机器学习基础-聚类算法-15

聚类算法

K-MEANS

python实现K-MEANS

import numpy as np
import matplotlib.pyplot as plt  

# 载入数据
data = np.genfromtxt("kmeans.txt", delimiter=" ")

plt.scatter(data[:,0],data[:,1])
plt.show()

训练模型

# 计算距离 
def euclDistance(vector1, vector2):  
    return np.sqrt(sum((vector2 - vector1)**2))
  
# 初始化质心
def initCentroids(data, k):  
    numSamples, dim = data.shape
    # k个质心，列数跟样本的列数一样
    centroids = np.zeros((k, dim))  
    # 随机选出k个质心
    for i in range(k):  
        # 随机选取一个样本的索引
        index = int(np.random.uniform(0, numSamples))  
        # 作为初始化的质心
        centroids[i, :] = data[index, :]  
    return centroids  
  
# 传入数据集和k的值
def kmeans(data, k):  
    # 计算样本个数
    numSamples = data.shape[0]   
    # 样本的属性，第一列保存该样本属于哪个簇，第二列保存该样本跟它所属簇的误差
    clusterData = np.array(np.zeros((numSamples, 2)))  
    # 决定质心是否要改变的变量
    clusterChanged = True  
  
    # 初始化质心  
    centroids = initCentroids(data, k)  
  
    while clusterChanged:  
        clusterChanged = False  
        # 循环每一个样本 
        for i in range(numSamples):  
            # 最小距离
            minDist  = 100000.0  
            # 定义样本所属的簇
            minIndex = 0  
            # 循环计算每一个质心与该样本的距离
            for j in range(k):  
                # 循环每一个质心和样本，计算距离
                distance = euclDistance(centroids[j, :], data[i, :])  
                # 如果计算的距离小于最小距离，则更新最小距离
                if distance < minDist:  
                    minDist  = distance 
                    # 更新最小距离
                    clusterData[i, 1] = minDist
                    # 更新样本所属的簇
                    minIndex = j  
              
            # 如果样本的所属的簇发生了变化
            if clusterData[i, 0] != minIndex:  
                # 质心要重新计算
                clusterChanged = True
                # 更新样本的簇
                clusterData[i, 0] = minIndex
  
        # 更新质心
        for j in range(k):  
            # 获取第j个簇所有的样本所在的索引
            cluster_index = np.nonzero(clusterData[:, 0] == j)
            # 第j个簇所有的样本点
            pointsInCluster = data[cluster_index]  
            # 计算质心
            centroids[j, :] = np.mean(pointsInCluster, axis = 0) 
#         showCluster(data, k, centroids, clusterData)
 
    return centroids, clusterData  
  
# 显示结果 
def showCluster(data, k, centroids, clusterData):  
    numSamples, dim = data.shape  
    if dim != 2:  
        print("dimension of your data is not 2!")  
        return 1  
  
    # 用不同颜色形状来表示各个类别
    mark = ['or', 'ob', 'og', 'ok', '^r', '+r', 'sr', 'dr', ', 'pr']  
    if k > len(mark):  
        print("Your k is too large!")  
        return 1  
  
    # 画样本点  
    for i in range(numSamples):  
        markIndex = int(clusterData[i, 0])  
        plt.plot(data[i, 0], data[i, 1], mark[markIndex])  
  
    # 用不同颜色形状来表示各个类别
    mark = ['*r', '*b', '*g', '*k', '^b', '+b', 'sb', 'db', ', 'pb']  
    # 画质心点 
    for i in range(k):  
        plt.plot(centroids[i, 0], centroids[i, 1], mark[i], markersize = 20)  
  
    plt.show()

# 设置k值
k = 4  
# centroids 簇的中心点 
# cluster Data样本的属性，第一列保存该样本属于哪个簇，第二列保存该样本跟它所属簇的误差
centroids, clusterData = kmeans(data, k)  
if np.isnan(centroids).any():
    print('Error')
else:
    print('cluster complete!')   
    # 显示结果
showCluster(data, k, centroids, clusterData)  

做预测

def predict(datas):
    return np.array([np.argmin(((np.tile(data,(k,1))-centroids)**2).sum(axis=1)) for data in datas])

画出簇的作用区域

# 获取数据值所在的范围
x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1
y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1

# 生成网格矩阵
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02),
                     np.arange(y_min, y_max, 0.02))

z = predict(np.c_[xx.ravel(), yy.ravel()])# ravel与flatten类似，多维数据转一维。flatten不会改变原始数据，ravel会改变原始数据
z = z.reshape(xx.shape)
# 等高线图
cs = plt.contourf(xx, yy, z)
# 显示结果
showCluster(data, k, centroids, clusterData)  

sklearn-K-MEANS

from sklearn.cluster import KMeans
import numpy as np
import matplotlib.pyplot as plt

# 载入数据
data = np.genfromtxt("kmeans.txt", delimiter=" ")
# 设置k值
k = 4  

# 训练模型
model = KMeans(n_clusters=k)
model.fit(data)

# 分类中心点坐标
centers = model.cluster_centers_
print(centers)

# 预测结果
result = model.predict(data)
print(result)

model.labels_

# 画出各个数据点，用不同颜色表示分类
mark = ['or', 'ob', 'og', 'oy']
for i,d in enumerate(data):
    plt.plot(d[0], d[1], mark[result[i]])

# 画出各个分类的中心点
mark = ['*r', '*b', '*g', '*y']
for i,center in enumerate(centers):
    plt.plot(center[0],center[1], mark[i], markersize=20)
    
plt.show()

# 获取数据值所在的范围
x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1
y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1

# 生成网格矩阵
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02),
                     np.arange(y_min, y_max, 0.02))

z = model.predict(np.c_[xx.ravel(), yy.ravel()])# ravel与flatten类似，多维数据转一维。flatten不会改变原始数据，ravel会改变原始数据
z = z.reshape(xx.shape)
# 等高线图
cs = plt.contourf(xx, yy, z)
# 显示结果
# 画出各个数据点，用不同颜色表示分类
mark = ['or', 'ob', 'og', 'oy']
for i,d in enumerate(data):
    plt.plot(d[0], d[1], mark[result[i]])

# 画出各个分类的中心点
mark = ['*r', '*b', '*g', '*y']
for i,center in enumerate(centers):
    plt.plot(center[0],center[1], mark[i], markersize=20)
    
plt.show()

Mini Batch K-Means

sklearn-Mini-Batch-K-MEANS

from sklearn.cluster import MiniBatchKMeans
import numpy as np
import matplotlib.pyplot as plt

# 载入数据
data = np.genfromtxt("kmeans.txt", delimiter=" ")
# 设置k值
k = 4  

# 训练模型
model = MiniBatchKMeans(n_clusters=k)
model.fit(data)

# 分类中心点坐标
centers = model.cluster_centers_
print(centers)

# 预测结果
result = model.predict(data)
print(result)

# 画出各个数据点，用不同颜色表示分类
mark = ['or', 'ob', 'og', 'oy']
for i,d in enumerate(data):
    plt.plot(d[0], d[1], mark[result[i]])

# 画出各个分类的中心点
mark = ['*r', '*b', '*g', '*y']
for i,center in enumerate(centers):
    plt.plot(center[0],center[1], mark[i], markersize=20)
    
plt.show()

# 获取数据值所在的范围
x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1
y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1

# 生成网格矩阵
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02),
                     np.arange(y_min, y_max, 0.02))

z = model.predict(np.c_[xx.ravel(), yy.ravel()])# ravel与flatten类似，多维数据转一维。flatten不会改变原始数据，ravel会改变原始数据
z = z.reshape(xx.shape)
# 等高线图
cs = plt.contourf(xx, yy, z)
# 显示结果
# 画出各个数据点，用不同颜色表示分类
mark = ['or', 'ob', 'og', 'oy']
for i,d in enumerate(data):
    plt.plot(d[0], d[1], mark[result[i]])

# 画出各个分类的中心点
mark = ['*r', '*b', '*g', '*y']
for i,center in enumerate(centers):
    plt.plot(center[0],center[1], mark[i], markersize=20)
    
plt.show()

python实现K-MEANS优化1

import numpy as np
import matplotlib.pyplot as plt  

# 载入数据
data = np.genfromtxt("kmeans.txt", delimiter=" ")

训练模型

# 计算距离 
def euclDistance(vector1, vector2):  
    return np.sqrt(sum((vector2 - vector1)**2))
  
# 初始化质心
def initCentroids(data, k):  
    numSamples, dim = data.shape
    # k个质心，列数跟样本的列数一样
    centroids = np.zeros((k, dim))  
    # 随机选出k个质心
    for i in range(k):  
        # 随机选取一个样本的索引
        index = int(np.random.uniform(0, numSamples))  
        # 作为初始化的质心
        centroids[i, :] = data[index, :]  
    return centroids  
  
# 传入数据集和k的值
def kmeans(data, k):  
    # 计算样本个数
    numSamples = data.shape[0]   
    # 样本的属性，第一列保存该样本属于哪个簇，第二列保存该样本跟它所属簇的误差
    clusterData = np.array(np.zeros((numSamples, 2)))  
    # 决定质心是否要改变的变量
    clusterChanged = True  
  
    # 初始化质心  
    centroids = initCentroids(data, k)  
  
    while clusterChanged:  
        clusterChanged = False  
        # 循环每一个样本 
        for i in range(numSamples):  
            # 最小距离
            minDist  = 100000.0  
            # 定义样本所属的簇
            minIndex = 0  
            # 循环计算每一个质心与该样本的距离
            for j in range(k):  
                # 循环每一个质心和样本，计算距离
                distance = euclDistance(centroids[j, :], data[i, :])  
                # 如果计算的距离小于最小距离，则更新最小距离
                if distance < minDist:  
                    minDist  = distance  
                    # 更新样本所属的簇
                    minIndex = j  
                    # 更新最小距离
                    clusterData[i, 1] = distance
              
            # 如果样本的所属的簇发生了变化
            if clusterData[i, 0] != minIndex:  
                # 质心要重新计算
                clusterChanged = True
                # 更新样本的簇
                clusterData[i, 0] = minIndex
  
        # 更新质心
        for j in range(k):  
            # 获取第j个簇所有的样本所在的索引
            cluster_index = np.nonzero(clusterData[:, 0] == j)
            # 第j个簇所有的样本点
            pointsInCluster = data[cluster_index]  
            # 计算质心
            centroids[j, :] = np.mean(pointsInCluster, axis = 0) 
#         showCluster(data, k, centroids, clusterData)
  
    return centroids, clusterData  
  
# 显示结果 
def showCluster(data, k, centroids, clusterData):  
    numSamples, dim = data.shape  
    if dim != 2:  
        print("dimension of your data is not 2!")  
        return 1  
  
    # 用不同颜色形状来表示各个类别
    mark = ['or', 'ob', 'og', 'ok', '^r', '+r', 'sr', 'dr', ', 'pr']  
    if k > len(mark):  
        print("Your k is too large!")  
        return 1  
  
    # 画样本点  
    for i in range(numSamples):  
        markIndex = int(clusterData[i, 0])  
        plt.plot(data[i, 0], data[i, 1], mark[markIndex])  
  
    # 用不同颜色形状来表示各个类别
    mark = ['*r', '*b', '*g', '*k', '^b', '+b', 'sb', 'db', ', 'pb']  
    # 画质心点 
    for i in range(k):  
        plt.plot(centroids[i, 0], centroids[i, 1], mark[i], markersize = 20)  
  
    plt.show()

list_lost = []
for k in range(2,10):
    min_loss = 10000
    min_loss_centroids = np.array([])
    min_loss_clusterData = np.array([])
    for i in range(50):
        # centroids 簇的中心点 
        # cluster Data样本的属性，第一列保存该样本属于哪个簇，第二列保存该样本跟它所属簇的误差
        centroids, clusterData = kmeans(data, k)  
        loss = sum(clusterData[:,1])/data.shape[0]
        if loss < min_loss:
            min_loss = loss
            min_loss_centroids = centroids
            min_loss_clusterData = clusterData
    list_lost.append(min_loss)
    
#     print('loss',min_loss)
# print('cluster complete!')      
# centroids = min_loss_centroids
# clusterData = min_loss_clusterData

# 显示结果
# showCluster(data, k, centroids, clusterData)

plt.plot(range(2,10),list_lost)
plt.xlabel('k')
plt.ylabel('loss')
plt.show()

做预测

画出簇的作用区域

# 获取数据值所在的范围
x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1
y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1

# 生成网格矩阵
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02),
                     np.arange(y_min, y_max, 0.02))

z = predict(np.c_[xx.ravel(), yy.ravel()])# ravel与flatten类似，多维数据转一维。flatten不会改变原始数据，ravel会改变原始数据
z = z.reshape(xx.shape)
# 等高线图
cs = plt.contourf(xx, yy, z)
# 显示结果
showCluster(data, k, centroids, clusterData)  

K-MEANS代价函数应用

import numpy as np
import matplotlib.pyplot as plt  

# 载入数据
data = np.genfromtxt("kmeans.txt", delimiter=" ")

训练模型

# 计算距离 
def euclDistance(vector1, vector2):  
    return np.sqrt(sum((vector2 - vector1)**2))
  
# 初始化质心
def initCentroids(data, k):  
    numSamples, dim = data.shape
    # k个质心，列数跟样本的列数一样
    centroids = np.zeros((k, dim))  
    # 随机选出k个质心
    for i in range(k):  
        # 随机选取一个样本的索引
        index = int(np.random.uniform(0, numSamples))  
        # 作为初始化的质心
        centroids[i, :] = data[index, :]  
    return centroids  
  
# 传入数据集和k的值
def kmeans(data, k):  
    # 计算样本个数
    numSamples = data.shape[0]   
    # 样本的属性，第一列保存该样本属于哪个簇，第二列保存该样本跟它所属簇的误差
    clusterData = np.array(np.zeros((numSamples, 2)))  
    # 决定质心是否要改变的变量
    clusterChanged = True  
  
    # 初始化质心  
    centroids = initCentroids(data, k)  
  
    while clusterChanged:  
        clusterChanged = False  
        # 循环每一个样本 
        for i in range(numSamples):  
            # 最小距离
            minDist  = 100000.0  
            # 定义样本所属的簇
            minIndex = 0  
            # 循环计算每一个质心与该样本的距离
            for j in range(k):  
                # 循环每一个质心和样本，计算距离
                distance = euclDistance(centroids[j, :], data[i, :])  
                # 如果计算的距离小于最小距离，则更新最小距离
                if distance < minDist:  
                    minDist  = distance  
                    # 更新样本所属的簇
                    minIndex = j  
                    # 更新最小距离
                    clusterData[i, 1] = distance
              
            # 如果样本的所属的簇发生了变化
            if clusterData[i, 0] != minIndex:  
                # 质心要重新计算
                clusterChanged = True
                # 更新样本的簇
                clusterData[i, 0] = minIndex
  
        # 更新质心
        for j in range(k):  
            # 获取第j个簇所有的样本所在的索引
            cluster_index = np.nonzero(clusterData[:, 0] == j)
            # 第j个簇所有的样本点
            pointsInCluster = data[cluster_index]  
            # 计算质心
            centroids[j, :] = np.mean(pointsInCluster, axis = 0) 
#         showCluster(data, k, centroids, clusterData)
  
    return centroids, clusterData  
  
# 显示结果 
def showCluster(data, k, centroids, clusterData):  
    numSamples, dim = data.shape  
    if dim != 2:  
        print("dimension of your data is not 2!")  
        return 1  
  
    # 用不同颜色形状来表示各个类别
    mark = ['or', 'ob', 'og', 'ok', '^r', '+r', 'sr', 'dr', ', 'pr']  
    if k > len(mark):  
        print("Your k is too large!")  
        return 1  
  
    # 画样本点  
    for i in range(numSamples):  
        markIndex = int(clusterData[i, 0])  
        plt.plot(data[i, 0], data[i, 1], mark[markIndex])  
  
    # 用不同颜色形状来表示各个类别
    mark = ['*r', '*b', '*g', '*k', '^b', '+b', 'sb', 'db', ', 'pb']  
    # 画质心点 
    for i in range(k):  
        plt.plot(centroids[i, 0], centroids[i, 1], mark[i], markersize = 20)  
  
    plt.show()

# 设置k值
k = 4  

min_loss = 10000
min_loss_centroids = np.array([])
min_loss_clusterData = np.array([])

for i in range(50):
    # centroids 簇的中心点 
    # cluster Data样本的属性，第一列保存该样本属于哪个簇，第二列保存该样本跟它所属簇的误差
    centroids, clusterData = kmeans(data, k)  
    loss = sum(clusterData[:,1])/data.shape[0]
    if loss < min_loss:
        min_loss = loss
        min_loss_centroids = centroids
        min_loss_clusterData = clusterData
        
#     print('loss',min_loss)
print('cluster complete!')      
centroids = min_loss_centroids
clusterData = min_loss_clusterData

# 显示结果
showCluster(data, k, centroids, clusterData)

DBSCAN

sklearn-DBSCAN1

from sklearn.cluster import DBSCAN
import numpy as np
import matplotlib.pyplot as plt

# 载入数据
data = np.genfromtxt("kmeans.txt", delimiter=" ")

# 训练模型
# eps距离阈值，min_samples核心对象在eps领域的样本数阈值
model = DBSCAN(eps=1.5, min_samples=4)
model.fit(data)

result = model.fit_predict(data)
result

# 画出各个数据点，用不同颜色表示分类
mark = ['or', 'ob', 'og', 'oy', 'ok', 'om']
for i,d in enumerate(data):
    plt.plot(d[0], d[1], mark[result[i]])
    
plt.show()

sklearn-DBSCAN2

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets

x1, y1 = datasets.make_circles(n_samples=2000, factor=0.5, noise=0.05)
x2, y2 = datasets.make_blobs(n_samples=1000, centers=[[1.2,1.2]], cluster_std=[[.1]])

x = np.concatenate((x1, x2))
plt.scatter(x[:, 0], x[:, 1], marker='o')
plt.show()

from sklearn.cluster import KMeans
y_pred = KMeans(n_clusters=3).fit_predict(x)
plt.scatter(x[:, 0], x[:, 1], c=y_pred)
plt.show()

from sklearn.cluster import DBSCAN
y_pred = DBSCAN().fit_predict(x)
plt.scatter(x[:, 0], x[:, 1], c=y_pred)
plt.show()

y_pred = DBSCAN(eps = 0.2).fit_predict(x)
plt.scatter(x[:, 0], x[:, 1], c=y_pred)
plt.show()

y_pred = DBSCAN(eps = 0.2, min_samples=50).fit_predict(x)
plt.scatter(x[:, 0], x[:, 1], c=y_pred)
plt.show()