def silhouette(cls, graph, clusters):
"""
Find the average silhouette distance for the clusters.
"""
paths = graph.paths()
# Calculate the distances for all pairs of nodes.
dists = {}
for node1, node2 in combinations(graph.nodes, 2):
value1 = node1.value
value2 = node2.value
dist = graph.dist(node1, node2, paths)
if not value1 in dists:
dists[value1] = {}
if not value2 in dists:
dists[value2] = {}
dists[value1][value2] = dist
dists[value2][value1] = dist
s = 0.0
for node in graph.nodes:
# Find a and b.
a = 0.0
b = float('inf')
for cluster in clusters:
if cluster.node(node.value):
if len(cluster.nodes) > 1:
a = sum([dists[node.value][onode.value] for onode in cluster.nodes if node.value != onode.value]) / float(len(cluster.nodes) - 1)
else:
a = 0.0
else:
b = min(b, sum([dists[node.value][onode.value] for onode in cluster.nodes]) / float(len(cluster.nodes)))
if b == float('inf'):
b = 0.0
s += (b - a) / max(a, b)
return s / len(graph.nodes)
def davies_bouldin(cls, graph, clusters):
"""
Return the davies bouldin index for the clusters.
Key arguments:
graph -- the original graph
clusters -- the clusters to analyze
"""
# If we only have one cluster, then return inf!
if len(clusters) < 2:
return float('inf')
# Special case, if all the clusters are singletons, return inf.
singletons = True
for cluster in clusters:
if len(cluster.nodes) > 1:
singletons = False
break
if singletons:
return float('inf')
# Calculate the diameters for each cluster.
diams = {}
for cluster in clusters:
diams[cluster] = 0.0
if len(cluster.nodes) > 1:
paths = cluster.paths()
for node1, node2 in combinations(cluster.nodes, 2):
diams[cluster] = max(diams[cluster], cluster.dist(node1, node2, paths))
# If it weren't for directed graphs, we could use the combinations method.
for node1 in paths:
for node2 in paths[node1]:
if node1 != node2 and paths[node1][node2]:
diams[cluster] = max(diams[cluster], cluster.dist(node1, node2, paths))
# Find all the graphs paths.
paths = graph.paths()
# Calculate the distances between each cluster.
dists = {}
for cluster1, cluster2 in combinations(clusters, 2):
if not cluster1 in dists:
dists[cluster1] = {}
if not cluster2 in dists:
dists[cluster2] = {}
# Find the average cluster distance between cluster i and j.
dist = sum([graph.dist(node1, node2, paths) for node1, node2 in product(cluster1.nodes, cluster2.nodes)]) / float(len(cluster1.nodes) * len(cluster2.nodes))
dists[cluster1][cluster2] = dist
dists[cluster2][cluster1] = dist
num = 0.0
for cluster1 in clusters:
max_db = 0.0
for cluster2 in clusters:
if cluster1 != cluster2:
max_db = max(max_db, (diams[cluster1] + diams[cluster2]) / dists[cluster1][cluster2])
num += max_db
return num / len(clusters)
