data_utils.py 文件源码

def bic(X, k):
    """
    Compute the BIC score.
    Implementarion from here:
    http://www.aladdin.cs.cmu.edu/papers/pdfs/y2000/xmeans.pdf
    with corrections from here:
    https://stats.stackexchange.com/questions/90769/using-bic-to-estimate-the-number-of-k-in-kmeans

    Params:
    --------
    X: numpy array with observations and features to be clustered
    k: number of clusters

    Returns:
    --------
    BIC: bic score
    """

    model = MiniBatchKMeans(init='k-means++', n_clusters=k, batch_size=50,
                          n_init=3, max_no_improvement=10, verbose=0)
    model.fit(X)

    centers = model.cluster_centers_
    centers = np.expand_dims(centers, axis=1)
    labels  = model.labels_
    N_C = np.bincount(labels)
    R, M = X.shape

    wcss = sum([sum(cdist(X[np.where(labels == c)], centers[c], 'euclidean')**2) for c in range(k)])
    var = (1.0/(R-k)/M) * wcss
    const_term = 0.5 * k * np.log(R) * (M+1)

    BIC = np.sum([ ( Rn * np.log(Rn) ) -
                   ( Rn * np.log(R) ) -
                   ( ((Rn * M) / 2) * np.log(2*np.pi*var) )  -
                   ( (Rn - 1) * M/ 2 )
                   for Rn in N_C]) - const_term

    return BIC