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_hierarchy.pyx
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_hierarchy.pyx
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# cython: boundscheck=False, wraparound=False, cdivision=True
import numpy as np
cimport numpy as np
from libc.math cimport sqrt
from libc.string cimport memset
from cpython.mem cimport PyMem_Malloc, PyMem_Free
cdef extern from "numpy/npy_math.h":
cdef enum:
NPY_INFINITYF
ctypedef unsigned char uchar
# _hierarchy_distance_update.pxi includes the definition of linkage_distance_update
# and the distance update functions for the supported linkage methods.
include "_hierarchy_distance_update.pxi"
cdef linkage_distance_update *linkage_methods = [
_single, _complete, _average, _centroid, _median, _ward, _weighted]
include "_structures.pxi"
cdef inline np.npy_int64 condensed_index(np.npy_int64 n, np.npy_int64 i,
np.npy_int64 j):
"""
Calculate the condensed index of element (i, j) in an n x n condensed
matrix.
"""
if i < j:
return n * i - (i * (i + 1) / 2) + (j - i - 1)
elif i > j:
return n * j - (j * (j + 1) / 2) + (i - j - 1)
cdef inline int is_visited(uchar *bitset, int i):
"""
Check if node i was visited.
"""
return bitset[i >> 3] & (1 << (i & 7))
cdef inline void set_visited(uchar *bitset, int i):
"""
Mark node i as visited.
"""
bitset[i >> 3] |= 1 << (i & 7)
cpdef void calculate_cluster_sizes(double[:, :] Z, double[:] cs, int n):
"""
Calculate the size of each cluster. The result is the fourth column of
the linkage matrix.
Parameters
----------
Z : ndarray
The linkage matrix. The fourth column can be empty.
cs : ndarray
The array to store the sizes.
n : ndarray
The number of observations.
"""
cdef int i, child_l, child_r
for i in range(n - 1):
child_l = <int>Z[i, 0]
child_r = <int>Z[i, 1]
if child_l >= n:
cs[i] += cs[child_l - n]
else:
cs[i] += 1
if child_r >= n:
cs[i] += cs[child_r - n]
else:
cs[i] += 1
def cluster_dist(double[:, :] Z, int[:] T, double cutoff, int n):
"""
Form flat clusters by distance criterion.
Parameters
----------
Z : ndarray
The linkage matrix.
T : ndarray
The array to store the cluster numbers. The i'th observation belongs to
cluster `T[i]`.
cutoff : double
Clusters are formed when distances are less than or equal to `cutoff`.
n : int
The number of observations.
"""
cdef double[:] max_dists = np.ndarray(n, dtype=np.double)
get_max_dist_for_each_cluster(Z, max_dists, n)
cluster_monocrit(Z, max_dists, T, cutoff, n)
def cluster_in(double[:, :] Z, double[:, :] R, int[:] T, double cutoff, int n):
"""
Form flat clusters by inconsistent criterion.
Parameters
----------
Z : ndarray
The linkage matrix.
R : ndarray
The inconsistent matrix.
T : ndarray
The array to store the cluster numbers. The i'th observation belongs to
cluster `T[i]`.
cutoff : double
Clusters are formed when the inconsistent values are less than or
or equal to `cutoff`.
n : int
The number of observations.
"""
cdef double[:] max_inconsists = np.ndarray(n, dtype=np.double)
get_max_Rfield_for_each_cluster(Z, R, max_inconsists, n, 3)
cluster_monocrit(Z, max_inconsists, T, cutoff, n)
def cluster_maxclust_dist(double[:, :] Z, int[:] T, int n, int mc):
"""
Form flat clusters by maxclust criterion.
Parameters
----------
Z : ndarray
The linkage matrix.
T : ndarray
The array to store the cluster numbers. The i'th observation belongs to
cluster `T[i]`.
n : int
The number of observations.
mc : int
The maximum number of clusters.
"""
cdef double[:] max_dists = np.ndarray(n, dtype=np.double)
get_max_dist_for_each_cluster(Z, max_dists, n)
# should use an O(n) algorithm
cluster_maxclust_monocrit(Z, max_dists, T, n, mc)
cpdef void cluster_maxclust_monocrit(double[:, :] Z, double[:] MC, int[:] T,
int n, int max_nc):
"""
Form flat clusters by maxclust_monocrit criterion.
Parameters
----------
Z : ndarray
The linkage matrix.
MC : ndarray
The monotonic criterion array.
T : ndarray
The array to store the cluster numbers. The i'th observation belongs to
cluster `T[i]`.
n : int
The number of observations.
max_nc : int
The maximum number of clusters.
"""
cdef int i, k, i_lc, i_rc, root, nc, lower_idx, upper_idx
cdef double thresh
cdef int[:] curr_node = np.ndarray(n, dtype=np.intc)
cdef int visited_size = (((n * 2) - 1) >> 3) + 1
cdef uchar *visited = <uchar *>PyMem_Malloc(visited_size)
if not visited:
raise MemoryError
lower_idx = 0
upper_idx = n - 1
while upper_idx - lower_idx > 1:
i = (lower_idx + upper_idx) >> 1
thresh = MC[i]
memset(visited, 0, visited_size)
nc = 0
k = 0
curr_node[0] = 2 * n - 2
while k >= 0:
root = curr_node[k] - n
i_lc = <int>Z[root, 0]
i_rc = <int>Z[root, 1]
if MC[root] <= thresh: # this subtree forms a cluster
nc += 1
if nc > max_nc: # illegal
break
k -= 1
set_visited(visited, i_lc)
set_visited(visited, i_rc)
continue
if not is_visited(visited, i_lc):
set_visited(visited, i_lc)
if i_lc >= n:
k += 1
curr_node[k] = i_lc
continue
else: # singleton cluster
nc += 1
if nc > max_nc:
break
if not is_visited(visited, i_rc):
set_visited(visited, i_rc)
if i_rc >= n:
k += 1
curr_node[k] = i_rc
continue
else: # singleton cluster
nc += 1
if nc > max_nc:
break
k -= 1
if nc > max_nc:
lower_idx = i
else:
upper_idx = i
PyMem_Free(visited)
cluster_monocrit(Z, MC, T, MC[upper_idx], n)
cpdef void cluster_monocrit(double[:, :] Z, double[:] MC, int[:] T,
double cutoff, int n):
"""
Form flat clusters by monocrit criterion.
Parameters
----------
Z : ndarray
The linkage matrix.
MC : ndarray
The monotonic criterion array.
T : ndarray
The array to store the cluster numbers. The i'th observation belongs to
cluster `T[i]`.
cutoff : double
Clusters are formed when the MC values are less than or equal to
`cutoff`.
n : int
The number of observations.
"""
cdef int k, i_lc, i_rc, root, n_cluster = 0, cluster_leader = -1
cdef int[:] curr_node = np.ndarray(n, dtype=np.intc)
cdef int visited_size = (((n * 2) - 1) >> 3) + 1
cdef uchar *visited = <uchar *>PyMem_Malloc(visited_size)
if not visited:
raise MemoryError
memset(visited, 0, visited_size)
k = 0
curr_node[0] = 2 * n - 2
while k >= 0:
root = curr_node[k] - n
i_lc = <int>Z[root, 0]
i_rc = <int>Z[root, 1]
if cluster_leader == -1 and MC[root] <= cutoff: # found a cluster
cluster_leader = root
n_cluster += 1
if i_lc >= n and not is_visited(visited, i_lc):
set_visited(visited, i_lc)
k += 1
curr_node[k] = i_lc
continue
if i_rc >= n and not is_visited(visited, i_rc):
set_visited(visited, i_rc)
k += 1
curr_node[k] = i_rc
continue
if i_lc < n:
if cluster_leader == -1: # singleton cluster
n_cluster += 1
T[i_lc] = n_cluster
if i_rc < n:
if cluster_leader == -1: # singleton cluster
n_cluster += 1
T[i_rc] = n_cluster
if cluster_leader == root: # back to the leader
cluster_leader = -1
k -= 1
PyMem_Free(visited)
def cophenetic_distances(double[:, :] Z, double[:] d, int n):
"""
Calculate the cophenetic distances between each observation
Parameters
----------
Z : ndarray
The linkage matrix.
d : ndarray
The condensed matrix to store the cophenetic distances.
n : int
The number of observations.
"""
cdef int i, j, k, root, i_lc, i_rc, n_lc, n_rc, right_start
cdef double dist
cdef int[:] curr_node = np.ndarray(n, dtype=np.intc)
cdef int[:] members = np.ndarray(n, dtype=np.intc)
cdef int[:] left_start = np.ndarray(n, dtype=np.intc)
cdef int visited_size = (((n * 2) - 1) >> 3) + 1
cdef uchar *visited = <uchar *>PyMem_Malloc(visited_size)
if not visited:
raise MemoryError
memset(visited, 0, visited_size)
k = 0
curr_node[0] = 2 * n - 2
left_start[0] = 0
while k >= 0:
root = curr_node[k] - n
i_lc = <int>Z[root, 0]
i_rc = <int>Z[root, 1]
if i_lc >= n: # left child is not a leaf
n_lc = <int>Z[i_lc - n, 3]
if not is_visited(visited, i_lc):
set_visited(visited, i_lc)
k += 1
curr_node[k] = i_lc
left_start[k] = left_start[k - 1]
continue # visit the left subtree
else:
n_lc = 1
members[left_start[k]] = i_lc
if i_rc >= n: # right child is not a leaf
n_rc = <int>Z[i_rc - n, 3]
if not is_visited(visited, i_rc):
set_visited(visited, i_rc)
k += 1
curr_node[k] = i_rc
left_start[k] = left_start[k - 1] + n_lc
continue # visit the right subtree
else:
n_rc = 1
members[left_start[k] + n_lc] = i_rc
# back to the root of current subtree
dist = Z[root, 2]
right_start = left_start[k] + n_lc
for i in range(left_start[k], right_start):
for j in range(right_start, right_start + n_rc):
d[condensed_index(n, members[i], members[j])] = dist
k -= 1 # back to parent node
PyMem_Free(visited)
cpdef void get_max_Rfield_for_each_cluster(double[:, :] Z, double[:, :] R,
double[:] max_rfs, int n, int rf):
"""
Get the maximum statistic for each non-singleton cluster. For the i'th
non-singleton cluster, max_rfs[i] = max{R[j, rf] j is a descendent of i}.
Parameters
----------
Z : ndarray
The linkage matrix.
R : ndarray
The R matrix.
max_rfs : ndarray
The array to store the result.
n : int
The number of observations.
rf : int
Indicate which column of `R` is used.
"""
cdef int k, i_lc, i_rc, root
cdef double max_rf, max_l, max_r
cdef int[:] curr_node = np.ndarray(n, dtype=np.intc)
cdef int visited_size = (((n * 2) - 1) >> 3) + 1
cdef uchar *visited = <uchar *>PyMem_Malloc(visited_size)
if not visited:
raise MemoryError
memset(visited, 0, visited_size)
k = 0
curr_node[0] = 2 * n - 2
while k >= 0:
root = curr_node[k] - n
i_lc = <int>Z[root, 0]
i_rc = <int>Z[root, 1]
if i_lc >= n and not is_visited(visited, i_lc):
set_visited(visited, i_lc)
k += 1
curr_node[k] = i_lc
continue
if i_rc >= n and not is_visited(visited, i_rc):
set_visited(visited, i_rc)
k += 1
curr_node[k] = i_rc
continue
max_rf = R[root, rf]
if i_lc >= n:
max_l = max_rfs[i_lc - n]
if max_l > max_rf:
max_rf = max_l
if i_rc >= n:
max_r = max_rfs[i_rc - n]
if max_r > max_rf:
max_rf = max_r
max_rfs[root] = max_rf
k -= 1
PyMem_Free(visited)
cpdef get_max_dist_for_each_cluster(double[:, :] Z, double[:] MD, int n):
"""
Get the maximum inconsistency coefficient for each non-singleton cluster.
Parameters
----------
Z : ndarray
The linkage matrix.
MD : ndarray
The array to store the result.
n : int
The number of observations.
"""
cdef int k, i_lc, i_rc, root
cdef double max_dist, max_l, max_r
cdef int[:] curr_node = np.ndarray(n, dtype=np.intc)
cdef int visited_size = (((n * 2) - 1) >> 3) + 1
cdef uchar *visited = <uchar *>PyMem_Malloc(visited_size)
if not visited:
raise MemoryError
memset(visited, 0, visited_size)
k = 0
curr_node[0] = 2 * n - 2
while k >= 0:
root = curr_node[k] - n
i_lc = <int>Z[root, 0]
i_rc = <int>Z[root, 1]
if i_lc >= n and not is_visited(visited, i_lc):
set_visited(visited, i_lc)
k += 1
curr_node[k] = i_lc
continue
if i_rc >= n and not is_visited(visited, i_rc):
set_visited(visited, i_rc)
k += 1
curr_node[k] = i_rc
continue
max_dist = Z[root, 2]
if i_lc >= n:
max_l = MD[i_lc - n]
if max_l > max_dist:
max_dist = max_l
if i_rc >= n:
max_r = MD[i_rc - n]
if max_r > max_dist:
max_dist = max_r
MD[root] = max_dist
k -= 1
PyMem_Free(visited)
def inconsistent(double[:, :] Z, double[:, :] R, int n, int d):
"""
Calculate the inconsistency statistics.
Parameters
----------
Z : ndarray
The linkage matrix.
R : ndarray
A (n - 1) x 4 matrix to store the result. The inconsistency statistics
`R[i]` are calculated over `d` levels below cluster i. `R[i, 0]` is the
mean of distances. `R[i, 1]` is the standard deviation of distances.
`R[i, 2]` is the number of clusters included. `R[i, 3]` is the
inconsistency coefficient.
.. math:: \\frac{\\mathtt{Z[i,2]}-\\mathtt{R[i,0]}} {R[i,1]}
n : int
The number of observations.
d : int
The number of levels included in calculation below a node.
"""
cdef int i, k, i_lc, i_rc, root, level_count
cdef int[:] curr_node = np.ndarray(n, dtype=np.intc)
cdef double level_sum, level_std_sum, level_std, dist
cdef int visited_size = (((n * 2) - 1) >> 3) + 1
cdef uchar *visited = <uchar *>PyMem_Malloc(visited_size)
if not visited:
raise MemoryError
for i in range(n - 1):
k = 0
level_count = 0
level_sum = 0
level_std_sum = 0
memset(visited, 0, visited_size)
curr_node[0] = i
while k >= 0:
root = curr_node[k]
if k < d - 1:
i_lc = <int>Z[root, 0]
if i_lc >= n and not is_visited(visited, i_lc):
set_visited(visited, i_lc)
k += 1
curr_node[k] = i_lc - n
continue
i_rc = <int>Z[root, 1]
if i_rc >= n and not is_visited(visited, i_rc):
set_visited(visited, i_rc)
k += 1
curr_node[k] = i_rc - n
continue
dist = Z[root, 2]
level_count += 1
level_sum += dist
level_std_sum += dist * dist
k -= 1
R[i, 0] = level_sum / level_count
R[i, 2] = level_count
if level_count < 2:
level_std = (level_std_sum - (level_sum * level_sum)) / level_count
else:
level_std = ((level_std_sum -
((level_sum * level_sum) / level_count)) /
(level_count - 1))
if level_std > 0:
level_std = sqrt(level_std)
R[i, 1] = level_std
R[i, 3] = (Z[i, 2] - R[i, 0]) / level_std
else:
R[i, 1] = 0
PyMem_Free(visited)
def leaders(double[:, :] Z, int[:] T, int[:] L, int[:] M, int nc, int n):
"""
Find the leader (root) of each flat cluster.
Parameters
----------
Z : ndarray
The linkage matrix.
T : ndarray
The flat clusters assignment returned by `fcluster` or `fclusterdata`.
L : ndarray
`L` and `M` store the result. The leader of flat cluster `L[i]` is
node `M[i]`.
M : ndarray
`L` and `M` store the result. The leader of flat cluster `L[i]` is
node `M[i]`.
nc : int
The number of flat clusters.
n : int
The number of observations.
Returns
-------
err_node : int
Found that `T` is invalid when examining node `err_node`.
`-1` indicates success.
"""
cdef int k, i_lc, i_rc, root, cid_lc, cid_rc, leader_idx, result = -1
cdef int[:] curr_node = np.ndarray(n, dtype=np.intc)
cdef int[:] cluster_ids = np.ndarray(n * 2 - 1, dtype=np.intc)
cdef int visited_size = (((n * 2) - 1) >> 3) + 1
cdef uchar *visited = <uchar *>PyMem_Malloc(visited_size)
if not visited:
raise MemoryError
memset(visited, 0, visited_size)
cluster_ids[:n] = T[:]
cluster_ids[n:] = -1
k = 0
curr_node[0] = 2 * n - 2
leader_idx = 0
while k >= 0:
root = curr_node[k] - n
i_lc = <int>Z[root, 0]
i_rc = <int>Z[root, 1]
if i_lc >= n and not is_visited(visited, i_lc):
set_visited(visited, i_lc)
k += 1
curr_node[k] = i_lc
continue
if i_rc >= n and not is_visited(visited, i_rc):
set_visited(visited, i_rc)
k += 1
curr_node[k] = i_rc
continue
cid_lc = cluster_ids[i_lc]
cid_rc = cluster_ids[i_rc]
if cid_lc == cid_rc: # left and right children in the same cluster
cluster_ids[root + n] = cid_lc
else: # left and right children are both leaders
if cid_lc != -1:
if leader_idx >= nc:
result = root + n
break
L[leader_idx] = i_lc
M[leader_idx] = cid_lc
leader_idx += 1
if cid_rc != -1:
if leader_idx >= nc:
result = root + n
break
L[leader_idx] = i_rc
M[leader_idx] = cid_rc
leader_idx += 1
cluster_ids[root + n] = -1
k -= 1
if result == -1:
i_lc = <int>Z[n - 2, 0]
i_rc = <int>Z[n - 2, 1]
cid_lc = cluster_ids[i_lc]
cid_rc = cluster_ids[i_rc]
if cid_lc == cid_rc and cid_lc != -1:
if leader_idx >= nc:
result = 2 * n - 2
else:
L[leader_idx] = 2 * n - 2
M[leader_idx] = cid_lc
PyMem_Free(visited)
return result # -1 means success here
def linkage(double[:] dists, np.npy_int64 n, int method):
"""
Perform hierarchy clustering.
Parameters
----------
dists : ndarray
A condensed matrix stores the pairwise distances of the observations.
n : int
The number of observations.
method : int
The linkage method. 0: single 1: complete 2: average 3: centroid
4: median 5: ward 6: weighted
Returns
-------
Z : ndarray, shape (n - 1, 4)
Computed linkage matrix.
"""
Z_arr = np.empty((n - 1, 4))
cdef double[:, :] Z = Z_arr
cdef int i, j, k, x, y, nx, ny, ni, id_x, id_y, id_i
cdef np.npy_int64 i_start
cdef double current_min
# inter-cluster dists
cdef double[:] D = np.ndarray(n * (n - 1) / 2, dtype=np.double)
# map the indices to node ids
cdef int[:] id_map = np.ndarray(n, dtype=np.intc)
cdef linkage_distance_update new_dist
new_dist = linkage_methods[method]
D[:] = dists
for i in range(n):
id_map[i] = i
for k in range(n - 1):
# find two closest clusters x, y (x < y)
current_min = NPY_INFINITYF
for i in range(n - 1):
if id_map[i] == -1:
continue
i_start = condensed_index(n, i, i + 1)
for j in range(n - i - 1):
if D[i_start + j] < current_min:
current_min = D[i_start + j]
x = i
y = i + j + 1
id_x = id_map[x]
id_y = id_map[y]
# get the original numbers of points in clusters x and y
nx = 1 if id_x < n else <int>Z[id_x - n, 3]
ny = 1 if id_y < n else <int>Z[id_y - n, 3]
# record the new node
Z[k, 0] = min(id_x, id_y)
Z[k, 1] = max(id_y, id_x)
Z[k, 2] = current_min
Z[k, 3] = nx + ny
id_map[x] = -1 # cluster x will be dropped
id_map[y] = n + k # cluster y will be replaced with the new cluster
# update the distance matrix
for i in range(n):
id_i = id_map[i]
if id_i == -1 or id_i == n + k:
continue
ni = 1 if id_i < n else <int>Z[id_i - n, 3]
D[condensed_index(n, i, y)] = new_dist(
D[condensed_index(n, i, x)],
D[condensed_index(n, i, y)],
current_min, nx, ny, ni)
if i < x:
D[condensed_index(n, i, x)] = NPY_INFINITYF
return Z_arr
cdef Pair find_min_dist(int n, double[:] D, int[:] size, int x):
cdef double current_min = NPY_INFINITYF
cdef int y = -1
cdef int i
cdef double dist
for i in range(x + 1, n):
if size[i] == 0:
continue
dist = D[condensed_index(n, x, i)]
if dist < current_min:
current_min = dist
y = i
return Pair(y, current_min)
def fast_linkage(double[:] dists, int n, int method):
"""Perform hierarchy clustering.
It implements "Generic Clustering Algorithm" from [1]. The worst case
time complexity is O(N^3), but the best case time complexity is O(N^2) and
it usually works quite close to the best case.
Parameters
----------
dists : ndarray
A condensed matrix stores the pairwise distances of the observations.
n : int
The number of observations.
method : int
The linkage method. 0: single 1: complete 2: average 3: centroid
4: median 5: ward 6: weighted
Returns
-------
Z : ndarray, shape (n - 1, 4)
Computed linkage matrix.
References
----------
.. [1] Daniel Mullner, "Modern hierarchical, agglomerative clustering
algorithms", :arXiv:`1109.2378v1`.
"""
cdef double[:, :] Z = np.empty((n - 1, 4))
cdef double[:] D = dists.copy() # Distances between clusters.
cdef int[:] size = np.ones(n, dtype=np.intc) # Sizes of clusters.
# ID of a cluster to put into linkage matrix.
cdef int[:] cluster_id = np.arange(n, dtype=np.intc)
# Nearest neighbor candidate and lower bound of the distance to the
# true nearest neighbor for each cluster among clusters with higher
# indices (thus size is n - 1).
cdef int[:] neighbor = np.empty(n - 1, dtype=np.intc)
cdef double[:] min_dist = np.empty(n - 1)
cdef linkage_distance_update new_dist = linkage_methods[method]
cdef int i, k
cdef int x, y, z
cdef int nx, ny, nz
cdef int id_x, id_y
cdef double dist
cdef Pair pair
for x in range(n - 1):
pair = find_min_dist(n, D, size, x)
neighbor[x] = pair.key
min_dist[x] = pair.value
cdef Heap min_dist_heap = Heap(min_dist)
for k in range(n - 1):
# Theoretically speaking, this can be implemented as "while True", but
# having a fixed size loop when floating point computations involved
# looks more reliable. The idea that we should find the two closest
# clusters in no more that n - k (1 for the last iteration) distance
# updates.
for i in range(n - k):
pair = min_dist_heap.get_min()
x, dist = pair.key, pair.value
y = neighbor[x]
if dist == D[condensed_index(n, x, y)]:
break
pair = find_min_dist(n, D, size, x)
y, dist = pair.key, pair.value
neighbor[x] = y
min_dist[x] = dist
min_dist_heap.change_value(x, dist)
min_dist_heap.remove_min()
id_x = cluster_id[x]
id_y = cluster_id[y]
nx = size[x]
ny = size[y]
if id_x > id_y:
id_x, id_y = id_y, id_x
Z[k, 0] = id_x
Z[k, 1] = id_y
Z[k, 2] = dist
Z[k, 3] = nx + ny
size[x] = 0 # Cluster x will be dropped.
size[y] = nx + ny # Cluster y will be replaced with the new cluster.
cluster_id[y] = n + k # Update ID of y.
# Update the distance matrix.
for z in range(n):
nz = size[z]
if nz == 0 or z == y:
continue
D[condensed_index(n, z, y)] = new_dist(
D[condensed_index(n, z, x)], D[condensed_index(n, z, y)],
dist, nx, ny, nz)
# Reassign neighbor candidates from x to y.
# This reassignment is just a (logical) guess.
for z in range(x):
if size[z] > 0 and neighbor[z] == x:
neighbor[z] = y
# Update lower bounds of distance.
for z in range(y):
if size[z] == 0:
continue
dist = D[condensed_index(n, z, y)]
if dist < min_dist[z]:
neighbor[z] = y
min_dist[z] = dist
min_dist_heap.change_value(z, dist)
# Find nearest neighbor for y.
if y < n - 1:
pair = find_min_dist(n, D, size, y)
z, dist = pair.key, pair.value
if z != -1:
neighbor[y] = z
min_dist[y] = dist
min_dist_heap.change_value(y, dist)
return Z.base
def nn_chain(double[:] dists, int n, int method):
"""Perform hierarchy clustering using nearest-neighbor chain algorithm.
Parameters
----------
dists : ndarray
A condensed matrix stores the pairwise distances of the observations.
n : int
The number of observations.
method : int
The linkage method. 0: single 1: complete 2: average 3: centroid
4: median 5: ward 6: weighted
Returns
-------
Z : ndarray, shape (n - 1, 4)
Computed linkage matrix.
"""
Z_arr = np.empty((n - 1, 4))
cdef double[:, :] Z = Z_arr
cdef double[:] D = dists.copy() # Distances between clusters.
cdef int[:] size = np.ones(n, dtype=np.intc) # Sizes of clusters.
cdef linkage_distance_update new_dist = linkage_methods[method]
# Variables to store neighbors chain.
cdef int[:] cluster_chain = np.ndarray(n, dtype=np.intc)
cdef int chain_length = 0
cdef int i, j, k, x, y, nx, ny, ni
cdef double dist, current_min
for k in range(n - 1):
if chain_length == 0:
chain_length = 1
for i in range(n):
if size[i] > 0:
cluster_chain[0] = i
break
# Go through chain of neighbors until two mutual neighbors are found.
while True:
x = cluster_chain[chain_length - 1]
# We want to prefer the previous element in the chain as the
# minimum, to avoid potentially going in cycles.
if chain_length > 1:
y = cluster_chain[chain_length - 2]
current_min = D[condensed_index(n, x, y)]
else:
current_min = NPY_INFINITYF
for i in range(n):
if size[i] == 0 or x == i:
continue
dist = D[condensed_index(n, x, i)]
if dist < current_min:
current_min = dist
y = i
if chain_length > 1 and y == cluster_chain[chain_length - 2]:
break
cluster_chain[chain_length] = y
chain_length += 1
# Merge clusters x and y and pop them from stack.
chain_length -= 2
# This is a convention used in fastcluster.
if x > y:
x, y = y, x
# get the original numbers of points in clusters x and y
nx = size[x]
ny = size[y]
# Record the new node.
Z[k, 0] = x
Z[k, 1] = y
Z[k, 2] = current_min
Z[k, 3] = nx + ny
size[x] = 0 # Cluster x will be dropped.
size[y] = nx + ny # Cluster y will be replaced with the new cluster
# Update the distance matrix.
for i in range(n):
ni = size[i]
if ni == 0 or i == y:
continue