append((i, result[i,k], k))
user_id, item_id, rank = zip(*uir)
mat_rank = ss.csr_matrix((rank, (user_id, item_id)), shape=test.shape)
return Eval.compute_item_metric(test, mat_rank, cand_count, cutoff)
def row_normalize_csr_matrix(matrix: csr_matrix) -> csr_matrix:
"""
Row normalize a csr matrix without mutating the input
:param matrix: scipy.sparse.csr_matrix instance
"""
if not isinstance(matrix, csr_matrix):
raise TypeError('expected input to be a scipy csr_matrix')
if any(matrix.data == 0):
raise ValueError(
'input must be scipy.sparse.csr_matrix and must not store zeros')
# get row index for every nonzero element in matrix
row_idx, col_idx = matrix.nonzero()
# compute unraveled row sums
row_sums = matrix.sum(axis=1).A1
# divide data by (broadcasted) row sums
normalized = matrix.data / row_sums[row_idx]
return csr_matrix((normalized, (row_idx, col_idx)), shape=matrix.shape)
def collect_basic_statistics(
X: csr_matrix,
cluster_labels: List[str],
cond_labels: List[str],
gene_names: List[str],
n_jobs: int,
temp_folder: str,
verbose: bool,
) -> List[pd.DataFrame]:
""" Collect basic statistics, triggering calc_basic_stat in parallel
"""
start = time.perf_counter()
sum_vec = cnt_vec = None
if cond_labels is None:
sum_vec = X.sum(axis=0).A1
cnt_vec = X.getnnz(axis=0)
result_list = Parallel(n_jobs=n_jobs, max_nbytes=1e7, temp_folder=temp_folder)(
delayed(calc_basic_stat)(
clust_id,
X.data,
X.indices,
X.indptr,
X.shape,
cluster_labels,
cond_labels,
gene_names,
sum_vec,
cnt_vec,
verbose,
)
for clust_id in cluster_labels.categories
)
end = time.perf_counter()
if verbose:
logger.info(
"Collecting basic statistics is done. Time spent = {:.2f}s.".format(
end - start
)
)
return result_list
def t_test(
X: csr_matrix,
cluster_labels: List[str],
cond_labels: List[str],
gene_names: List[str],
n_jobs: int,
temp_folder: str,
verbose: bool,
) -> List[pd.DataFrame]:
""" Run Welch's t-test, triggering calc_t in parallel
"""
start = time.time()
sum_vec = sum2_vec = None
if cond_labels is None:
sum_vec = X.sum(axis=0).A1
sum2_vec = X.power(2).sum(axis=0).A1
result_list = Parallel(n_jobs=n_jobs,
max_nbytes=1e7,
temp_folder=temp_folder)(delayed(calc_t)(
clust_id,
X.data,
X.indices,
X.indptr,
X.shape,
cluster_labels,
cond_labels,
gene_names,
sum_vec,
sum2_vec,
verbose,
) for clust_id in cluster_labels.categories)
end = time.time()
if verbose:
logger.info(
"Welch's t-test is done. Time spent = {:.2f}s.".format(end -
start))
return result_list
def calculate_min_violations(A: csr_matrix) -> (float, float):
"""
Calculate the minimum number of violations in a graph for all possible rankings
A violaton is an edge going from a lower ranked node to a higher ranked one
Minimum number is calculated by summing bidirectional interactions.
Input:
A: graph adjacency matrix where A[i,j] is the weight of an edge from node i to j
Output:
minimum number of violations
proportion of all edges against minimum violations
"""
ii, ji, v = scipy.sparse.find(
A
) # I,J,V contain the row, column indices, and values of the nonzero entries.
min_viol = 0.0
for e in range(len(v)): # for all nodes interactions
i, j = ii[e], ji[e]
if A[i, j] > 0 and A[j, i] > 0:
min_viol = min_viol + min(A[i, j], A[j, i])
m = A.sum()
return (min_viol, min_viol / m)
def vertex_degree(graph: sp.csr_matrix, vertex: int):
return graph.sum(axis=0)[vertex]
def axis_norms(X: sparse.csr_matrix,
norm: str = "l1",
axis: int = 1) -> np.ndarray:
if norm == "l1":
return np.asarray(X.sum(axis=axis)).reshape(-1)
return np.sqrt(np.asarray(X.power(2).sum(axis=axis)).reshape(-1))
def __init__(self, adj: sparse.csr_matrix, nodes, tp: ConfigType):
self._adj = adj
self._nodes: List[Node] = nodes
self._size = len(nodes)
self._type = tp
self._edges = int(adj.sum() / 2)
def get_inv_propensity(train_y: csr_matrix, a=0.55, b=1.5):
n, number = train_y.shape[0], np.asarray(train_y.sum(axis=0)).squeeze()
c = (np.log(n) - 1) * ((b + 1)**a)
return 1.0 + c * (number + b)**(-a)
def normalize_relative_frequency(matrix: sparse.csr_matrix, axis: AxisType):
if axis == AxisType.REPERTOIRES:
return sparse.diags(1 / matrix.sum(axis=1).A.ravel()) @ matrix
if axis == AxisType.FEATURES:
return matrix @ sparse.diags(1 / matrix.sum(axis=0).A.ravel())
def preprocess_graph(
adj: sp.csr_matrix,
same_type_nodes: bool = True
) -> Tuple[np.array, np.array, Tuple[int, int]]:
"""
Parameters
----------
adj : sp.csr_matrix
Adjacency matrix.
same_type_nodes : bool
Is adjacency matrix for nodes of same type or not?
E.g. drug-drug, protein-protein adj or drug-protein, protein-drug.
Returns
-------
np.array
Pairs of edges in normalized adjacency matrix with nonzero values.
np.array
Nonzero values of normalized adjacency matrix.
Tuple[int, int]
Shape of normalized adjacency matrix.
Notes
-----
Updating embeddings on new layer can be written as
H(l+1) = σ(SUM_r A_r_normalize @ H(l) @ W_r(l))
A_r_normalize --- normalized adj matrix for r edge type.
So we have two variants of normalization for A_r (further just A).
1. Adj matrix for nodes of same type. It is symmetric.
A_ = A + I,
to add information of current node when collecting information from neighbors
with same type.
E.g. collecting info from drug nodes when update current drug embedding.
D: degree matrix (diagonal matrix with number of neighbours on the diagonal).
A_normalize = D^(-1/2) @ A_ @ D^(-1/2),
to symmetric normalization (division by sqrt(N_r^i) * sqrt(N_r^j)
in formula from original paper).
2. Adj matrix for nodes of different type.
Here we don't need to add information from the current node.
D_row: output degree matrix --- diagonal matrix with number of output
neighbours (i.e. i -> neighbours) on the diagonal.
D_col: input degree matrix --- diagonal matrix with number of input
neighbours (i.e. neighbours -> i) on the diagonal.
A_normalize = D_row^(-1/2) @ A @ D_col^(-1/2),
to symmetric normalization (division by sqrt(N_r^i) * sqrt(N_r^j)
in formula from original paper).
"""
adj = sp.coo_matrix(adj)
if same_type_nodes:
adj_ = adj + sp.eye(adj.shape[0])
rowsum = np.array(adj_.sum(1))
degree_mat_inv_sqrt = sp.diags(np.power(rowsum, -0.5).flatten())
adj_normalized = adj_.dot(degree_mat_inv_sqrt).transpose().dot(
degree_mat_inv_sqrt).tocoo()
else:
rowsum = np.array(adj.sum(1))
colsum = np.array(adj.sum(0))
rowdegree_mat_inv = sp.diags(
np.nan_to_num(np.power(rowsum, -0.5)).flatten())
coldegree_mat_inv = sp.diags(
np.nan_to_num(np.power(colsum, -0.5)).flatten())
adj_normalized = rowdegree_mat_inv.dot(adj).dot(
coldegree_mat_inv).tocoo()
return preprocessing.sparse_to_tuple(adj_normalized)
