手写KMeans算法

KMeans算法是一种无监督学习，它会将相似的对象归到同一类中。

其基本思想是：

1.随机计算k个类中心作为起始点。

2. 将数据点分配到理其最近的类中心。

3.移动类中心。

4.重复2,3直至类中心不再改变或者达到限定迭代次数。

具体的实现如下：

from numpy import *
import matplotlib.pyplot as plt
import pandas as pd
# Load dataset
url = "https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data"
names = ['sepal-length', 'sepal-width', 'petal-length', 'petal-width', 'class']
dataset = pd.read_csv(url, names=names)
dataset['class'][dataset['class']=='Iris-setosa']=0
dataset['class'][dataset['class']=='Iris-versicolor']=1
dataset['class'][dataset['class']=='Iris-virginica']=2
#对类别进行编码，3个类别分别赋值0，1，2
#算距离
def distEclud(vecA, vecB):                  #两个向量间欧式距离
    return sqrt(sum(power(vecA - vecB, 2))) #la.norm(vecA-vecB)
#初始化聚类中心：通过在区间范围随机产生的值作为新的中心点
def randCent(dataSet, k):
    #获取特征维度
    n = shape(dataSet)[1]
    #创建聚类中心0矩阵 k x n
    centroids = mat(zeros((k,n)))
    #遍历n维特征
    for j in range(n):
        #第j维特征属性值min   ,1x1矩阵
        minJ = min(dataSet[:,j])
        #区间值max-min，float数值
        rangeJ = float(max(dataSet[:,j]) - minJ)
        #第j维，每次随机生成k个中心
        centroids[:,j] = mat(minJ + rangeJ * random.rand(k,1))
    return centroids
def randChosenCent(dataSet,k):
    # 样本数
    m=shape(dataSet)[0]
    # 初始化列表
    centroidsIndex=[]
    #生成类似于样本索引的列表
    dataIndex=list(range(m))
    for i in range(k):
        #生成随机数
        randIndex=random.randint(0,len(dataIndex))
        #将随机产生的样本的索引放入centroidsIndex
        centroidsIndex.append(dataIndex[randIndex])
        #删除已经被抽中的样本
        del dataIndex[randIndex]
    #根据索引获取样本
    centroids = dataSet.iloc[centroidsIndex]
    return mat(centroids)
def kMeans(dataSet, k):
    # 样本总数
    m = shape(dataSet)[0]
    # 分配样本到最近的簇：存[簇序号,距离的平方]
    # m行  2 列
    clusterAssment = mat(zeros((m, 2)))
    # step1:
    # 通过随机产生的样本点初始化聚类中心
    centroids = randChosenCent(dataSet, k)
    print('最初的中心=', centroids)
    # 标志位，如果迭代前后样本分类发生变化值为Tree，否则为False
    clusterChanged = True
    # 查看迭代次数
    iterTime = 0
    # 所有样本分配结果不再改变，迭代终止
    while clusterChanged:
        clusterChanged = False
        # step2:分配到最近的聚类中心对应的簇中
        for i in range(m):
            # 初始定义距离为无穷大
            minDist = inf;
            # 初始化索引值
            minIndex = -1
            # 计算每个样本与k个中心点距离
            for j in range(k):
                # 计算第i个样本到第j个中心点的距离
                distJI = distEclud(centroids[j, :], dataSet.values[i, :])
                # 判断距离是否为最小
                if distJI < minDist:
                    # 更新获取到最小距离
                    minDist = distJI
                    # 获取对应的簇序号
                    minIndex = j
            # 样本上次分配结果跟本次不一样，标志位clusterChanged置True
            if clusterAssment[i, 0] != minIndex:
                clusterChanged = True
            clusterAssment[i, :] = minIndex, minDist ** 2  # 分配样本到最近的簇
        iterTime += 1
        sse = sum(clusterAssment[:, 1])
        print('the SSE of %d' % iterTime + 'th iteration is %f' % sse)
        # step3:更新聚类中心
        for cent in range(k):  # 样本分配结束后，重新计算聚类中心
            # 获取该簇所有的样本点
            ptsInClust = dataSet.iloc[nonzero(clusterAssment[:, 0].A == cent)[0]]
            # 更新聚类中心：axis=0沿列方向求均值。
            centroids[cent, :] = mean(ptsInClust, axis=0)
    return centroids, clusterAssment
def kMeansSSE(dataSet,k,distMeas=distEclud, createCent=randChosenCent):
    m = shape(dataSet)[0]
    #分配样本到最近的簇：存[簇序号,距离的平方]
    clusterAssment=mat(zeros((m,2)))
    #step1:#初始化聚类中心
    centroids = createCent(dataSet, k)
    print('initial centroids=',centroids)
    sseOld=0
    sseNew=inf
    iterTime=0 #查看迭代次数
    while(abs(sseNew-sseOld)>0.0001):
        sseOld=sseNew
        #step2:将样本分配到最近的质心对应的簇中
        for i in range(m):
            minDist=inf;minIndex=-1
            for j in range(k):
                #计算第i个样本与第j个质心之间的距离
                distJI=distMeas(centroids[j,:],dataSet.values[i,:])
                #获取到第i样本最近的质心的距离,及对应簇序号
                if distJI<minDist:
                    minDist=distJI;minIndex=j
            clusterAssment[i,:]=minIndex,minDist**2 #分配样本到最近的簇
        iterTime+=1
        sseNew=sum(clusterAssment[:,1])
        print('the SSE of %d'%iterTime + 'th iteration is %f'%sseNew)
        #step3:更新聚类中心
        for cent in range(k):
            #样本分配结束后，重新计算聚类中心
            ptsInClust=dataSet[nonzero(clusterAssment[:,0].A==cent)[0]]
            #按列取平均,mean()对array类型
            centroids[cent,:] = mean(ptsInClust, axis=0)
    return centroids, clusterAssment
# 2维数据聚类效果显示
def datashow(dataSet, k, centroids, clusterAssment):  # 二维空间显示聚类结果
    from matplotlib import pyplot as plt
    num, dim = shape(dataSet)  # 样本数num ,维数dim
    if dim != 2:
        print('sorry,the dimension of your dataset is not 2!')
        return 1
    marksamples = ['or', 'ob', 'og', 'ok', '^r', '^b', '<g']  # 样本图形标记
    if k > len(marksamples):
        print('sorry,your k is too large,please add length of the marksample!')
        return 1
        # 绘所有样本
    for i in range(num):
        markindex = int(clusterAssment[i, 0])  # 矩阵形式转为int值, 簇序号
        # 特征维对应坐标轴x,y；样本图形标记及大小
        plt.plot(dataSet.iat[i, 0], dataSet.iat[i, 1], marksamples[markindex], markersize=6)
    # 绘中心点
    markcentroids = ['o', '*', '^']  # 聚类中心图形标记
    label = ['0', '1', '2']
    c = ['yellow', 'pink', 'red']
    for i in range(k):
        plt.plot(centroids[i, 0], centroids[i, 1], markcentroids[i], markersize=15, label=label[i], c=c[i])
        plt.legend(loc='upper left')
    plt.xlabel('sepal length')
    plt.ylabel('sepal width')
    plt.title('k-means cluster result')  # 标题
    plt.show()
# 画出实际图像
def trgartshow(dataSet, k, labels):
    from matplotlib import pyplot as plt
    num, dim = shape(dataSet)
    label = ['0', '1', '2']
    marksamples = ['ob', 'or', 'og', 'ok', '^r', '^b', '<g']
    # 通过循环的方式，完成分组散点图的绘制
    for i in range(num):
        plt.plot(datamat.iat[i, 0], datamat.iat[i, 1], marksamples[int(labels.iat[i, 0])], markersize=6)
    for i in range(0, num, 50):
        plt.plot(datamat.iat[i, 0], datamat.iat[i, 1], marksamples[int(labels.iat[i, 0])], markersize=6,
                 label=label[int(labels.iat[i, 0])])
    plt.legend(loc='upper left')
    # 添加轴标签和标题
    plt.xlabel('sepal length')
    plt.ylabel('sepal width')
    plt.title('iris true result')  # 标题
    # 显示图形
    plt.show()
    # label=labels.iat[i,0]
#聚类前，绘制原始的样本点
def originalDatashow(dataSet):
        #样本的个数和特征维数
    num,dim=shape(dataSet)
    marksamples=['ob'] #样本图形标记
    for i in range(num):
        plt.plot(datamat.iat[i,0],datamat.iat[i,1],marksamples[0],markersize=5)
    plt.title('original dataset')
    plt.xlabel('sepal length')
    plt.ylabel('sepal width') #标题
    plt.show()
if __name__ == '__main__':
    # =====kmeans聚类
    # # #获取样本数据
    datamat = dataset.loc[:, ['sepal-length', 'sepal-width']]
    # 真实的标签
    labels = dataset.loc[:, ['class']]
    # #原始数据显示
    originalDatashow(datamat)
    # #*****kmeans聚类
    k = 3  # 用户定义聚类数
    mycentroids, clusterAssment = kMeans(datamat, k)
    # mycentroids,clusterAssment=kMeansSSE(datamat,k)
    # 绘图显示
    datashow(datamat, k, mycentroids, clusterAssment)
    trgartshow(datamat, 3, labels)

下面，使用TensorFlow，实现如下：

import tensorflow as tf
import numpy as np
from tensorflow.contrib.factorization import KMeans
import os
os.environ['CUDA_VISIBLE_DEVICES']=''
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets('/tmp/data',one_hot=True)
full_data_x = mnist.train.images
num_steps = 50
batch_size = 1024
k = 25
num_classes = 10
num_features = 28*28
X = tf.placeholder(tf.float32,[None,num_features])
y = tf.placeholder(tf.float32,[None,num_classes])
kmeans = KMeans(inputs=X,num_clusters=k,distance_metric='cosine',use_mini_batch=True)
# Build KMeans graph
all_scores, cluster_idx, scores, cluster_centers_initialized,init_op, training_op = kmeans.training_graph()
cluster_idx = cluster_idx[0]
avg_distance = tf.reduce_mean(scores)
# Initialize the variables (i.e. assign their default value)
init_vars = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init_vars, feed_dict={X: full_data_x})
sess.run(init_op, feed_dict={X: full_data_x})
# Training
for i in range(1, num_steps + 1):
    _, d, idx = sess.run([training_op, avg_distance, cluster_idx],
                         feed_dict={X: full_data_x})
    if i % 10 == 0 or i == 1:
        print("Step %i, Avg Distance: %f" % (i, d))
counts = np.zeros(shape=(k, num_classes))
for i in range(len(idx)):
    counts[idx[i]] += mnist.train.labels[i]
# Assign the most frequent label to the centroid
labels_map = [np.argmax(c) for c in counts]
labels_map = tf.convert_to_tensor(labels_map)
# Evaluation ops
# Lookup: centroid_id -> label
cluster_label = tf.nn.embedding_lookup(labels_map, cluster_idx)
# Compute accuracy
correct_prediction = tf.equal(cluster_label, tf.cast(tf.argmax(y, 1), tf.int32))
accuracy_op = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
# Test Model
test_x, test_y = mnist.test.images, mnist.test.labels
print("Test Accuracy:", sess.run(accuracy_op, feed_dict={X: test_x, y: test_y}))