python - 通过间隙统计和预测强度估计集群数量

Question

我正在尝试翻译差距统计和预测强度的 R 实现 http://edchedch.wordpress.com/2011/03/19/counting-clusters/进入 python 脚本，用于估计具有 3 个集群的 iris 数据中的集群数量。我没有得到 3 个集群，而是在几乎没有估计的 3 个(实际集群数量)的不同运行中得到不同的结果。 Graph显示估计数字为 10 而不是 3。我错过了什么吗？谁能帮我定位问题？

import random
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans


def dispersion (data, k):
    if k == 1:
        cluster_mean = np.mean(data, axis=0)
        distances_from_mean = np.sum((data - cluster_mean)**2,axis=1)
        dispersion_val = np.log(sum(distances_from_mean))
    else:
        k_means_model_ = KMeans(n_clusters=k, max_iter=50, n_init=5).fit(data)
        distances_from_mean = range(k)
        for i in range(k):
            distances_from_mean[i] = int()
            for idx, label in enumerate(k_means_model_.labels_):
                if i == label:
                    distances_from_mean[i] += sum((data[idx] - k_means_model_.cluster_centers_[i])**2)
        dispersion_val = np.log(sum(distances_from_mean))

    return dispersion_val

def reference_dispersion(data, num_clusters, num_reference_bootstraps):
    dispersions = [dispersion(generate_uniform_points(data), num_clusters) for i in range(num_reference_bootstraps)]
    mean_dispersion = np.mean(dispersions)
    stddev_dispersion = float(np.std(dispersions)) / np.sqrt(1. + 1. / num_reference_bootstraps) 
    return mean_dispersion

def generate_uniform_points(data):
    mins = np.argmin(data, axis=0)
    maxs = np.argmax(data, axis=0)

    num_dimensions = data.shape[1]
    num_datapoints = data.shape[0]

    reference_data_set = np.zeros((num_datapoints,num_dimensions))
    for i in range(num_datapoints):
        for j in range(num_dimensions):
            reference_data_set[i][j] = random.uniform(data[mins[j]][j],data[maxs[j]][j])

    return reference_data_set   

def gap_statistic (data, nthCluster, referenceDatasets):
    actual_dispersion = dispersion(data, nthCluster)
    ref_dispersion = reference_dispersion(data, nthCluster, num_reference_bootstraps)
    return actual_dispersion, ref_dispersion

if __name__ == "__main__":

    data=np.loadtxt('iris.mat', delimiter=',', dtype=float)

    maxClusters = 10
    num_reference_bootstraps = 10
    dispersion_values = np.zeros((maxClusters,2))

    for cluster in range(1, maxClusters+1):
        dispersion_values_actual,dispersion_values_reference = gap_statistic(data, cluster, num_reference_bootstraps)
        dispersion_values[cluster-1][0] = dispersion_values_actual
        dispersion_values[cluster-1][1] = dispersion_values_reference

    gaps = dispersion_values[:,1] - dispersion_values[:,0]

    print gaps
    print "The estimated number of clusters is ", range(maxClusters)[np.argmax(gaps)]+1

    plt.plot(range(len(gaps)), gaps)
    plt.show()

Answer 1

您的图表显示正确的值 3。让我解释一下

• 随着集群数量的增加，距离指标肯定会降低。因此，您假设正确的值为 10。如果将其增加到 10 以上，距离度量将进一步减小。但这不应该是我们的决策标准
• 我们需要找到拐点(这里用红色标记)。这是斜率平滑的点。您可能想看看 elbow curves
• 基于以上2点，拐点为3(这也是正确解)

希望对你有帮助