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# mutual reachability distance computations
# Authors: Leland McInnes <leland.mcinnes@gmail.com>
# Meekail Zain <zainmeekail@gmail.com>
# Guillaume Lemaitre <g.lemaitre58@gmail.com>
# Copyright (c) 2015, Leland McInnes
# All rights reserved.
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
# 3. Neither the name of the copyright holder nor the names of its contributors
# may be used to endorse or promote products derived from this software without
# specific prior written permission.
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
cimport numpy as cnp
import numpy as np
from scipy.sparse import issparse
from cython cimport floating, integral
from libc.math cimport isfinite, INFINITY
from ...utils._typedefs cimport intp_t
cnp.import_array()
def mutual_reachability_graph(
distance_matrix, min_samples=5, max_distance=0.0
):
"""Compute the weighted adjacency matrix of the mutual reachability graph.
The mutual reachability distance used to build the graph is defined as::
max(d_core(x_p), d_core(x_q), d(x_p, x_q))
and the core distance `d_core` is defined as the distance between a point
`x_p` and its k-th nearest neighbor.
Note that all computations are done in-place.
Parameters
----------
distance_matrix : {ndarray, sparse matrix} of shape (n_samples, n_samples)
Array of distances between samples. If sparse, the array must be in
`CSR` format.
min_samples : int, default=5
The number of points in a neighbourhood for a point to be considered
a core point.
max_distance : float, default=0.0
The distance which `np.inf` is replaced with. When the true mutual-
reachability distance is measured to be infinite, it is instead
truncated to `max_dist`. Only used when `distance_matrix` is a sparse
matrix.
Returns
-------
mututal_reachability_graph: {ndarray, sparse matrix} of shape \
(n_samples, n_samples)
Weighted adjacency matrix of the mutual reachability graph.
References
----------
.. [1] Campello, R. J., Moulavi, D., & Sander, J. (2013, April).
Density-based clustering based on hierarchical density estimates.
In Pacific-Asia Conference on Knowledge Discovery and Data Mining
(pp. 160-172). Springer Berlin Heidelberg.
"""
further_neighbor_idx = min_samples - 1
if issparse(distance_matrix):
if distance_matrix.format != "csr":
raise ValueError(
"Only sparse CSR matrices are supported for `distance_matrix`."
)
_sparse_mutual_reachability_graph(
distance_matrix.data,
distance_matrix.indices,
distance_matrix.indptr,
distance_matrix.shape[0],
further_neighbor_idx=further_neighbor_idx,
max_distance=max_distance,
)
else:
_dense_mutual_reachability_graph(
distance_matrix, further_neighbor_idx=further_neighbor_idx
)
return distance_matrix
def _dense_mutual_reachability_graph(
floating[:, :] distance_matrix,
intp_t further_neighbor_idx,
):
"""Dense implementation of mutual reachability graph.
The computation is done in-place, i.e. the distance matrix is modified
directly.
Parameters
----------
distance_matrix : ndarray of shape (n_samples, n_samples)
Array of distances between samples.
further_neighbor_idx : int
The index of the furthest neighbor to use to define the core distances.
"""
cdef:
intp_t i, j, n_samples = distance_matrix.shape[0]
floating mutual_reachibility_distance
floating[::1] core_distances
# We assume that the distance matrix is symmetric. We choose to sort every
# row to have the same implementation than the sparse case that requires
# CSR matrix.
core_distances = np.ascontiguousarray(
np.partition(
distance_matrix, further_neighbor_idx, axis=1
)[:, further_neighbor_idx]
)
with nogil:
# TODO: Update w/ prange with thread count based on
# _openmp_effective_n_threads
for i in range(n_samples):
for j in range(n_samples):
mutual_reachibility_distance = max(
core_distances[i],
core_distances[j],
distance_matrix[i, j],
)
distance_matrix[i, j] = mutual_reachibility_distance
def _sparse_mutual_reachability_graph(
cnp.ndarray[floating, ndim=1, mode="c"] data,
cnp.ndarray[integral, ndim=1, mode="c"] indices,
cnp.ndarray[integral, ndim=1, mode="c"] indptr,
intp_t n_samples,
intp_t further_neighbor_idx,
floating max_distance,
):
"""Sparse implementation of mutual reachability graph.
The computation is done in-place, i.e. the distance matrix is modified
directly. This implementation only accepts `CSR` format sparse matrices.
Parameters
----------
distance_matrix : sparse matrix of shape (n_samples, n_samples)
Sparse matrix of distances between samples. The sparse format should
be `CSR`.
further_neighbor_idx : int
The index of the furthest neighbor to use to define the core distances.
max_distance : float
The distance which `np.inf` is replaced with. When the true mutual-
reachability distance is measured to be infinite, it is instead
truncated to `max_dist`. Only used when `distance_matrix` is a sparse
matrix.
"""
cdef:
integral i, col_ind, row_ind
floating mutual_reachibility_distance
floating[:] core_distances
floating[:] row_data
if floating is float:
dtype = np.float32
else:
dtype = np.float64
core_distances = np.empty(n_samples, dtype=dtype)
for i in range(n_samples):
row_data = data[indptr[i]:indptr[i + 1]]
if further_neighbor_idx < row_data.size:
core_distances[i] = np.partition(
row_data, further_neighbor_idx
)[further_neighbor_idx]
else:
core_distances[i] = INFINITY
with nogil:
for row_ind in range(n_samples):
for i in range(indptr[row_ind], indptr[row_ind + 1]):
col_ind = indices[i]
mutual_reachibility_distance = max(
core_distances[row_ind], core_distances[col_ind], data[i]
)
if isfinite(mutual_reachibility_distance):
data[i] = mutual_reachibility_distance
elif max_distance > 0:
data[i] = max_distance
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