# Source code for nltk.cluster.gaac

```# Natural Language Toolkit: Group Average Agglomerative Clusterer
#
# Copyright (C) 2001-2022 NLTK Project
# Author: Trevor Cohn <tacohn@cs.mu.oz.au>
# URL: <https://www.nltk.org/>

try:
import numpy
except ImportError:
pass

from nltk.cluster.util import Dendrogram, VectorSpaceClusterer, cosine_distance

[docs]class GAAClusterer(VectorSpaceClusterer):
"""
The Group Average Agglomerative starts with each of the N vectors as singleton
clusters. It then iteratively merges pairs of clusters which have the
closest centroids.  This continues until there is only one cluster. The
order of merges gives rise to a dendrogram: a tree with the earlier merges
lower than later merges. The membership of a given number of clusters c, 1
<= c <= N, can be found by cutting the dendrogram at depth c.

This clusterer uses the cosine similarity metric only, which allows for
efficient speed-up in the clustering process.
"""

[docs]    def __init__(self, num_clusters=1, normalise=True, svd_dimensions=None):
VectorSpaceClusterer.__init__(self, normalise, svd_dimensions)
self._num_clusters = num_clusters
self._dendrogram = None
self._groups_values = None

[docs]    def cluster(self, vectors, assign_clusters=False, trace=False):
# stores the merge order
self._dendrogram = Dendrogram(
[numpy.array(vector, numpy.float64) for vector in vectors]
)
return VectorSpaceClusterer.cluster(self, vectors, assign_clusters, trace)

[docs]    def cluster_vectorspace(self, vectors, trace=False):
# variables describing the initial situation
N = len(vectors)
cluster_len =  * N
cluster_count = N
index_map = numpy.arange(N)

# construct the similarity matrix
dims = (N, N)
dist = numpy.ones(dims, dtype=float) * numpy.inf
for i in range(N):
for j in range(i + 1, N):
dist[i, j] = cosine_distance(vectors[i], vectors[j])

while cluster_count > max(self._num_clusters, 1):
i, j = numpy.unravel_index(dist.argmin(), dims)
if trace:
print("merging %d and %d" % (i, j))

# update similarities for merging i and j
self._merge_similarities(dist, cluster_len, i, j)

# remove j
dist[:, j] = numpy.inf
dist[j, :] = numpy.inf

# merge the clusters
cluster_len[i] = cluster_len[i] + cluster_len[j]
self._dendrogram.merge(index_map[i], index_map[j])
cluster_count -= 1

# update the index map to reflect the indexes if we
index_map[j + 1 :] -= 1
index_map[j] = N

self.update_clusters(self._num_clusters)

def _merge_similarities(self, dist, cluster_len, i, j):
# the new cluster i merged from i and j adopts the average of
# i and j's similarity to each other cluster, weighted by the
# number of points in the clusters i and j
i_weight = cluster_len[i]
j_weight = cluster_len[j]
weight_sum = i_weight + j_weight

# update for x<i
dist[:i, i] = dist[:i, i] * i_weight + dist[:i, j] * j_weight
dist[:i, i] /= weight_sum
# update for i<x<j
dist[i, i + 1 : j] = (
dist[i, i + 1 : j] * i_weight + dist[i + 1 : j, j] * j_weight
)
# update for i<j<x
dist[i, j + 1 :] = dist[i, j + 1 :] * i_weight + dist[j, j + 1 :] * j_weight
dist[i, i + 1 :] /= weight_sum

[docs]    def update_clusters(self, num_clusters):
clusters = self._dendrogram.groups(num_clusters)
self._centroids = []
for cluster in clusters:
assert len(cluster) > 0
if self._should_normalise:
centroid = self._normalise(cluster)
else:
centroid = numpy.array(cluster)
for vector in cluster[1:]:
if self._should_normalise:
centroid += self._normalise(vector)
else:
centroid += vector
centroid /= len(cluster)
self._centroids.append(centroid)
self._num_clusters = len(self._centroids)

[docs]    def classify_vectorspace(self, vector):
best = None
for i in range(self._num_clusters):
centroid = self._centroids[i]
dist = cosine_distance(vector, centroid)
if not best or dist < best:
best = (dist, i)
return best

[docs]    def dendrogram(self):
"""
:return: The dendrogram representing the current clustering
:rtype:  Dendrogram
"""
return self._dendrogram

[docs]    def num_clusters(self):
return self._num_clusters

def __repr__(self):
return "<GroupAverageAgglomerative Clusterer n=%d>" % self._num_clusters

[docs]def demo():
"""
Non-interactive demonstration of the clusterers with simple 2-D data.
"""

from nltk.cluster import GAAClusterer

# use a set of tokens with 2D indices
vectors = [numpy.array(f) for f in [[3, 3], [1, 2], [4, 2], [4, 0], [2, 3], [3, 1]]]

# test the GAAC clusterer with 4 clusters
clusterer = GAAClusterer(4)
clusters = clusterer.cluster(vectors, True)

print("Clusterer:", clusterer)
print("Clustered:", vectors)
print("As:", clusters)
print()

# show the dendrogram
clusterer.dendrogram().show()

# classify a new vector
vector = numpy.array([3, 3])
print("classify(%s):" % vector, end=" ")
print(clusterer.classify(vector))
print()

if __name__ == "__main__":
demo()
```