【时间序列聚类】KMedoids聚类+DTW算法

前言

KMedoids的聚类有时比KMeans的聚类效果要好。手上正好有一批时序数据，今天用KMedoids试下聚类效果

安装

KMedoids可以使用sklearn的拓展聚类模块scikit-learn-extra，模块需要保证

• Python (>=3.6)

• scikit-learn(>=0.22)

安装 scikit-learn-extra

PyPi: pip install scikit-learn-extra
Conda: conda install -c conda-forge scikit-learn-extra
Git: pip install https://github.com/scikit-learn-contrib/scikit-learn-extra/archive/master.zip

安装 tslearn

PyPi: python -m pip install tslearn
Conda: conda install -c conda-forge tslearn
Git: python -m pip install https://github.com/tslearn-team/tslearn/archive/master.zip

为什么要使用scikit-learn-extra和tslearn两个模块？因为sklearn里面没有自带的KMedoids，也没有类似DTW的时序度量算法，但组合两者恰好能解决问题

测试

import numpy as np
from sklearn_extra.cluster import KMedoids
import tslearn.metrics as metrics
# 自定义数据处理
import data_process
from tslearn.clustering import silhouette_score
from tslearn.preprocessing import TimeSeriesScalerMeanVariance
from tslearn.generators import random_walks
from sklearn.preprocessing import StandardScaler
import matplotlib.pyplot as plt

# shape(X) = (100,2800+)
X = np.loadtxt("top100.txt",dtype=np.float,delimiter=",")
# 降成30维
X = data_process.downsample(X,30)
seed = 0

# elbow法则找最佳聚类数，结果：elbow = 5
def test_elbow():
    global X,seed
    distortions = []
    dists = metrics.cdist_dtw(X) # dba + dtw
    # dists = metrics.cdist_soft_dtw_normalized(X,gamma=.5) # softdtw
    for i in  range ( 2 , 15 ):
        km = KMedoids(n_clusters=i,random_state=seed,metric="precomputed")
        km.fit(dists)
        #记录误差和
        distortions.append(km.inertia_)
    plt.plot(range ( 2 , 15 ), distortions, marker= 'o' )
    plt.xlabel( 'Number of clusters' )
    plt.ylabel( 'Distortion' )
    plt.show()

def test_kmedoids():
   
    num_cluster = 5
    # 声明precomputed自定义相似度计算方法
    km = KMedoids(n_clusters= num_cluster, random_state=0,metric="precomputed")
    # 采用tslearn中的DTW系列及变种算法计算相似度，生成距离矩阵dists
    dists = metrics.cdist_dtw(X) # dba + dtw
    # dists = metrics.cdist_soft_dtw_normalized(X,gamma=0.5) # softdtw
    y_pred = km.fit_predict(dists)
    np.fill_diagonal(dists,0)
    score = silhouette_score(dists,y_pred,metric="precomputed")
    print(X.shape)
    print(y_pred.shape)
    print("silhouette_score: " + str(score))
    for yi in range(num_cluster):
        plt.subplot(3, 2, yi + 1)
        for xx in X[y_pred == yi]:
            plt.plot(xx.ravel(), "k-", alpha=.3)
        # 注意这里的_cluster_centers要写成X[km.medoid_indices_[yi]]，因为你是precomputed，源码里面当precomputed时_cluster_centers等于None
        plt.plot(X[km.medoid_indices_[yi]], "r-")
        plt.text(0.55, 0.85,'Cluster %d' % (yi + 1),
                transform=plt.gca().transAxes)
        if yi == 1:
            plt.title("KMedoids" + " + DBA-DTW")

    plt.tight_layout()
    plt.show()


#test_elbow()
test_kmedoids()

采用KMedoids + DBA-DTW聚类效果  # 轮廓系数silhouette_score: 0.5465097470777784

采用KMedoids + SoftDTW聚类效果   # 轮廓系数silhouette_score: 0.6528261125440392

直接采用欧氏距离的聚类效果    # 轮廓系数silhouette_score: 0.5209641775604567

相比采用KMeans，KMedoids在的聚类中心（红线部分）从视觉上要似乎要更好（KMeans+DTW聚类效果可见该文章最后一节），但轮廓系数却不如KMeans。但仅欧氏距离而言，KMedoids的轮廓系数要比KMeans更好那么一点