def sparse_correlation(ind1, data1, ind2, data2, n_features):
mu_x = 0.0
mu_y = 0.0
dot_product = 0.0
if ind1.shape[0] == 0 and ind2.shape[0] == 0:
return 0.0
elif ind1.shape[0] == 0 or ind2.shape[0] == 0:
return 1.0
for i in range(data1.shape[0]):
mu_x += data1[i]
for i in range(data2.shape[0]):
mu_y += data2[i]
mu_x /= n_features
mu_y /= n_features
shifted_data1 = np.empty(data1.shape[0], dtype=np.float32)
shifted_data2 = np.empty(data2.shape[0], dtype=np.float32)
for i in range(data1.shape[0]):
shifted_data1[i] = data1[i] - mu_x
for i in range(data2.shape[0]):
shifted_data2[i] = data2[i] - mu_y
norm1 = np.sqrt(
(norm(shifted_data1) ** 2) + (n_features - ind1.shape[0]) * (mu_x ** 2)
)
norm2 = np.sqrt(
(norm(shifted_data2) ** 2) + (n_features - ind2.shape[0]) * (mu_y ** 2)
)
dot_prod_inds, dot_prod_data = sparse_mul(ind1, shifted_data1, ind2, shifted_data2)
common_indices = set(dot_prod_inds)
for i in range(dot_prod_data.shape[0]):
dot_product += dot_prod_data[i]
for i in range(ind1.shape[0]):
if ind1[i] not in common_indices:
dot_product -= shifted_data1[i] * (mu_y)
for i in range(ind2.shape[0]):
if ind2[i] not in common_indices:
dot_product -= shifted_data2[i] * (mu_x)
all_indices = arr_union(ind1, ind2)
dot_product += mu_x * mu_y * (n_features - all_indices.shape[0])
if norm1 == 0.0 and norm2 == 0.0:
return 0.0
elif dot_product == 0.0:
return 1.0
else:
return 1.0 - (dot_product / (norm1 * norm2))
def sparse_cosine(ind1, data1, ind2, data2):
aux_inds, aux_data = sparse_mul(ind1, data1, ind2, data2)
result = 0.0
norm1 = norm(data1)
norm2 = norm(data2)
for i in range(aux_data.shape[0]):
result += aux_data[i]
return 1.0 - (result / (norm1 * norm2))
def sparse_correlation(ind1, data1, ind2, data2, n_features):
mu_x = 0.0
mu_y = 0.0
dot_product = 0.0
for i in range(data1.shape[0]):
mu_x += data1[i]
for i in range(data2.shape[0]):
mu_y += data2[i]
mu_x /= n_features
mu_y /= n_features
shifted_data1 = np.empty(data1.shape[0], dtype=np.float64)
shifted_data2 = np.empty(data2.shape[0], dtype=np.float64)
for i in range(data1.shape[0]):
shifted_data1[i] = data1[i] - mu_x
for i in range(data2.shape[0]):
shifted_data2[i] = data2[i] - mu_y
norm1 = norm(shifted_data1)
norm2 = norm(shifted_data2)
dot_prod_inds, dot_prod_data = sparse_mul(ind1, shifted_data1,
ind2, shifted_data2)
if dot_prod_data.shape[0] == 0:
return 1.0
for i in range(dot_prod_data.shape[0]):
dot_product += dot_prod_data[i]
if dot_product == 0.0:
return 1.0
else:
return (1.0 - (dot_product / (norm1 * norm2)))
def angular_random_projection_split(data, indices, rng_state):
"""Given a set of ``indices`` for data points from ``data``, create
a random hyperplane to split the data, returning two arrays indices
that fall on either side of the hyperplane. This is the basis for a
random projection tree, which simply uses this splitting recursively.
This particular split uses cosine distance to determine the hyperplane
and which side each data sample falls on.
Parameters
----------
data: array of shape (n_samples, n_features)
The original data to be split
indices: array of shape (tree_node_size,)
The indices of the elements in the ``data`` array that are to
be split in the current operation.
rng_state: array of int64, shape (3,)
The internal state of the rng
Returns
-------
indices_left: array
The elements of ``indices`` that fall on the "left" side of the
random hyperplane.
indices_right: array
The elements of ``indices`` that fall on the "left" side of the
random hyperplane.
"""
dim = data.shape[1]
# Select two random points, set the hyperplane between them
left_index = tau_rand_int(rng_state) % indices.shape[0]
right_index = tau_rand_int(rng_state) % indices.shape[0]
right_index += left_index == right_index
right_index = right_index % indices.shape[0]
left = indices[left_index]
right = indices[right_index]
left_norm = norm(data[left])
right_norm = norm(data[right])
if abs(left_norm) < EPS:
left_norm = 1.0
if abs(right_norm) < EPS:
right_norm = 1.0
# Compute the normal vector to the hyperplane (the vector between
# the two points)
hyperplane_vector = np.empty(dim, dtype=np.float32)
for d in range(dim):
hyperplane_vector[d] = (data[left, d] / left_norm) - (data[right, d] /
right_norm)
hyperplane_norm = norm(hyperplane_vector)
if abs(hyperplane_norm) < EPS:
hyperplane_norm = 1.0
for d in range(dim):
hyperplane_vector[d] = hyperplane_vector[d] / hyperplane_norm
# For each point compute the margin (project into normal vector)
# If we are on lower side of the hyperplane put in one pile, otherwise
# put it in the other pile (if we hit hyperplane on the nose, flip a coin)
n_left = 0
n_right = 0
side = np.empty(indices.shape[0], np.int8)
for i in range(indices.shape[0]):
margin = 0.0
for d in range(dim):
margin += hyperplane_vector[d] * data[indices[i], d]
if abs(margin) < EPS:
side[i] = tau_rand_int(rng_state) % 2
if side[i] == 0:
n_left += 1
else:
n_right += 1
elif margin > 0:
side[i] = 0
n_left += 1
else:
side[i] = 1
n_right += 1
# Now that we have the counts allocate arrays
indices_left = np.empty(n_left, dtype=np.int64)
indices_right = np.empty(n_right, dtype=np.int64)
# Populate the arrays with indices according to which side they fell on
n_left = 0
n_right = 0
for i in range(side.shape[0]):
if side[i] == 0:
indices_left[n_left] = indices[i]
n_left += 1
else:
indices_right[n_right] = indices[i]
n_right += 1
return indices_left, indices_right, hyperplane_vector, None
def sparse_angular_random_projection_split(inds, indptr, data, indices,
rng_state):
"""Given a set of ``indices`` for data points from a sparse data set
presented in csr sparse format as inds, indptr and data, create
a random hyperplane to split the data, returning two arrays indices
that fall on either side of the hyperplane. This is the basis for a
random projection tree, which simply uses this splitting recursively.
This particular split uses cosine distance to determine the hyperplane
and which side each data sample falls on.
Parameters
----------
inds: array
CSR format index array of the matrix
indptr: array
CSR format index pointer array of the matrix
data: array
CSR format data array of the matrix
indices: array of shape (tree_node_size,)
The indices of the elements in the ``data`` array that are to
be split in the current operation.
rng_state: array of int64, shape (3,)
The internal state of the rng
Returns
-------
indices_left: array
The elements of ``indices`` that fall on the "left" side of the
random hyperplane.
indices_right: array
The elements of ``indices`` that fall on the "left" side of the
random hyperplane.
"""
# Select two random points, set the hyperplane between them
left_index = tau_rand_int(rng_state) % indices.shape[0]
right_index = tau_rand_int(rng_state) % indices.shape[0]
right_index += left_index == right_index
right_index = right_index % indices.shape[0]
left = indices[left_index]
right = indices[right_index]
left_inds = inds[indptr[left]:indptr[left + 1]]
left_data = data[indptr[left]:indptr[left + 1]]
right_inds = inds[indptr[right]:indptr[right + 1]]
right_data = data[indptr[right]:indptr[right + 1]]
left_norm = norm(left_data)
right_norm = norm(right_data)
if abs(left_norm) < EPS:
left_norm = 1.0
if abs(right_norm) < EPS:
right_norm = 1.0
# Compute the normal vector to the hyperplane (the vector between
# the two points)
normalized_left_data = left_data / left_norm
normalized_right_data = right_data / right_norm
hyperplane_inds, hyperplane_data = sparse_diff(left_inds,
normalized_left_data,
right_inds,
normalized_right_data)
hyperplane_norm = norm(hyperplane_data)
if abs(hyperplane_norm) < EPS:
hyperplane_norm = 1.0
for d in range(hyperplane_data.shape[0]):
hyperplane_data[d] = hyperplane_data[d] / hyperplane_norm
# For each point compute the margin (project into normal vector)
# If we are on lower side of the hyperplane put in one pile, otherwise
# put it in the other pile (if we hit hyperplane on the nose, flip a coin)
n_left = 0
n_right = 0
side = np.empty(indices.shape[0], np.int8)
for i in range(indices.shape[0]):
margin = 0.0
i_inds = inds[indptr[indices[i]]:indptr[indices[i] + 1]]
i_data = data[indptr[indices[i]]:indptr[indices[i] + 1]]
mul_inds, mul_data = sparse_mul(hyperplane_inds, hyperplane_data,
i_inds, i_data)
for d in range(mul_data.shape[0]):
margin += mul_data[d]
if abs(margin) < EPS:
side[i] = tau_rand_int(rng_state) % 2
if side[i] == 0:
n_left += 1
else:
n_right += 1
elif margin > 0:
side[i] = 0
n_left += 1
else:
side[i] = 1
n_right += 1
# Now that we have the counts allocate arrays
indices_left = np.empty(n_left, dtype=np.int64)
indices_right = np.empty(n_right, dtype=np.int64)
# Populate the arrays with indices according to which side they fell on
n_left = 0
n_right = 0
for i in range(side.shape[0]):
if side[i] == 0:
indices_left[n_left] = indices[i]
n_left += 1
else:
indices_right[n_right] = indices[i]
n_right += 1
hyperplane = np.vstack((hyperplane_inds, hyperplane_data))
return indices_left, indices_right, hyperplane, None
