深度学习 自组织映射网络 ——python实现SOM（用于聚类）

• 摘要
• python实现代码
• 计算实例

摘要

SOM（Self Organizing Maps ） 的目标是用低维目标空间的点来表示高维空间中的点，并且尽可能保持对应点的距离和邻近关系（拓扑关系）。该算法可用于降维和聚类等方面，本文通过python实现了该算法在聚类方面的应用，并将代码进行了封装，方便读者调用。
下图为正文计算实例的可视化图形。

python实现代码

net：竞争层的拓扑结构，支持一维及二维，1表示该输出节点存在，0表示不存在该输出节点
epochs：最大迭代次数
.r_t：[C,B] 领域半径参数，r = C*e**(-B * t/eoochs),其中t表示当前迭代次数
eps：[C,B] learning rate的阈值
用法：指定竞争层的拓扑结构、 最大迭代次数、领域半径参数、学习率阈值（后三个参数也可不指定），竞争层的拓扑结构的节点数代表了聚类数目，然后直接调用fit(X) 进行数据集的聚类。

# -*- coding: utf-8 -*- # @Time : 2021/1/12 22:37 # @Author : CyrusMay WJ # @FileName: SOM.py # @Software: PyCharm # @Blog ：https://blog.csdn.net/Cyrus_May import numpy as np import randomnp.random.seed(22)class CyrusSOM(object):def __init__(self,net=[[1,1],[1,1]],epochs = 50,r_t = [None,None],eps=1e-6):""":param net: 竞争层的拓扑结构，支持一维及二维，1表示该输出节点存在，0表示不存在该输出节点:param epochs: 最大迭代次数:param r_t: [C,B] 领域半径参数，r = C*e**(-B*t/eoochs),其中t表示当前迭代次数:param eps: learning rate的阈值"""self.epochs = epochsself.C = r_t[0]self.B = r_t[1]self.eps = epsself.output_net = np.array(net)if len(self.output_net.shape) == 1:self.output_net = self.output_net.reshape([-1,1])self.coord = np.zeros([self.output_net.shape[0],self.output_net.shape[1],2])for i in range(self.output_net.shape[0]):for j in range(self.output_net.shape[1]):self.coord[i,j] = [i,j]print(self.coord)def __r_t(self,t):if not self.C:return 0.5else:return self.C*np.exp(-self.B*t/self.epochs)def __lr(self,t,distance):return (self.epochs-t)/self.epochs*np.exp(-distance)def standard_x(self,x):x = np.array(x)for i in range(x.shape[0]):x[i,:] = [value/(((x[i,:])**2).sum()**0.5) for value in x[i,:]]return xdef standard_w(self,w):for i in range(w.shape[0]):for j in range(w.shape[1]):w[i,j,:] = [value/(((w[i,j,:])**2).sum()**0.5) for value in w[i,j,:]]return wdef cal_similar(self,x,w):similar = (x*w).sum(axis=2)coord = np.where(similar==similar.max())return [coord[0][0],coord[1][0]]def update_w(self,center_coord,x,step):for i in range(self.coord.shape[0]):for j in range(self.coord.shape[1]):distance = (((center_coord-self.coord[i,j])**2).sum())**0.5if distance <= self.__r_t(step):self.W[i,j] = self.W[i,j] + self.__lr(step,distance)*(x-self.W[i,j])def transform_fit(self,x):self.train_x = self.standard_x(x)self.W = np.zeros([self.output_net.shape[0],self.output_net.shape[1],self.train_x.shape[1]])for i in range(self.W.shape[0]):for j in range(self.W.shape[1]):self.W[i,j,:] = self.train_x[random.choice(range(self.train_x.shape[0])),:]self.W = self.standard_w(self.W)for step in range(int(self.epochs)):j = 0if self.__lr(step,0) <= self.eps:breakfor index in range(self.train_x.shape[0]):print("*"*8,"({},{})/{} W:\n".format(step,j,self.epochs),self.W)center_coord = self.cal_similar(self.train_x[index,:],self.W)self.update_w(center_coord,self.train_x[index,:],step)self.W = self.standard_w(self.W)j += 1label = []for index in range(self.train_x.shape[0]):center_coord = self.cal_similar(self.train_x[index, :], self.W)label.append(center_coord[1]*self.coord.shape[1] + center_coord[0])class_dict = {}for index in range(self.train_x.shape[0]):if label[index] in class_dict.keys():class_dict[label[index]].append(index)else:class_dict[label[index]] = [index]cluster_center = {}for key,value in class_dict.items():cluster_center[key] = np.array([x[i, :] for i in value]).mean(axis=0)self.cluster_center = cluster_centerreturn labeldef fit(self,x):self.train_x = self.standard_x(x)self.W = np.random.rand(self.output_net.shape[0], self.output_net.shape[1], self.train_x.shape[1])self.W = self.standard_w(self.W)for step in range(int(self.epochs)):j = 0if self.__lr(step,0) <= self.eps:breakfor index in range(self.train_x.shape[0]):print("*"*8,"({},{})/{} W:\n".format(step, j, self.epochs), self.W)center_coord = self.cal_similar(self.train_x[index, :], self.W)self.update_w(center_coord, self.train_x[index, :], step)self.W = self.standard_w(self.W)j += 1label = []for index in range(self.train_x.shape[0]):center_coord = self.cal_similar(self.train_x[index, :], self.W)label.append(center_coord[1] * self.coord.shape[1] + center_coord[1])class_dict = {}for index in range(self.train_x.shape[0]):if label[index] in class_dict.keys():class_dict[label[index]].append(index)else:class_dict[label[index]] = [index]cluster_center = {}for key, value in class_dict.items():cluster_center[key] = np.array([x[i, :] for i in value]).mean(axis=0)self.cluster_center = cluster_centerdef predict(self,x):self.pre_x = self.standard_x(x)label = []for index in range(self.pre_x.shape[0]):center_coord = self.cal_similar(self.pre_x[index, :], self.W)label.append(center_coord[1] * self.coord.shape[1] + center_coord[1])return label

计算实例

对簇形状数据集进行聚类
仅需五步即可实现较好的聚类结果

from sklearn.datasets import load_iris,make_blobs import matplotlib.pyplot as plt from sklearn.metrics import classification_report if __name__ == '__main__':SOM = CyrusSOM(epochs=5)data = make_blobs(n_samples=1000,n_features=2,centers=4,cluster_std=0.3)x = data[0]y_pre = SOM.transform_fit(x)colors = "rgby"figure = plt.figure(figsize=[20,12])plt.scatter(x[:,0],x[:,1],c=[colors[i] for i in y_pre])plt.show() ******** (4,998)/5 W:[[[-0.90394221 -0.42765463][-0.99859415 -0.05300684]][[-0.77166042 0.63603475][-0.23064699 0.9730375 ]]] ******** (4,999)/5 W:[[[-0.89968359 -0.4365426 ][-0.99859415 -0.05300684]][[-0.77166042 0.63603475][-0.23064699 0.9730375 ]]]

by CyrusMay 2021 01 13

最深刻 的故事
最永恒 的传说
不过 是你 是我
能够 平凡生活
——————五月天（因为你 所以我）——————

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