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}))
