k-medoidsとは

暇な時に書きたい

k-medoidsのコード

import numpy as np
import sys
import random
from scipy.spatial.distance import cdist
from sklearn.preprocessing import LabelBinarizer
import matplotlib.pyplot as plt

class kMedoids(object):
    #D_method is metric in distance.cdist
    def __init__(self,n_cluster=4,max_iter=10,D_method="euclidean",init_method="random",eps=0):
        self.n_cluster = n_cluster
        self.max_iter = max_iter
        self.D_method = D_method
        self.D_matrix = None
        self.labels = None
        self.objective_value = float("inf")
        self.loop_flag = True
        self.eps = eps
        self.lb = LabelBinarizer()
    def calculate_D(self,data):
        print("Calculate distance matrix (method is %s)"%self.D_method)
        self.D_matrix = cdist(data,data,self.D_method)
        return self.D_matrix
    
    def _init_centroids(self):
        l=list(range(self.D_matrix.shape[0]))
        centroids = np.random.choice(l,n_cluster,replace=False)
        return centroids
    
    def _labels_to_membership(self):
        if self.n_cluster == 2:
            u = np.hstack((self.labels.reshape([self.n_data,1]),1-self.labels.reshape([self.n_data,1])))
        else:
            self.lb.fit(self.labels) 
            u = self.lb.transform(self.labels)
        return u
    
    def fit(self,data=None,D_matrix=None):
        if D_matrix is None and data is None:
            sys.stderr.write('Please give data or D_matrix as argument!!!')
            return
        elif data is not None:
            self.D_matrix = self.calculate_D(data)
        elif self.D_matrix is None:
            self.D_matrix = self.calculate_D(data)
            
        self.n_data = self.D_matrix.shape[0]
        print("fit by k-Medoids")
        centroids = self._init_centroids()
        u = self._updateMembership(centroids)
        num_loop = 0
        while num_loop < self.max_iter and self.loop_flag:
            centroids = self._updateCentroids(u)
            u = self._updateMembership(centroids)
            print("loop:%s objective_value:%s"%(num_loop,self.objective_value))
            num_loop += 1
        print("kMedoids is finish!!!")
        self.loop_flag = True
    def predict(self):        
        return self.labels 
    
    def _updateCentroids(self,u):
        data_in_clusters = u==1
        D_in_clusters = (data_in_clusters[np.newaxis,:,:]*data_in_clusters[:,np.newaxis,:]).swapaxes(0,2)
        D_in_clusters = D_in_clusters*self.D_matrix[np.newaxis,:,:]
        temp = np.sum(D_in_clusters,axis=2)
        np.place(temp,temp==0,float("inf"))
        centroids = np.argmin(temp,axis=1)
        objective_value = np.sum(D_in_clusters[:,centroids])
        
        if np.absolute(objective_value - self.objective_value) <= self.eps:
            self.loop_flag = False
        else:
            self.objective_value = objective_value
        return centroids
    
    def _updateMembership(self,centroids):
        self.labels = np.argmin(self.D_matrix[:,centroids],axis=1)
        #print("test",self.labels)
        u = self._labels_to_membership()
        #print("test1",u)
        return u
    
    def objective_value(self):
        return self.objective_value

テストデータ作成

from sklearn.datasets import make_blobs
data, a = make_blobs(n_samples=100,
                            n_features=2,
                            centers=3,
                            cluster_std=3.5,
                            shuffle=True
                            )

テストデータに対してkMedoidsを適用

n_cluster=4
km =kMedoids(n_cluster)
km.fit(data)

Calculate distance matrix (method is euclidean)
fit by k-Medoids
loop:0 objective_value:192.74729208157845
loop:1 objective_value:184.15560018589713
loop:2 objective_value:179.3414992176697
loop:3 objective_value:164.5655157771438
loop:4 objective_value:163.04503531227357
loop:5 objective_value:161.1913508723207
loop:6 objective_value:161.1913508723207
kMedoids is finish!!!

可視化

正規化および軸の比率調整はしてないので注意

今後の課題

初期クラスタ中心の選択方法としてkmeas++的なのを追加する
実装が合ってるかはほとんどテストしてないのでテストすべき