k-means 质心标签在同一程序的运行中发生变化？

Posted 2023-03-12

【中文标题】k-means 质心标签在同一程序的运行中发生变化？

【英文标题】：k-means centroid labels change across runs of the same program?

【发布时间】：2020-09-05 07:24:43

【问题描述】：

我观察到同一程序的后续运行会为 k-means 集群提供不同的标签，尽管原始特征是相同的。该程序将一组转换应用于原始数据帧，然后应用于新数据帧，管道由 - 按此顺序 - StandardScaler--> PCA -> K-means 组成。根据初始数据确定的 PCA 和 k-means 模型用于下一个数据集。最后，程序进行逆变换，使质心显示在初始特征空间中。所以我对不同的标签感到困惑，这里的相关功能是k-means .predict()

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler
def get_kmeans_score(data, center):
    '''
    returns the kmeans score regarding SSE for points to centers
    INPUT:
        data - the dataset you want to fit kmeans to
        center - the number of centers you want (the k value)
    OUTPUT:
        score - the SSE score for the kmeans model fit to the data
    '''
    #instantiate kmeans
    kmeans = KMeans(n_clusters=center)

    # Then fit the model to your data using the fit method
    model = kmeans.fit(data)

    # Obtain a score related to the model fit
    score = np.abs(model.score(data))

    return score
data = 
    'apples': [3, 2, 0, 9, 2, 1],
    'oranges': [0, 7.6, 7, 2, 7, 6],
    'figs':[1.4, 11, 10.999, 3.99, 10, 2],
    'pears': [5, 2, 6, 2.45, 1, 7],
    'berries': [1.3, 4, 10, 0, 5,21],
    'tomatoes': [5, 15, 3, 4, 17,5],
    'onions': [11,3, 3, 1, 0, 10]

purchases = pd.DataFrame(data, index=['June', 'Robert', 'Lily', 'David', 'Bob', 'Karen'])
print('ORIGINAL DATA')
print(purchases)
Y1 = pd.DataFrame(np.round(purchases,0), columns = purchases.keys())
scaler = StandardScaler()
Y = scaler.fit_transform(Y1)
pca = PCA(n_components=3)
W = pca.fit_transform(Y)
# apply k-means
scores = []
centers = list(range(1,5))
for center in centers:
    scores.append(get_kmeans_score(W, center))
X = zip(centers, scores)
print('k-means results on original data as a function of # centers')
for i in X:
        print(i)
# from the above results, assume the elbow is 4 clusters
print('_________________________________________')
n_c = 4
kmeans = KMeans(n_clusters=4)
model = kmeans.fit(W)
score = np.abs(model.score(W))
print('k-means score on ', n_c, ' clusters for the original dataset = ',score)
# model is the k-means model that will also be applied to the new dataset
#
NEW_data = 
    'apples': [9, 20, 10, 2, 12,1],
    'oranges': [10, 3, 12, 1, 18, 5],
    'figs':[34, 11, 3.999, 1, 0, 12],
    'pears': [5, 2, 16, 2.45, 10, 11],
    'berries': [13, 4, 1, 2, 15, 4],
    'tomatoes': [7, 2, 1, 14, 27, 2],
    'onions': [1,10, 11, 2, 4, 10]

purchases_N = pd.DataFrame(NEW_data)
purchases_N = pd.DataFrame(NEW_data, index=['June', 'Robert', 'Lily', 'David', 'Bob', 'Karen'])
print('NEW DATA')
print(purchases_N)
YY1 = pd.DataFrame(np.round(purchases_N,0), columns = purchases_N.keys())
YY = scaler.fit_transform(YY1)
W1 = pca.transform(YY)
scoreNew = np.abs(model.score(W1))
print('k-means score on ', n_c, ' clusters for the new dataset = ',scoreNew)
print(scoreNew)
# k-means score the new dataset using the model determined on original ds
# predictions for the 2 datasets using the k-means model based on orig data
predict_purchases_dataset = model.predict(W)
predict_purchases_NewDataset = model.predict(W1)
print('original data upon PCA using n_components=3')
print(W)
print('k-means predictions --- original data')
print(predict_purchases_dataset)
print('_________________________________________')
print('new data upon PCA using n_components=3')
print(W1)
print('k-means predictions --- new data')
print(predict_purchases_NewDataset)
# the output matches the prediction on orig dataset:
# there are 2 customers in cluster 2, 2 customers in cluster 1, 1 in cluster 3 and 1 in 0
L = len(purchases.index)
x = [i for i in range (10)]
orig = []
NEW = []
for i in range(10):
    orig.append((predict_purchases_dataset== i).sum()/L)
    NEW.append((predict_purchases_NewDataset== i).sum()/L)
print('proportion of k-means clusters for original data')
print(orig)
print('proportion of k-means clusters for new data')
print(NEW)

#df_summary = pd.DataFrame('cluster' : x, 'propotion_orig' : orig, 'proportion_NEW': NEW)
#df_summary.plot(x='cluster', y= ['propotion_orig','proportion_NEW' ], kind='bar')
model.cluster_centers_
#
IPCA = pca.inverse_transform(model.cluster_centers_)
APPROX = scaler.inverse_transform(IPCA)
approx_df =pd.DataFrame(APPROX, columns=purchases.columns)
print('k-means centers coordinates in original features space')
print(approx_df)

【参考方案1】：

当您定义KMeans 时，如果您想为质心初始化生成确定性随机数，请确保设置(random_state=int)。 见：https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html

【参考方案2】：

是的，由于 k-means 的初始集群种子分配是随机的，因此这种行为是预期的。当然，分配初始集群种子有不同的方法，但默认情况下，您的实现使用kmeans++ 策略。 （参见init 来自KMeans documentation）