KMeans, bisecting KMeans

wepe · wepe · commit 0786c3bbe723 · 2015-08-20T17:26:23.000+08:00
Python implement , based on numpy and matplotlib
diff --git a/KMeans/data.pkl b/KMeans/data.pkl
diff --git a/KMeans/kmeans.py b/KMeans/kmeans.py
@@ -0,0 +1,170 @@
+#coding=utf-8
+
+'''
+@author: wepon, http://2hwp.com
+Reference:
+            Book: <<Machine Learning in Action>>
+            Software: sklearn.cluster.KMeans
+
+'''
+import numpy as np
+
+class KMeans(object):
+    """
+    - 参数
+        n_clusters:
+            聚类个数，即k
+        initCent:
+            质心初始化方式，可选"random"或指定一个具体的array,默认random，即随机初始化
+        max_iter:
+            最大迭代次数
+    """
+    def __init__(self,n_clusters=5,initCent='random',max_iter=300):
+        if hasattr(initCent, '__array__'):
+            n_clusters = initCent.shape[0]
+            self.centroids = np.asarray(initCent, dtype=np.float)
+        else:
+            self.centroids = None
+        
+        self.n_clusters = n_clusters
+        self.max_iter = max_iter
+        self.initCent = initCent
+        self.clusterAssment = None
+        self.labels = None   
+        self.sse = None 
+    
+    #计算两点的欧式距离
+    def _distEclud(self, vecA, vecB):
+        return np.linalg.norm(vecA - vecB)
+        
+    #随机选取k个质心,必须在数据集的边界内
+    def _randCent(self, X, k):
+        n = X.shape[1]        #特征维数
+        centroids = np.empty((k,n))  #k*n的矩阵，用于存储质心
+        for j in range(n):           #产生k个质心，一维一维地随机初始化
+            minJ = min(X[:,j]) 
+            rangeJ = float(max(X[:,j]) - minJ)
+            centroids[:,j] = (minJ + rangeJ * np.random.rand(k,1)).flatten()
+        return centroids
+        
+    def fit(self, X):
+        #类型检查
+        if not isinstance(X,np.ndarray):
+            try:
+                X = np.asarray(X)
+            except:
+                raise TypeError("numpy.ndarray required for X")
+        
+        m = X.shape[0]#m代表样本数量
+        self.clusterAssment = np.empty((m,2))#m*2的矩阵，第一列存储样本点所属的族的索引值，
+                                               #第二列存储该点与所属族的质心的平方误差
+        if self.initCent == 'random':
+             self.centroids = self._randCent(X, self.n_clusters)
+        
+        clusterChanged = True
+        for _ in range(self.max_iter):
+            clusterChanged = False
+            for i in range(m):#将每个样本点分配到离它最近的质心所属的族
+                minDist = np.inf; minIndex = -1
+                for j in range(self.n_clusters):
+                    distJI = self._distEclud(self.centroids[j,:],X[i,:])
+                    if distJI < minDist:
+                        minDist = distJI; minIndex = j
+                if self.clusterAssment[i,0] != minIndex:
+                    clusterChanged = True
+                    self.clusterAssment[i,:] = minIndex,minDist**2
+                    
+            if not clusterChanged:#若所有样本点所属的族都不改变,则已收敛，结束迭代
+                break   
+            for i in range(self.n_clusters):#更新质心，即将每个族中的点的均值作为质心
+                ptsInClust = X[np.nonzero(self.clusterAssment[:,0]==i)[0]]#取出属于第i个族的所有点
+                self.centroids[i,:] = np.mean(ptsInClust, axis=0)
+        
+        self.labels = self.clusterAssment[:,0]
+        self.sse = sum(self.clusterAssment[:,1])
+
+    
+    def predict(self,X):#根据聚类结果，预测新输入数据所属的族
+        #类型检查
+        if not isinstance(X,np.ndarray):
+            try:
+                X = np.asarray(X)
+            except:
+                raise TypeError("numpy.ndarray required for X")
+        
+        m = X.shape[0]#m代表样本数量
+        preds = np.empty((m,))
+        for i in range(m):#将每个样本点分配到离它最近的质心所属的族
+            minDist = np.inf
+            for j in range(self.n_clusters):
+                distJI = self._distEclud(self.centroids[j,:],X[i,:])
+                if distJI < minDist:
+                    minDist = distJI
+                    preds[i] = j
+        return preds
+    
+    
+class biKMeans(object):
+    def __init__(self,n_clusters=5):
+        self.n_clusters = n_clusters
+        self.centroids = None
+        self.clusterAssment = None
+        self.labels = None
+        self.sse = None
+        
+    
+    #计算两点的欧式距离
+    def _distEclud(self, vecA, vecB):
+        return np.linalg.norm(vecA - vecB)
+        
+    def fit(self,X):
+        m = X.shape[0]
+        self.clusterAssment = np.zeros((m,2))
+        centroid0 = np.mean(X, axis=0).tolist()
+        centList =[centroid0]
+        for j in range(m):#计算每个样本点与质心之间初始的平方误差
+            self.clusterAssment[j,1] = self._distEclud(np.asarray(centroid0), X[j,:])**2
+        
+        while (len(centList) < self.n_clusters):
+            lowestSSE = np.inf
+            for i in range(len(centList)):#尝试划分每一族,选取使得误差最小的那个族进行划分
+                ptsInCurrCluster = X[np.nonzero(self.clusterAssment[:,0]==i)[0],:]
+                clf = KMeans(n_clusters=2)
+                clf.fit(ptsInCurrCluster)
+                centroidMat, splitClustAss = clf.centroids, clf.clusterAssment#划分该族后，所得到的质心、分配结果及误差矩阵
+                sseSplit = sum(splitClustAss[:,1])
+                sseNotSplit = sum(self.clusterAssment[np.nonzero(self.clusterAssment[:,0]!=i)[0],1])
+                if (sseSplit + sseNotSplit) < lowestSSE:
+                    bestCentToSplit = i
+                    bestNewCents = centroidMat
+                    bestClustAss = splitClustAss.copy()
+                    lowestSSE = sseSplit + sseNotSplit
+            #该族被划分成两个子族后,其中一个子族的索引变为原族的索引，另一个子族的索引变为len(centList),然后存入centList
+            bestClustAss[np.nonzero(bestClustAss[:,0] == 1)[0],0] = len(centList)
+            bestClustAss[np.nonzero(bestClustAss[:,0] == 0)[0],0] = bestCentToSplit
+            centList[bestCentToSplit] = bestNewCents[0,:].tolist()
+            centList.append(bestNewCents[1,:].tolist())
+            self.clusterAssment[np.nonzero(self.clusterAssment[:,0] == bestCentToSplit)[0],:]= bestClustAss 
+                   
+        self.labels = self.clusterAssment[:,0] 
+        self.sse = sum(self.clusterAssment[:,1])
+        self.centroids = np.asarray(centList)
+                                
+    def predict(self,X):#根据聚类结果，预测新输入数据所属的族
+        #类型检查
+        if not isinstance(X,np.ndarray):
+            try:
+                X = np.asarray(X)
+            except:
+                raise TypeError("numpy.ndarray required for X")
+        
+        m = X.shape[0]#m代表样本数量
+        preds = np.empty((m,))
+        for i in range(m):#将每个样本点分配到离它最近的质心所属的族
+            minDist = np.inf
+            for j in range(self.n_clusters):
+                distJI = self._distEclud(self.centroids[j,:],X[i,:])
+                if distJI < minDist:
+                    minDist = distJI
+                    preds[i] = j
+        return preds
diff --git a/KMeans/test.py b/KMeans/test.py
@@ -0,0 +1,37 @@
+#coding=utf-8
+import cPickle
+import matplotlib.pyplot as plt
+import numpy as np
+from kmeans import KMeans,biKMeans
+    
+if __name__ == "__main__":
+    #加载数据
+    X,y = cPickle.load(open('data.pkl','r'))
+
+    #依次画出迭代1次、2次、3次...的图
+    for max_iter in range(6):
+        #设置参数
+        n_clusters = 10
+        initCent = X[50:60] #将初始质心初始化为X[50:60]
+        #训练模型
+        clf = KMeans(n_clusters,initCent,max_iter)
+        clf.fit(X)
+        cents = clf.centroids
+        labels = clf.labels
+        sse = clf.sse
+        #画出聚类结果，每一类用一种颜色
+        colors = ['b','g','r','k','c','m','y','#e24fff','#524C90','#845868']
+        for i in range(n_clusters):
+            index = np.nonzero(labels==i)[0]
+            x0 = X[index,0]
+            x1 = X[index,1]
+            y_i = y[index]
+            for j in range(len(x0)):
+                plt.text(x0[j],x1[j],str(int(y_i[j])),color=colors[i],\
+                         fontdict={'weight': 'bold', 'size': 9})
+            plt.scatter(cents[i,0],cents[i,1],marker='x',color=colors[i],linewidths=12)
+        plt.title("SSE={:.2f}".format(sse))
+        plt.axis([-30,30,-30,30])
+        #plt.savefig("{}.png".format(max_iter))
+        #plt.close()
+        plt.show()
diff --git a/README.md b/README.md
@@ -1,15 +1,11 @@
 MachineLearning
 ====================
 
-This project contain some machine learning algrithm demo.Maybe the code is also useful to you.
 
-这个仓库包含一些常用的机器学习算法的实现代码，代码中也有会一些具体的小应用。
-
-此外，每个算法我都会写一篇文章来地介绍它们，同时详细地解读代码。文章发表在我的CSDN专栏以及个人网站上：
 
-CSDN：[wepon的专栏](http://blog.csdn.net/u012162613)
+这个仓库包含一些常用的机器学习算法的实现代码，代码中也有会一些具体的小应用。
 
-个人网站：[Wepon's blog](http://2hwp.com)
+此外，每个算法我都会写一篇文章来地介绍它们，同时详细地解读代码。文章发表在我的CSDN专栏以及个人网站上。欢迎所有的机器学习爱好者参与进来，并请保证文章和代码高质量。
 
 
 ##目录介绍
@@ -58,9 +54,17 @@ CSDN：[wepon的专栏](http://blog.csdn.net/u012162613)
 
 - **DecisionTree**
 
-	Python、Numpy、Matplotlib实现的ID3、C4.5，其中C4.5有待完善，后续加入CART。文章待总结
+	Python、Numpy、Matplotlib实现的ID3、C4.5，其中C4.5有待完善，后续加入CART。文章待总结。[代码](https://github.com/wepe/MachineLearning/tree/master/DecisionTree)
+
+- **KMeans**
+
+	介绍了聚类分析中最常用的KMeans算法（及二分KMeans算法），基于NumPy的算法实现，以及基于Matplotlib的聚类过程可视化。[文章链接]()
+
+##Contributor
+
+- [wepon](https://github.com/wepe)
+- [Gogary](https://github.com/enjoyhot)
 
-##Contributing
 
-欢迎加入本项目，任何机器学习/深度学习的demo都可以push进来，并且最好有相应的博文介绍代码。
+欢迎加入本项目，任何机器学习/深度学习的demo都可以push进来，辅以详细的博文介绍。
  
