Single linkage clustering of edit distance matrix

问题:

I'm trying to assign flat, single-linkage clusters to sequence IDs separated by an edit distance < n, given a square distance matrix. I believe scipy.cluster.hierarchy.fclusterdata() with criterion='distance' may be a way to do this, but it isn't quite returning the clusters I'd expect for this toy example.

Specifically, in the 4x4 distance matrix example below, I would expect clusters_50 (which uses t=50) to create 2 clusters, where actually it finds 3. I think the issue is that fclusterdata() doesn't expect a distance matrix, but fcluster() doesn't seem to do what I want either.

I've also looked at sklearn.cluster.AgglomerativeClustering but this requires n_clusters to be specified, and I want to create as many clusters as needed until the distance threshold I specify has been satisfied.

I see that there is a currently unmerged scikit-learn pull request for this exact feature: https://github.com/scikit-learn/scikit-learn/pull/9069

Can anyone point me in the right direction? Clustering with an absolute distance threshold criterion seems like a commmon use case.

import pandas as pd
from scipy.cluster.hierarchy import fclusterdata

cols = ['a', 'b', 'c', 'd']

df = pd.DataFrame([{'a': 0, 'b': 29467, 'c': 35, 'd': 13},
                   {'a': 29467, 'b': 0, 'c': 29468, 'd': 29470},
                   {'a': 35, 'b': 29468, 'c': 0, 'd': 38},
                   {'a': 13, 'b': 29470, 'c': 38, 'd': 0}],
                  index=cols)

clusters_20 = fclusterdata(df.values, t=20, criterion='distance')
clusters_50 = fclusterdata(df.values, t=50, criterion='distance')
clusters_100 = fclusterdata(df.values, t=100, criterion='distance')

names_clusters_20 = {n: c for n, c in zip(cols, clusters_20)}
names_clusters_50 = {n: c for n, c in zip(cols, clusters_50)}
names_clusters_100 = {n: c for n, c in zip(cols, clusters_100)}

names_clusters_20  # Expecting 3 clusters, finds 3
>>> {'a': 1, 'b': 3, 'c': 2, 'd': 1}

names_clusters_50  # Expecting 2 clusters, finds 3
>>> {'a': 1, 'b': 3, 'c': 2, 'd': 1}

names_clusters_100 # Expecting 2 clusters, finds 2
>>> {'a': 1, 'b': 2, 'c': 1, 'd': 1}

回答1:

You did not set the metric parameter.

The default then is metric='euclidean', not precomputed.

回答2:

Figured it out by passing linkage() to fcluster(), which supports metric='precomputed' unlike fclusterdata().

fcluster(linkage(condensed_dm, metric='precomputed'), criterion='distance', t=20)

Solution:

import pandas as pd
from scipy.spatial.distance import squareform
from scipy.cluster.hierarchy import linkage, fcluster

cols = ['a', 'b', 'c', 'd']

df = pd.DataFrame([{'a': 0, 'b': 29467, 'c': 35, 'd': 13},
                   {'a': 29467, 'b': 0, 'c': 29468, 'd': 29470},
                   {'a': 35, 'b': 29468, 'c': 0, 'd': 38},
                   {'a': 13, 'b': 29470, 'c': 38, 'd': 0}],
                  index=cols)

dm_cnd = squareform(df.values)

clusters_20 = fcluster(linkage(dm_cnd, metric='precomputed'), criterion='distance', t=20)
clusters_50 = fcluster(linkage(dm_cnd, metric='precomputed'), criterion='distance', t=50)
clusters_100 = fcluster(linkage(dm_cnd, metric='precomputed'), criterion='distance', t=100)

names_clusters_20 = {n: c for n, c in zip(cols, clusters_20)}
names_clusters_50 = {n: c for n, c in zip(cols, clusters_50)}
names_clusters_100 = {n: c for n, c in zip(cols, clusters_100)}

names_clusters_20
>>> {'a': 1, 'b': 3, 'c': 2, 'd': 1}

names_clusters_50
>>> {'a': 1, 'b': 2, 'c': 1, 'd': 1}

names_clusters_100
>>> {'a': 1, 'b': 2, 'c': 1, 'd': 1}

As a function:

import pandas as pd
from scipy.spatial.distance import squareform
from scipy.cluster.hierarchy import fcluster, linkage

def cluster_df(df, method='single', threshold=100):
    '''
    Accepts a square distance matrix as an indexed DataFrame and returns a dict of index keyed flat clusters 
    Performs single linkage clustering by default, see scipy.cluster.hierarchy.linkage docs for others
    '''

    dm_cnd = squareform(df.values)
    clusters = fcluster(linkage(dm_cnd,
                                method=method,
                                metric='precomputed'),
                        criterion='distance',
                        t=threshold)
    names_clusters = {s:c for s, c in zip(df.columns, clusters)}
return names_clusters