Dunn index for sklearn-generated clusters

dunn-sklearn.py

def dunn(c, distances):
    """
    Dunn index for cluster validation (the bigger, the better)
    
    .. math:: D = \\min_{i = 1 \\ldots n_c; j = i + 1\ldots n_c} \\left\\lbrace \\frac{d \\left( c_i,c_j \\right)}{\\max_{k = 1 \\ldots n_c} \\left(diam \\left(c_k \\right) \\right)} \\right\\rbrace
    
    where :math:`d(c_i,c_j)` represents the distance between
    clusters :math:`c_i` and :math:`c_j`, given by the distances between its
    two closest data points, and :math:`diam(c_k)` is the diameter of cluster
    :math:`c_k`, given by the distance between its two farthest data points.
    
    The bigger the value of the resulting Dunn index, the better the clustering
    result is considered, since higher values indicate that clusters are
    compact (small :math:`diam(c_k)`) and far apart.
    
    .. [Kovacs2005] Kovács, F., Legány, C., & Babos, A. (2005). Cluster validity measurement techniques. 6th International Symposium of Hungarian Researchers on Computational Intelligence.
    """
    unique_cluster_distances = np.unique(min_cluster_distances(c, distances))
    max_diameter = max(diameter(c, distances))

    if np.size(unique_cluster_distances) > 1:
        return unique_cluster_distances[1] / max_diameter
    else:
        return unique_cluster_distances[0] / max_diameter

def min_cluster_distances(c, distances):
    """Calculates the distances between the two nearest points of each cluster"""
    min_distances = np.zeros((max(c) + 1, max(c) + 1))
    for i in np.arange(0, len(c)):
        if c[i] == -1: continue
        for ii in np.arange(i + 1, len(c)):
            if c[ii] == -1: continue
            if c[i] != c[ii] and distances[i, ii] > min_distances[c[i], c[ii]]:
                min_distances[c[i], c[ii]] = min_distances[c[ii], c[i]] = distances[i, ii]
    return min_distances

def diameter(c, distances):
    """Calculates cluster diameters (the distance between the two farthest data points in a cluster)"""
    diameters = np.zeros(max(c) + 1)
    for i in np.arange(0, len(c)):
        if c[i] == -1: continue
        for ii in np.arange(i + 1, len(c)):
            if c[ii] == -1: continue
            if c[i] != -1 or c[ii] != -1 and c[i] == c[ii] and distances[i, ii] > diameters[c[i]]:
                diameters[c[i]] = distances[i, ii]
    return diameters