【原】KMeans与深度学习自编码AutoEncoder结合提高聚类效果
这几天在做用户画像，特征是用户的消费商品的消费金额，原始数据（部分）是这样的：
1 id goods_name goods_amount 2 1 男士手袋 1882.0 3 2 淑女装 2491.0 4 2 女士手袋 345.0 5 4 基础内衣 328.0 6 5 商务正装 4985.0 7 5 时尚 969.0 8 5 女饰品 86.0 9 6 专业运动 399.0 10 6 童装（中大童) 2033.0 11 6 男士配件 38.0
我们看到同一个id下面有不同的消费记录，这个数据不能直接拿来用，写了python程序来进行处理：test.py
1 #!/usr/bin/python 2 #coding:utf-8 3 #Author：Charlotte 4 import pandas as pd 5 import numpy as np 6 import time 7 8 #加载数据文件(你可以加载自己的文件，文件格式如上所示) 9 x=pd.read_table('test.txt',sep = " ") 10 11 #去除NULL值 12 x.dropna() 13 14 a1=list(x.iloc[:,0]) 15 a2=list(x.iloc[:,1]) 16 a3=list(x.iloc[:,2]) 17 18 #A是商品类别 19 dicta=dict(zip(a2,zip(a1,a3))) 20 A=list(dicta.keys()) 21 #B是用户id 22 B=list(set(a1)) 23 24 # data_class = pd.DataFrame(A,lista) 25 26 #创建商品类别字典 27 a = np.arange(len(A)) 28 lista = list(a) 29 dict_class = dict(zip(A,lista)) 30 print dict_class 31 32 f=open('class.txt','w') 33 for k ,v in dict_class.items(): 34 f.write(str(k)+'\t'+str(v)+'\n') 35 f.close() 36 37 #计算运行时间 38 start=time.clock() 39 40 #创建大字典存储数据 41 dictall = {} 42 for i in xrange(len(a1)): 43 if a1[i] in dictall.keys(): 44 value = dictall[a1[i]] 45 j = dict_class[a2[i]] 46 value[j] = a3[i] 47 dictall[a1[i]]=value 48 else: 49 value = list(np.zeros(len(A))) 50 j = dict_class[a2[i]] 51 value[j] = a3[i] 52 dictall[a1[i]]=value 53 54 #将字典转化为dataframe 55 dictall1 = pd.DataFrame(dictall) 56 dictall_matrix = dictall1.T 57 print dictall_matrix 58 59 end = time.clock() 60 print "赋值过程运行时间是:%f s"%(end-start)
输出结果：
{'\xe4\xb8\x93\xe4\xb8\x9a\xe8\xbf\x90\xe5\x8a\xa8': 4, '\xe7\x94\xb7\xe5\xa3\xab\xe6\x89\x8b\xe8\xa2\x8b': 1, '\xe5\xa5\xb3\xe5\xa3\xab\xe6\x89\x8b\xe8\xa2\x8b': 2, '\xe7\xab\xa5\xe8\xa3\x85\xef\xbc\x88\xe4\xb8\xad\xe5\xa4\xa7\xe7\xab\xa5)': 3, '\xe7\x94\xb7\xe5\xa3\xab\xe9\x85\x8d\xe4\xbb\xb6': 9, '\xe5\x9f\xba\xe7\xa1\x80\xe5\x86\x85\xe8\xa1\xa3': 8, '\xe6\x97\xb6\xe5\xb0\x9a': 6, '\xe6\xb7\x91\xe5\xa5\xb3\xe8\xa3\x85': 7, '\xe5\x95\x86\xe5\x8a\xa1\xe6\xad\xa3\xe8\xa3\x85': 5, '\xe5\xa5\xb3\xe9\xa5\xb0\xe5\x93\x81': 0}
0 1 2 3 4 5 6 7 8 9
1 0 1882 0 0 0 0 0 0 0 0
2 0 0 345 0 0 0 0 2491 0 0
4 0 0 0 0 0 0 0 0 328 0
5 86 0 0 0 0 4985 969 0 0 0
6 0 0 0 2033 399 0 0 0 0 38
赋值过程运行时间是:0.004497 s
linux环境下字符编码不同，class.txt:
专业运动 4
男士手袋 1
女士手袋 2
童装（中大童) 3
男士配件 9
基础内衣 8
时尚 6
淑女装 7
商务正装 5
女饰品 0
得到的dicta_matrix 就是我们拿来跑数据的格式，每一列是商品名称，每一行是用户id
现在我们来跑AE模型（Auto-encoder），简单说说AE模型，主要步骤很简单，有三层，输入-隐含-输出，把数据input进去，encode然后再decode，cost_function就是output与input之间的“差值”（有公式），差值越小，目标函数值越优。简单地说，就是你输入n维的数据，输出的还是n维的数据，有人可能会问，这有什么用呢，其实也没什么用，主要是能够把数据缩放，如果你输入的维数比较大，譬如实际的特征是几千维的，全部拿到算法里跑，效果不见得好，因为并不是所有特征都是有用的，用AE模型后，你可以压缩成m维（就是隐含层的节点数），如果输出的数据和原始数据的大小变换比例差不多，就证明这个隐含层的数据是可用的。这样看来好像和降维的思想类似，当然AE模型的用法远不止于此，具体贴一篇梁博的博文
不过梁博的博文是用c++写的，这里使用python写的代码（开源代码，有少量改动）：
1 #/usr/bin/python 2 #coding:utf-8 3 4 import pandas as pd 5 import numpy as np 6 import matplotlib.pyplot as plt 7 from sklearn import preprocessing 8 9 class AutoEncoder(): 10 """ Auto Encoder 11 layer 1 2 ... ... L-1 L 12 W 0 1 ... ... L-2 13 B 0 1 ... ... L-2 14 Z 0 1 ... L-3 L-2 15 A 0 1 ... L-3 L-2 16 """ 17 18 def __init__(self, X, Y, nNodes): 19 # training samples 20 self.X = X 21 self.Y = Y 22 # number of samples 23 self.M = len(self.X) 24 # layers of networks 25 self.nLayers = len(nNodes) 26 # nodes at layers 27 self.nNodes = nNodes 28 # parameters of networks 29 self.W = list() 30 self.B = list() 31 self.dW = list() 32 self.dB = list() 33 self.A = list() 34 self.Z = list() 35 self.delta = list() 36 for iLayer in range(self.nLayers - 1): 37 self.W.append( np.random.rand(nNodes[iLayer]*nNodes[iLayer+1]).reshape(nNodes[iLayer],nNodes[iLayer+1]) ) 38 self.B.append( np.random.rand(nNodes[iLayer+1]) ) 39 self.dW.append( np.zeros([nNodes[iLayer], nNodes[iLayer+1]]) ) 40 self.dB.append( np.zeros(nNodes[iLayer+1]) ) 41 self.A.append( np.zeros(nNodes[iLayer+1]) ) 42 self.Z.append( np.zeros(nNodes[iLayer+1]) ) 43 self.delta.append( np.zeros(nNodes[iLayer+1]) ) 44 45 # value of cost function 46 self.Jw = 0.0 47 # active function (logistic function) 48 self.sigmod = lambda z: 1.0 / (1.0 + np.exp(-z)) 49 # learning rate 1.2 50 self.alpha = 2.5 51 # steps of iteration 30000 52 self.steps = 10000 53 54 def BackPropAlgorithm(self): 55 # clear values 56 self.Jw -= self.Jw 57 for iLayer in range(self.nLayers-1): 58 self.dW[iLayer] -= self.dW[iLayer] 59 self.dB[iLayer] -= self.dB[iLayer] 60 # propagation (iteration over M samples) 61 for i in range(self.M): 62 # Forward propagation 63 for iLayer in range(self.nLayers - 1): 64 if iLayer==0: # first layer 65 self.Z[iLayer] = np.dot(self.X[i], self.W[iLayer]) 66 else: 67 self.Z[iLayer] = np.dot(self.A[iLayer-1], self.W[iLayer]) 68 self.A[iLayer] = self.sigmod(self.Z[iLayer] + self.B[iLayer]) 69 # Back propagation 70 for iLayer in range(self.nLayers - 1)[::-1]: # reserve 71 if iLayer==self.nLayers-2:# last layer 72 self.delta[iLayer] = -(self.X[i] - self.A[iLayer]) * (self.A[iLayer]*(1-self.A[iLayer])) 73 self.Jw += np.dot(self.Y[i] - self.A[iLayer], self.Y[i] - self.A[iLayer])/self.M 74 else: 75 self.delta[iLayer] = np.dot(self.W[iLayer].T, self.delta[iLayer+1]) * (self.A[iLayer]*(1-self.A[iLayer])) 76 # calculate dW and dB 77 if iLayer==0: 78 self.dW[iLayer] += self.X[i][:, np.newaxis] * self.delta[iLayer][:, np.newaxis].T 79 else: 80 self.dW[iLayer] += self.A[iLayer-1][:, np.newaxis] * self.delta[iLayer][:, np.newaxis].T 81 self.dB[iLayer] += self.delta[iLayer] 82 # update 83 for iLayer in range(self.nLayers-1): 84 self.W[iLayer] -= (self.alpha/self.M)*self.dW[iLayer] 85 self.B[iLayer] -= (self.alpha/self.M)*self.dB[iLayer] 86 87 def PlainAutoEncoder(self): 88 for i in range(self.steps): 89 self.BackPropAlgorithm() 90 print "step:%d" % i, "Jw=%f" % self.Jw 91 92 def ValidateAutoEncoder(self): 93 for i in range(self.M): 94 print self.X[i] 95 for iLayer in range(self.nLayers - 1): 96 if iLayer==0: # input layer 97 self.Z[iLayer] = np.dot(self.X[i], self.W[iLayer]) 98 else: 99 self.Z[iLayer] = np.dot(self.A[iLayer-1], self.W[iLayer]) 100 self.A[iLayer] = self.sigmod(self.Z[iLayer] + self.B[iLayer]) 101 print "\t layer=%d" % iLayer, self.A[iLayer] 102 103 data=[] 104 index=[] 105 f=open('./data_matrix.txt','r') 106 for line in f.readlines(): 107 ss=line.replace('\n','').split('\t') 108 index.append(ss[0]) 109 ss1=ss[1].split(' ') 110 tmp=[] 111 for i in xrange(len(ss1)): 112 tmp.append(float(ss1[i])) 113 data.append(tmp) 114 f.close() 115 116 x = np.array(data) 117 #归一化处理 118 xx = preprocessing.scale(x) 119 nNodes = np.array([ 10, 5, 10]) 120 ae3 = AutoEncoder(xx,xx,nNodes) 121 ae3.PlainAutoEncoder() 122 ae3.ValidateAutoEncoder() 123 124 #这是个例子，输出的结果也是这个 125 # xx = np.array([[0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0], [0,0,0,0,0,1,0,0], [0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0], [0,0,1,0,0,0,0,0]]) 126 # nNodes = np.array([ 8, 3, 8 ]) 127 # ae2 = AutoEncoder(xx,xx,nNodes) 128 # ae2.PlainAutoEncoder() 129 # ae2.ValidateAutoEncoder()
这里我拿的例子做的结果，真实数据在服务器上跑，大家看看这道啥意思就行了
[0 0 0 0 0 0 0 1] layer=0 [ 0.76654705 0.04221051 0.01185895] layer=1 [ 4.67403977e-03 5.18624788e-03 2.03185410e-02 1.24383559e-02 1.54423619e-02 1.69197292e-03 2.34471751e-05 9.72956513e-01] [0 0 0 0 0 0 1 0] layer=0 [ 0.08178768 0.96348458 0.98583155] layer=1 [ 8.18926274e-04 7.30041977e-04 1.06452565e-02 9.94423121e-03 3.47329848e-03 1.32582980e-02 9.80648863e-01 8.42319408e-08] [0 0 0 0 0 1 0 0] layer=0 [ 0.04752084 0.01144966 0.67313608] layer=1 [ 4.38577163e-03 4.12704649e-03 1.83408905e-02 1.59209302e-05 2.32400619e-02 9.71429772e-01 1.78538577e-02 2.20897151e-03] [0 0 0 0 1 0 0 0] layer=0 [ 0.00819346 0.37410028 0.0207633 ] layer=1 [ 8.17965283e-03 7.94760145e-03 4.59916741e-05 2.03558668e-02 9.68811657e-01 2.09241369e-02 6.19909778e-03 1.51964053e-02] [0 0 0 1 0 0 0 0] layer=0 [ 0.88632868 0.9892662 0.07575306] layer=1 [ 1.15787916e-03 1.25924912e-03 3.72748604e-03 9.79510789e-01 1.09439392e-02 7.81892291e-08 1.06705286e-02 1.77993321e-02] [0 0 1 0 0 0 0 0] layer=0 [ 0.9862938 0.2677048 0.97331042] layer=1 [ 6.03115828e-04 6.37411444e-04 9.75530999e-01 4.06825647e-04 2.66386294e-07 1.27802666e-02 8.66599313e-03 1.06025228e-02]
可以很明显看layer1和原始数据是对应的，所以我们可以把layer0作为降维后的新数据。
最后在进行聚类，这个就比较简单了，用sklearn的包，就几行代码：
1 # !/usr/bin/python 2 # coding:utf-8 3 # Author :Charlotte 4 5 from matplotlib import pyplot 6 import scipy as sp 7 import numpy as np 8 import matplotlib.pyplot as plt 9 from sklearn.cluster import KMeans 10 from scipy import sparse 11 import pandas as pd 12 import Pycluster as pc 13 from sklearn import preprocessing 14 from sklearn.preprocessing import StandardScaler 15 from sklearn import metrics 16 import pickle 17 from sklearn.externals import joblib 18 19 20 #加载数据 21 data = pd.read_table('data_new.txt',header = None,sep = " ") 22 x = data.ix[:,1:141] 23 card = data.ix[:,0] 24 x1 = np.array(x) 25 xx = preprocessing.scale(x1) 26 num_clusters = 5 27 28 clf = KMeans(n_clusters=num_clusters, n_init=1, n_jobs = -1,verbose=1) 29 clf.fit(xx) 30 print(clf.labels_) 31 labels = clf.labels_ 32 #score是轮廓系数 33 score = metrics.silhouette_score(xx, labels) 34 # clf.inertia_用来评估簇的个数是否合适，距离越小说明簇分的越好 35 print clf.inertia_ 36 print score
这个数据是拿来做例子的，维度少，效果不明显，真实环境下的数据是30W*142维的，写的mapreduce程序进行数据处理，然后通过AE模型降到50维后，两者的clf.inertia_和silhouette(轮廓系数)有显著差异:
|
clf.inertia_ |
silhouette |
|
| base版本 |
252666.064229 |
0.676239435 |
| AE模型跑后的版本 |
662.704257502 |
0.962147623 |
所以可以看到没有用AE模型直接聚类的模型跑完后的clf.inertia_比用了AE模型之后跑完的clf.inertia_大了几个数量级，AE的效果还是很显著的。
以上是随手整理的，如有错误，欢迎指正：）
