Question

我正在尝试将差距统计和预测强度http://edchedch.wordpress.com/2011/03/19/counting-clusters/的R实现转换为python脚本，以估计具有3个簇的虹膜数据中的簇数。我没有获得3个集群，而是在不同的运行中获得了不同的结果，其中3（实际的集群数）几乎没有估计。 Graph显示估计的数字为10而不是3.我错过了什么？任何人都可以帮我找到问题吗？

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

您的图形显示的正确值为3。让我解释一下

随着群集数量的增加，距离度量当然会降低。因此，您假定正确的值为10。如果将其增加到10以上，则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（在此处以红色标记）。这是坡度平滑的点。您可能想看看elbow curves
基于以上2个点，拐点为3（这也是正确的解决方案）

希望这会有所帮助

Answer 2

您可以看一下这段代码，并可以更改输出绘图格式

[![# coding: utf-8

# Implémentation de K-means clustering python


#Chargement des bibliothèques
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn import datasets


#chargement de jeu des données Iris
iris = datasets.load_iris()

#importer le jeu de données Iris dataset à l'aide du module pandas
x = pd.DataFrame(iris.data)

x.columns = \['Sepal_Length','Sepal_width','Petal_Length','Petal_width'\]


y = pd.DataFrame(iris.target)


y.columns = \['Targets'\]


#Création d'un objet K-Means avec un regroupement en 3 clusters (groupes)
model=KMeans(n_clusters=3)



#application du modèle sur notre jeu de données Iris
model.fit(x)



#Visualisation des clusters
plt.scatter(x.Petal_Length, x.Petal_width)
plt.show()




colormap=np.array(\['Red','green','blue'\])



#Visualisation du jeu de données sans altération de ce dernier (affichage des fleurs selon leur étiquettes)
plt.scatter(x.Petal_Length, x.Petal_width,c=colormap\[y.Targets\],s=40)
plt.title('Classification réelle')
plt.show()

#Visualisation des clusters formés par K-Means
plt.scatter(x.Petal_Length, x.Petal_width,c=colormap\[model.labels_\],s=40)
plt.title('Classification K-means ')
plt.show()][1]][1]

Output 1

通过间隙统计和预测强度估计群集数量

2 个答案: