下面的demo是根据kmeans算法原理实现的demo，使用到的数据是kmeans.txt
1 1.658985 4.285136 2 -3.453687 3.424321 3 4.838138 -1.151539 4 -5.379713 -3.362104 5 0.972564 2.924086 6 -3.567919 1.531611 7 0.450614 -3.302219 8 -3.487105 -1.724432 9 2.668759 1.594842 10 -3.156485 3.191137 11 3.165506 -3.999838 12 -2.786837 -3.099354 13 4.208187 2.984927 14 -2.123337 2.943366 15 0.704199 -0.479481 16 -0.392370 -3.963704 17 2.831667 1.574018 18 -0.790153 3.343144 19 2.943496 -3.357075 20 -3.195883 -2.283926 21 2.336445 2.875106 22 -1.786345 2.554248 23 2.190101 -1.906020 24 -3.403367 -2.778288 25 1.778124 3.880832 26 -1.688346 2.230267 27 2.592976 -2.054368 28 -4.007257 -3.207066 29 2.257734 3.387564 30 -2.679011 0.785119 31 0.939512 -4.023563 32 -3.674424 -2.261084 33 2.046259 2.735279 34 -3.189470 1.780269 35 4.372646 -0.822248 36 -2.579316 -3.497576 37 1.889034 5.190400 38 -0.798747 2.185588 39 2.836520 -2.658556 40 -3.837877 -3.253815 41 2.096701 3.886007 42 -2.709034 2.923887 43 3.367037 -3.184789 44 -2.121479 -4.232586 45 2.329546 3.179764 46 -3.284816 3.273099 47 3.091414 -3.815232 48 -3.762093 -2.432191 49 3.542056 2.778832 50 -1.736822 4.241041 51 2.127073 -2.983680 52 -4.323818 -3.938116 53 3.792121 5.135768 54 -4.786473 3.358547 55 2.624081 -3.260715 56 -4.009299 -2.978115 57 2.493525 1.963710 58 -2.513661 2.642162 59 1.864375 -3.176309 60 -3.171184 -3.572452 61 2.894220 2.489128 62 -2.562539 2.884438 63 3.491078 -3.947487 64 -2.565729 -2.012114 65 3.332948 3.983102 66 -1.616805 3.573188 67 2.280615 -2.559444 68 -2.651229 -3.103198 69 2.321395 3.154987 70 -1.685703 2.939697 71 3.031012 -3.620252 72 -4.599622 -2.185829 73 4.196223 1.126677 74 -2.133863 3.093686 75 4.668892 -2.562705 76 -2.793241 -2.149706 77 2.884105 3.043438 78 -2.967647 2.848696 79 4.479332 -1.764772 80 -4.905566 -2.911070
1 import numpy as np 2 import matplotlib.pyplot as plt 3 # 载入数据 4 data = np.genfromtxt("kmeans.txt", delimiter=" ") 5 6 plt.scatter(data[:,0],data[:,1]) 7 plt.show() 8 print(data.shape) 9 #训练模型 10 # 计算距离 11 def euclDistance(vector1, vector2): 12 return np.sqrt(sum((vector2 - vector1) ** 2)) 13 14 15 # 初始化质心 16 def initCentroids(data, k): 17 numSamples, dim = data.shape 18 # k个质心，列数跟样本的列数一样 19 centroids = np.zeros((k, dim)) 20 # 随机选出k个质心 21 for i in range(k): 22 # 随机选取一个样本的索引 23 index = int(np.random.uniform(0, numSamples))#从一个均匀分布[low,high)中随机采样 24 # 作为初始化的质心 25 centroids[i, :] = data[index, :] 26 return centroids 27 28 29 # 传入数据集和k的值 30 def kmeans(data, k): 31 # 计算样本个数 32 numSamples = data.shape[0] 33 # 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 34 clusterData = np.array(np.zeros((numSamples, 2))) 35 # 决定质心是否要改变的变量 36 clusterChanged = True 37 38 # 初始化质心 39 centroids = initCentroids(data, k) 40 41 while clusterChanged: 42 clusterChanged = False 43 # 循环每一个样本 44 for i in range(numSamples): 45 # 最小距离 46 minDist = 100000.0 47 # 定义样本所属的簇 48 minIndex = 0 49 # 循环计算每一个质心与该样本的距离 50 for j in range(k): 51 # 循环每一个质心和样本，计算距离 52 distance = euclDistance(centroids[j, :], data[i, :]) 53 # 如果计算的距离小于最小距离，则更新最小距离 54 if distance < minDist: 55 minDist = distance 56 # 更新最小距离 57 clusterData[i, 1] = minDist 58 # 更新样本所属的簇 59 minIndex = j 60 61 # 如果样本的所属的簇发生了变化 62 if clusterData[i, 0] != minIndex: 63 # 质心要重新计算 64 clusterChanged = True 65 # 更新样本的簇 66 clusterData[i, 0] = minIndex 67 68 # 更新质心 69 for j in range(k): 70 # 获取第j个簇所有的样本所在的索引 71 cluster_index = np.nonzero(clusterData[:, 0] == j) 72 # 第j个簇所有的样本点 73 pointsInCluster = data[cluster_index] 74 # 计算质心 75 centroids[j, :] = np.mean(pointsInCluster, axis=0) 76 # showCluster(data, k, centroids, clusterData) 77 78 return centroids, clusterData 79 80 81 # 显示结果 82 def showCluster(data, k, centroids, clusterData): 83 numSamples, dim = data.shape 84 if dim != 2: 85 print("dimension of your data is not 2!") 86 return 1 87 88 # 用不同颜色形状来表示各个类别 89 mark = ['or', 'ob', 'og', 'ok', '^r', '+r', 'sr', 'dr', '<r', 'pr'] 90 if k > len(mark): 91 print("Your k is too large!") 92 return 1 93 94 # 画样本点 95 for i in range(numSamples): 96 markIndex = int(clusterData[i, 0]) 97 plt.plot(data[i, 0], data[i, 1], mark[markIndex]) 98 99 # 用不同颜色形状来表示各个类别 100 mark = ['*r', '*b', '*g', '*k', '^b', '+b', 'sb', 'db', '<b', 'pb'] 101 # 画质心点 102 for i in range(k): 103 plt.plot(centroids[i, 0], centroids[i, 1], mark[i], markersize=20) 104 105 plt.show() 106 # 设置k值 107 k = 4 108 # centroids 簇的中心点 109 # 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 110 centroids, clusterData = kmeans(data, k) 111 if np.isnan(centroids).any(): 112 print('Error') 113 else: 114 print('cluster complete!') 115 # 显示结果 116 showCluster(data, k, centroids, clusterData) 117 print(centroids) 118 # 做预测 119 x_test = [0,1] 120 np.tile(x_test,(k,1)) 121 # 误差 122 np.tile(x_test,(k,1))-centroids 123 # 误差平方 124 (np.tile(x_test,(k,1))-centroids)**2 125 # 误差平方和 126 ((np.tile(x_test,(k,1))-centroids)**2).sum(axis=1) 127 # 最小值所在的索引号 128 np.argmin(((np.tile(x_test,(k,1))-centroids)**2).sum(axis=1)) 129 def predict(datas): 130 return np.array([np.argmin(((np.tile(data,(k,1))-centroids)**2).sum(axis=1)) for data in datas]) 131 #画出簇的作用区域 132 # 获取数据值所在的范围 133 x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1 134 y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1 135 136 # 生成网格矩阵 137 xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02), 138 np.arange(y_min, y_max, 0.02)) 139 140 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 141 z = z.reshape(xx.shape) 142 # 等高线图 143 cs = plt.contourf(xx, yy, z) 144 # 显示结果 145 showCluster(data, k, centroids, clusterData)
下面这个demo是使用sklearn库实现聚类
1 from sklearn.cluster import KMeans 2 import numpy as np 3 from matplotlib import pyplot as plt 4 data = np.genfromtxt('kmeans.txt',delimiter=" ")# 载入数据 5 k = 4# 设置k值 6 model = KMeans(n_clusters=4)# 训练模型 7 model.fit(data) 8 print(model.labels_)# 结果 9 centers = model.cluster_centers_# 分类中心点坐标 10 print(centers) 11 result = model.labels_ 12 mark = ['or','ob','og','oy']# 画出各个数据点，用不同颜色表示分类 13 for i,d in enumerate(data): 14 plt.plot(d[0],d[1],mark[result[i]]) 15 mark = ['*r','*b','*g','*y']# 画出各个分类的中心点 16 for i,center in enumerate(centers): 17 plt.plot(center[0],center[1],mark[i],markersize = 20) 18 plt.show() 19 x_min, x_max = data[:,0].min() - 1,data[:,0].max() +1# 获取数据值所在的范围 20 y_min, y_max = data[:,1].min() - 1,data[:,1].max() +1 21 xx ,yy= np.meshgrid(np.arange(x_min,x_max,0.02),np.arange(y_min,y_max,0.02))# 生成网格矩阵 22 z = model.predict(np.c_[xx.ravel(),yy.ravel()]) 23 z = z.reshape(xx.shape) 24 cs = plt.contourf(xx,yy,z)# 等高线图 25 mark = ['or','ob','og','oy'] 26 for i,d in enumerate(centers): 27 plt.plot(d[0],d[1],mark[result[i]]) 28 mark = ['*r','*b','*g','*y'] 29 for i,center in enumerate(centers): 30 plt.plot(center[0],center[1],mark[i],markersize = 20) 31 plt.show()
当数据量很大的时候，会出现原始聚类算法效率很低，计算速度很慢，因此可以使用mini batch k-means在数据量很大的时候提高速度
1 from sklearn.cluster import MiniBatchKMeans 2 import numpy as np 3 from matplotlib import pyplot as plt 4 data = np.genfromtxt('kmeans.txt',delimiter=" ")# 载入数据 5 k = 4# 设置k值 6 model = MiniBatchKMeans(n_clusters=4)# 训练模型 7 model.fit(data) 8 print(model.labels_)# 结果 9 centers = model.cluster_centers_# 分类中心点坐标 10 print(centers) 11 result = model.labels_ 12 mark = ['or','ob','og','oy']# 画出各个数据点，用不同颜色表示分类 13 for i,d in enumerate(data): 14 plt.plot(d[0],d[1],mark[result[i]]) 15 mark = ['*r','*b','*g','*y']# 画出各个分类的中心点 16 for i,center in enumerate(centers): 17 plt.plot(center[0],center[1],mark[i],markersize = 20) 18 plt.show() 19 x_min, x_max = data[:,0].min() - 1,data[:,0].max() +1# 获取数据值所在的范围 20 y_min, y_max = data[:,1].min() - 1,data[:,1].max() +1 21 xx ,yy= np.meshgrid(np.arange(x_min,x_max,0.02),np.arange(y_min,y_max,0.02))# 生成网格矩阵 22 z = model.predict(np.c_[xx.ravel(),yy.ravel()]) 23 z = z.reshape(xx.shape) 24 cs = plt.contourf(xx,yy,z)# 等高线图 25 mark = ['or','ob','og','oy'] 26 for i,d in enumerate(centers): 27 plt.plot(d[0],d[1],mark[result[i]]) 28 mark = ['*r','*b','*g','*y'] 29 for i,center in enumerate(centers): 30 plt.plot(center[0],center[1],mark[i],markersize = 20) 31 plt.show()
当然传统聚类算法有一些弊端（sklearn提供的Kmeans已经解决了下面两个问题），如下
该问题可以通过多次初始化随机点的选取，然后选择代价函数最小的那个
下面的demo实现了优化
1 import numpy as np 2 import matplotlib.pyplot as plt 3 # 载入数据 4 data = np.genfromtxt("kmeans.txt", delimiter=" ") 5 6 7 # 计算距离 8 def euclDistance(vector1, vector2): 9 return np.sqrt(sum((vector2 - vector1) ** 2)) 10 11 12 # 初始化质心 13 def initCentroids(data, k): 14 numSamples, dim = data.shape 15 # k个质心，列数跟样本的列数一样 16 centroids = np.zeros((k, dim)) 17 # 随机选出k个质心 18 for i in range(k): 19 # 随机选取一个样本的索引 20 index = int(np.random.uniform(0, numSamples)) 21 # 作为初始化的质心 22 centroids[i, :] = data[index, :] 23 return centroids 24 25 26 # 传入数据集和k的值 27 def kmeans(data, k): 28 # 计算样本个数 29 numSamples = data.shape[0] 30 # 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 31 clusterData = np.array(np.zeros((numSamples, 2))) 32 # 决定质心是否要改变的变量 33 clusterChanged = True 34 35 # 初始化质心 36 centroids = initCentroids(data, k) 37 38 while clusterChanged: 39 clusterChanged = False 40 # 循环每一个样本 41 for i in range(numSamples): 42 # 最小距离 43 minDist = 100000.0 44 # 定义样本所属的簇 45 minIndex = 0 46 # 循环计算每一个质心与该样本的距离 47 for j in range(k): 48 # 循环每一个质心和样本，计算距离 49 distance = euclDistance(centroids[j, :], data[i, :]) 50 # 如果计算的距离小于最小距离，则更新最小距离 51 if distance < minDist: 52 minDist = distance 53 # 更新样本所属的簇 54 minIndex = j 55 # 更新最小距离 56 clusterData[i, 1] = distance 57 58 # 如果样本的所属的簇发生了变化 59 if clusterData[i, 0] != minIndex: 60 # 质心要重新计算 61 clusterChanged = True 62 # 更新样本的簇 63 clusterData[i, 0] = minIndex 64 65 # 更新质心 66 for j in range(k): 67 # 获取第j个簇所有的样本所在的索引 68 cluster_index = np.nonzero(clusterData[:, 0] == j) 69 # 第j个簇所有的样本点 70 pointsInCluster = data[cluster_index] 71 # 计算质心 72 centroids[j, :] = np.mean(pointsInCluster, axis=0) 73 # showCluster(data, k, centroids, clusterData) 74 75 return centroids, clusterData 76 77 78 # 显示结果 79 def showCluster(data, k, centroids, clusterData): 80 numSamples, dim = data.shape 81 if dim != 2: 82 print("dimension of your data is not 2!") 83 return 1 84 85 # 用不同颜色形状来表示各个类别 86 mark = ['or', 'ob', 'og', 'ok', '^r', '+r', 'sr', 'dr', '<r', 'pr'] 87 if k > len(mark): 88 print("Your k is too large!") 89 return 1 90 91 # 画样本点 92 for i in range(numSamples): 93 markIndex = int(clusterData[i, 0]) 94 plt.plot(data[i, 0], data[i, 1], mark[markIndex]) 95 96 # 用不同颜色形状来表示各个类别 97 mark = ['*r', '*b', '*g', '*k', '^b', '+b', 'sb', 'db', '<b', 'pb'] 98 # 画质心点 99 for i in range(k): 100 plt.plot(centroids[i, 0], centroids[i, 1], mark[i], markersize=20) 101 102 plt.show() 103 104 105 # 设置k值 106 k = 4 107 108 min_loss = 10000 109 min_loss_centroids = np.array([]) 110 min_loss_clusterData = np.array([]) 111 112 for i in range(50): 113 # centroids 簇的中心点 114 # 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 115 centroids, clusterData = kmeans(data, k) 116 loss = sum(clusterData[:, 1]) / data.shape[0] 117 if loss < min_loss: 118 min_loss = loss 119 min_loss_centroids = centroids 120 min_loss_clusterData = clusterData 121 122 # print('loss',min_loss) 123 print('cluster complete!') 124 centroids = min_loss_centroids 125 clusterData = min_loss_clusterData 126 127 # 显示结果 128 showCluster(data, k, centroids, clusterData) 129 # 做预测 130 x_test = [0,1] 131 np.tile(x_test,(k,1)) 132 # 误差 133 np.tile(x_test,(k,1))-centroids 134 # 误差平方 135 (np.tile(x_test,(k,1))-centroids)**2 136 # 误差平方和 137 ((np.tile(x_test,(k,1))-centroids)**2).sum(axis=1) 138 # 最小值所在的索引号 139 np.argmin(((np.tile(x_test,(k,1))-centroids)**2).sum(axis=1)) 140 def predict(datas): 141 return np.array([np.argmin(((np.tile(data,(k,1))-centroids)**2).sum(axis=1)) for data in datas]) 142 # 获取数据值所在的范围 143 x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1 144 y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1 145 146 # 生成网格矩阵 147 xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02), 148 np.arange(y_min, y_max, 0.02)) 149 150 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 151 z = z.reshape(xx.shape) 152 # 等高线图 153 cs = plt.contourf(xx, yy, z) 154 # 显示结果 155 showCluster(data, k, centroids, clusterData)
关于k值选择，一个方法是肘部法，另一个方法是按照自己的需要选择分为几类，下面的demo是根据肘部法选择K值
1 import numpy as np 2 import matplotlib.pyplot as plt 3 # 载入数据 4 data = np.genfromtxt("kmeans.txt", delimiter=" ") 5 6 7 # 计算距离 8 def euclDistance(vector1, vector2): 9 return np.sqrt(sum((vector2 - vector1) ** 2)) 10 11 12 # 初始化质心 13 def initCentroids(data, k): 14 numSamples, dim = data.shape 15 # k个质心，列数跟样本的列数一样 16 centroids = np.zeros((k, dim)) 17 # 随机选出k个质心 18 for i in range(k): 19 # 随机选取一个样本的索引 20 index = int(np.random.uniform(0, numSamples)) 21 # 作为初始化的质心 22 centroids[i, :] = data[index, :] 23 return centroids 24 25 26 # 传入数据集和k的值 27 def kmeans(data, k): 28 # 计算样本个数 29 numSamples = data.shape[0] 30 # 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 31 clusterData = np.array(np.zeros((numSamples, 2))) 32 # 决定质心是否要改变的变量 33 clusterChanged = True 34 35 # 初始化质心 36 centroids = initCentroids(data, k) 37 38 while clusterChanged: 39 clusterChanged = False 40 # 循环每一个样本 41 for i in range(numSamples): 42 # 最小距离 43 minDist = 100000.0 44 # 定义样本所属的簇 45 minIndex = 0 46 # 循环计算每一个质心与该样本的距离 47 for j in range(k): 48 # 循环每一个质心和样本，计算距离 49 distance = euclDistance(centroids[j, :], data[i, :]) 50 # 如果计算的距离小于最小距离，则更新最小距离 51 if distance < minDist: 52 minDist = distance 53 # 更新样本所属的簇 54 minIndex = j 55 # 更新最小距离 56 clusterData[i, 1] = distance 57 58 # 如果样本的所属的簇发生了变化 59 if clusterData[i, 0] != minIndex: 60 # 质心要重新计算 61 clusterChanged = True 62 # 更新样本的簇 63 clusterData[i, 0] = minIndex 64 65 # 更新质心 66 for j in range(k): 67 # 获取第j个簇所有的样本所在的索引 68 cluster_index = np.nonzero(clusterData[:, 0] == j) 69 # 第j个簇所有的样本点 70 pointsInCluster = data[cluster_index] 71 # 计算质心 72 centroids[j, :] = np.mean(pointsInCluster, axis=0) 73 # showCluster(data, k, centroids, clusterData) 74 75 return centroids, clusterData 76 77 78 # 显示结果 79 def showCluster(data, k, centroids, clusterData): 80 numSamples, dim = data.shape 81 if dim != 2: 82 print("dimension of your data is not 2!") 83 return 1 84 85 # 用不同颜色形状来表示各个类别 86 mark = ['or', 'ob', 'og', 'ok', '^r', '+r', 'sr', 'dr', '<r', 'pr'] 87 if k > len(mark): 88 print("Your k is too large!") 89 return 1 90 91 # 画样本点 92 for i in range(numSamples): 93 markIndex = int(clusterData[i, 0]) 94 plt.plot(data[i, 0], data[i, 1], mark[markIndex]) 95 96 # 用不同颜色形状来表示各个类别 97 mark = ['*r', '*b', '*g', '*k', '^b', '+b', 'sb', 'db', '<b', 'pb'] 98 # 画质心点 99 for i in range(k): 100 plt.plot(centroids[i, 0], centroids[i, 1], mark[i], markersize=20) 101 102 plt.show() 103 104 105 list_lost = [] 106 for k in range(2, 10): 107 min_loss = 10000 108 min_loss_centroids = np.array([]) 109 min_loss_clusterData = np.array([]) 110 for i in range(50): 111 # centroids 簇的中心点 112 # 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 113 centroids, clusterData = kmeans(data, k) 114 loss = sum(clusterData[:, 1]) / data.shape[0] 115 if loss < min_loss: 116 min_loss = loss 117 min_loss_centroids = centroids 118 min_loss_clusterData = clusterData 119 list_lost.append(min_loss) 120 121 # print('loss',min_loss) 122 # print('cluster complete!') 123 # centroids = min_loss_centroids 124 # clusterData = min_loss_clusterData 125 126 # 显示结果 127 # showCluster(data, k, centroids, clusterData) 128 print(list_lost) 129 plt.plot(range(2,10),list_lost) 130 plt.xlabel('k') 131 plt.ylabel('loss') 132 plt.show() 133 # 做预测 134 x_test = [0,1] 135 np.tile(x_test,(k,1)) 136 # 误差 137 np.tile(x_test,(k,1))-centroids 138 # 误差平方 139 (np.tile(x_test,(k,1))-centroids)**2 140 # 误差平方和 141 ((np.tile(x_test,(k,1))-centroids)**2).sum(axis=1) 142 # 最小值所在的索引号 143 np.argmin(((np.tile(x_test,(k,1))-centroids)**2).sum(axis=1)) 144 def predict(datas): 145 return np.array([np.argmin(((np.tile(data,(k,1))-centroids)**2).sum(axis=1)) for data in datas]) 146 # 获取数据值所在的范围 147 x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1 148 y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1 149 150 # 生成网格矩阵 151 xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02), 152 np.arange(y_min, y_max, 0.02)) 153 154 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 155 z = z.reshape(xx.shape) 156 # 等高线图 157 cs = plt.contourf(xx, yy, z) 158 # 显示结果 159 showCluster(data, k, centroids, clusterData)
from sklearn.cluster import DBSCAN import numpy as np from matplotlib import pyplot as plt data = np.genfromtxt("kmeans.txt",delimiter=' ') model = DBSCAN(eps=1.5,min_samples=4) model.fit(data) result = model.fit_predict(data) print(result) mark = ['or', 'ob', 'og', 'oy', 'ok', 'om'] for i,d in enumerate(data): plt.plot(d[0],d[1],mark[result[i]]) plt.show()
1 import numpy as np 2 import matplotlib.pyplot as plt 3 from sklearn import datasets 4 x1, y1 = datasets.make_circles(n_samples=2000, factor=0.5, noise=0.05) 5 x2, y2 = datasets.make_blobs(n_samples=1000, centers=[[1.2,1.2]], cluster_std=[[.1]]) 6 7 x = np.concatenate((x1, x2)) 8 plt.scatter(x[:, 0], x[:, 1], marker='o') 9 plt.show() 10 from sklearn.cluster import KMeans 11 y_pred = KMeans(n_clusters=3).fit_predict(x) 12 plt.scatter(x[:, 0], x[:, 1], c=y_pred) 13 plt.show() 14 from sklearn.cluster import DBSCAN 15 y_pred = DBSCAN().fit_predict(x) 16 plt.scatter(x[:, 0], x[:, 1], c=y_pred) 17 plt.show() 18 y_pred = DBSCAN(eps = 0.2).fit_predict(x) 19 plt.scatter(x[:, 0], x[:, 1], c=y_pred) 20 plt.show() 21 y_pred = DBSCAN(eps = 0.2, min_samples=50).fit_predict(x) 22 plt.scatter(x[:, 0], x[:, 1], c=y_pred) 23 plt.show()