chapter5 自编码的秘密

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#神经网络

本文介绍了自编码器的原理及其实现过程，并通过两个案例详细展示了如何使用自编码器进行特征提取与数据重构。

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自编码使得训练出的y直接对着自己的输入层x

自编码是由编码器和解码器组成的，编码器是输入层映射到隐藏层，解码器是隐藏层映射到输出层。编码器将输入层向量通过。。函数转移至隐藏层转换成新功能。解码器转移这些功能回到原始的输入层。

require(autoencoder)
require(ripa)
data(logo)
image(logo)

> logo
size:  77 x 101 
type:  grey

> x_train<-t(logo)
> x_train
size:  101 x 77 
type:  grey

set.seed(2016)
fit<-autoencode(X.train=x_train,X.test = NULL,nl=3,N.hidden = 60,
                unit.type = "logistic",lambda = 1e-5,beta=1e-5,rho=0.3,
                epsilon = 0.1,max.iterations = 100,optim.method = c("BFGS"),
                rel.tol = 0.01,rescale.flag = TRUE,rescaling.offset = 0.001)

#将x_train图像转化为函数，nl=3设置神经网络分为3层，logistic函数的隐藏节点数为60
#lambda是衰减参数，这是数值比较小
#beta是稀疏惩罚的权重，同样比较小
#稀疏度rho设置为0.3，服从正态分布
#最大步长为100
#rescale.flag表示x_train矩阵的缩放范围允许在0-1之间

autoencoding...
Optimizer counts:
function gradient 
      88       86 
Optimizer: successful convergence.
Optimizer: convergence = 0, message = 
J.init = 5.513073, J.final = 0.1928874, mean(rho.hat.final) = 0.627708

> attributes(fit)
$names
 [1] "W"                       "b"                       "unit.type"              
 [4] "rescaling"               "nl"                      "sl"                     
 [7] "N.input"                 "N.hidden"                "mean.error.training.set"
[10] "mean.error.test.set"    

$class
[1] "autoencoder"

> fit$mean.error.training.set
[1] 0.3489713

我们已经看出，在隐藏层抽取特征非常有用，简单的获取方式是使用predict函数：hidden.output=TRUE

features<-predict(fit,X.input = x_train,hidden.output = TRUE)
image(t(features$X.output))

> pred<-predict(fit,X.input = x_train,hidden.output = FALSE)
> pred$mean.error
[1] 0.3503714

aburl='http://archive.ics.uci.edu/ml/machine-learning-databases/abalone/abalone.data'
names=c('sex','length','diameter','height','whole.weight','shucked.weight',
        'viscera.weight','shell.weight','rings')
data=read.table(aburl,header=F,sep=',',col.names = names)
summary(data)

 sex          length         diameter          height        whole.weight   
 F:1307   Min.   :0.075   Min.   :0.0550   Min.   :0.0000   Min.   :0.0020  
 I:1342   1st Qu.:0.450   1st Qu.:0.3500   1st Qu.:0.1150   1st Qu.:0.4415  
 M:1528   Median :0.545   Median :0.4250   Median :0.1400   Median :0.7995  
          Mean   :0.524   Mean   :0.4079   Mean   :0.1395   Mean   :0.8287  
          3rd Qu.:0.615   3rd Qu.:0.4800   3rd Qu.:0.1650   3rd Qu.:1.1530  
          Max.   :0.815   Max.   :0.6500   Max.   :1.1300   Max.   :2.8255  
 shucked.weight   viscera.weight    shell.weight        rings       
 Min.   :0.0010   Min.   :0.0005   Min.   :0.0015   Min.   : 1.000  
 1st Qu.:0.1860   1st Qu.:0.0935   1st Qu.:0.1300   1st Qu.: 8.000  
 Median :0.3360   Median :0.1710   Median :0.2340   Median : 9.000  
 Mean   :0.3594   Mean   :0.1806   Mean   :0.2388   Mean   : 9.934  
 3rd Qu.:0.5020   3rd Qu.:0.2530   3rd Qu.:0.3290   3rd Qu.:11.000  
 Max.   :1.4880   Max.   :0.7600   Max.   :1.0050   Max.   :29.000

> data[data$height==0,]
     sex length diameter height whole.weight shucked.weight viscera.weight
1258   I  0.430     0.34      0        0.428         0.2065         0.0860
3997   I  0.315     0.23      0        0.134         0.0575         0.0285
     shell.weight rings
1258       0.1150     8
3997       0.3505     6

#找缺失值
data[data$height==0,]
#删除缺失值
data$height[data$height==0]=NA
data<-na.omit(data)
data$sex<-NULL
summary(data)

     length          diameter          height        whole.weight    shucked.weight  
 Min.   :0.0750   Min.   :0.0550   Min.   :0.0100   Min.   :0.0020   Min.   :0.0010  
 1st Qu.:0.4500   1st Qu.:0.3500   1st Qu.:0.1150   1st Qu.:0.4422   1st Qu.:0.1862  
 Median :0.5450   Median :0.4250   Median :0.1400   Median :0.8000   Median :0.3360  
 Mean   :0.5241   Mean   :0.4079   Mean   :0.1396   Mean   :0.8290   Mean   :0.3595  
 3rd Qu.:0.6150   3rd Qu.:0.4800   3rd Qu.:0.1650   3rd Qu.:1.1535   3rd Qu.:0.5020  
 Max.   :0.8150   Max.   :0.6500   Max.   :1.1300   Max.   :2.8255   Max.   :1.4880  
 viscera.weight    shell.weight        rings       
 Min.   :0.0005   Min.   :0.0015   Min.   : 1.000  
 1st Qu.:0.0935   1st Qu.:0.1300   1st Qu.: 8.000  
 Median :0.1710   Median :0.2340   Median : 9.000  
 Mean   :0.1807   Mean   :0.2388   Mean   : 9.935  
 3rd Qu.:0.2530   3rd Qu.:0.3287   3rd Qu.:11.000  
 Max.   :0.7600   Max.   :1.0050   Max.   :29.000

data1<-t(data)
data1<-as.matrix(data1)
require(autoencoder)
set.seed(2016)
n=nrow(data)
train<-sample(1:n,10,FALSE)
fit<-autoencode(X.train = data1[,train],X.test = NULL,nl=3,N.hidden = 5,
                unit.type = "logistic",lambda = 1e-5,beta=1e-5,rho=0.07,
                epsilon = 0.1,max.iterations = 100,optim.method = c("BFGS"),
                rel.tol = 0.01,rescale.flag = TRUE,rescaling.offset = 0.001)

autoencoding...
Optimizer counts:
function gradient 
      34       32 
Optimizer: successful convergence.
Optimizer: convergence = 0, message = 
J.init = 1.038595, J.final = 0.01098651, mean(rho.hat.final) = 0.5697456

> fit$mean.error.training.set
[1] 0.01654644
> features<-predict(fit,X.input = data1[,train],hidden.output = TRUE)
> features$X.output
                       [,1]         [,2]         [,3]         [,4]         [,5]
length         6.572353e-01 7.459814e-01 4.025650e-01 5.306412e-01 6.325756e-01
diameter       7.149880e-01 7.907795e-01 4.670981e-01 5.899761e-01 6.929413e-01
height         8.119831e-01 8.628111e-01 5.986132e-01 7.009952e-01 7.956291e-01
whole.weight   4.901213e-01 6.072550e-01 2.545919e-01 3.770476e-01 4.642603e-01
shucked.weight 7.437931e-01 8.128396e-01 5.023596e-01 6.205615e-01 7.235000e-01
viscera.weight 7.893552e-01 8.464983e-01 5.645063e-01 6.734824e-01 7.718709e-01
shell.weight   7.721268e-01 8.337987e-01 5.403436e-01 6.532020e-01 7.534961e-01
rings          1.855435e-09 1.038285e-08 1.111354e-09 9.623515e-09 1.471309e-09

> pred<-predict(fit,X.input = data1[,train],hidden.output = FALSE)

> pred
$X.output
                     [,1]      [,2]      [,3]       [,4]        [,5]        [,6]
length          0.5843936 0.5338661 0.6988651  0.5914587 0.017422624  0.16787938
diameter        0.3886484 0.3786442 0.5063712  0.3952463 0.012960351  0.10031409
height          0.1891073 0.2051164 0.2854515  0.1935582 0.008717783  0.04205945
whole.weight    1.7357320 1.3348344 1.6519252  1.7294214 0.047866685  0.70391258
shucked.weight  0.3154349 0.3174224 0.4292071  0.3215069 0.011363892  0.07750871
viscera.weight  0.2245608 0.2376717 0.3275103  0.2295557 0.009443400  0.05144013
shell.weight    0.2556035 0.2654247 0.3631185  0.2610123 0.010089224  0.06003454
rings          12.1850860 9.4368786 9.9615860 12.0389287 1.413263792 12.10066454
                    [,7]       [,8]       [,9]     [,10]
length         0.4133904  0.7215291  0.4240386 0.3911886
diameter       0.2878643  0.5106162  0.2686229 0.2690845
height         0.1516875  0.2759206  0.1203867 0.1383446
whole.weight   1.0948191  1.8092411  1.4439660 1.0658803
shucked.weight 0.2392124  0.4275806  0.2128008 0.2221398
viscera.weight 0.1768079  0.3197935  0.1457233 0.1622826
shell.weight   0.1983995  0.3572845  0.1683064 0.1829217
rings          9.1683347 10.9723027 12.5646378 9.2603170

$hidden.output
[1] FALSE

$mean.error
[1] 3.727675

下一步绘制雷达图

#第一步，设置各个变量的取值范围（即最小值和最大值）
maxmin<-data.frame(length=c(1,0),diameter=c(1,0),height=c(1,0),whole.weight=c(5,0),
                   shucked.weight=c(1,0),viscera.weight=c(1,0),shell.weight=c(1,0),rings=c(20,0))
#第二步，设置准备绘图的指标类型的数据，如x1的8种observed和reconstructed的贡献率
dat.A<-data.frame(length=c(0.455,0.584),diameter=c(0.365,0.389),height=c(0.095,0.189),whole.weight=c(0.514,1.736),
                  shucked.weight=c(0.2245,0.315),viscera.weight=c(0.101,0.225),shell.weight=c(0.15,0.257),rings=c(15,12.19))
#第三步，把数据集合并到一起
dat.B<-rbind(maxmin,dat.A)
#第四步，绘图，安装fmsb包
#install.packages("fmsb")
library(fmsb)
radarchart(dat.B,axistype = 0,seg = 8,centerzero = T)