r - 为什么神经网络在一个简单的分类案例中失败

Question

我有下面的代码，其中形成了一个简单的基于规则的分类数据集:

# # Data preparation
data = data.frame(A = round(runif(100)), B = round(runif(100)), C = round(runif(100)))
# Y - is the classification output column
data$Y = ifelse((data$A == 1 & data$B == 1 & data$C == 0), 1, ifelse((data$A == 0 & data$B == 1 & data$C == 1), 1, ifelse((data$A == 0 & data$B ==0 & data$C == 0), 1, 0)))
# Shuffling the data set
data = data[sample(rownames(data)), ]

我将数据集划分为训练和测试，以便我可以在测试集上验证我的结果:

# # Divide into train and test
library(caret)
trainIndex = createDataPartition(data[, "Y"], p = .7, list = FALSE, times = 1) # for balanced sampling
train = data[trainIndex, ]
test = data[-trainIndex, ]

我尝试构建一个简单的神经网络，其中隐藏层中的神经元数量是通过循环选择的(如前所述 here)

# # Build a neural net
library(neuralnet)
for(alpha in 2:10)
{
    nHidden = round(nrow(train)/(alpha*(3+1)))
    nn = neuralnet(Y ~ A + B + C, train, linear.output = F, likelihood = T, err.fct = "ce", hidden = nHidden)

    # Calculate Mean Squared Error for Train and Test
    trainMSE = mean((round(nn$net.result[[1]]) - train$Y)^2)
    testPred = round(compute(nn,test[-length(ncol(test))])$net.result)
    testMSE = mean((testPred - test$Y)^2)

    print(paste("Train Error: " , round(trainMSE, 4), ", Test Error: ", round(testMSE, 4), ", #. Hidden = ", nHidden, sep = ""))
}

[1] "Train Error: 0, Test Error: 0.6, #. Hidden = 9"

[1] "Train Error: 0, Test Error: 0.6, #. Hidden = 6"

[1] "Train Error: 0, Test Error: 0.6, #. Hidden = 4"

[1] "Train Error: 0, Test Error: 0.6, #. Hidden = 4"

[1] "Train Error: 0.1429, Test Error: 0.8333, #. Hidden = 3"

[1] "Train Error: 0.1429, Test Error: 0.8333, #. Hidden = 2"

[1] "Train Error: 0.0857, Test Error: 0.6, #. Hidden = 2"

[1] "Train Error: 0.1429, Test Error: 0.8333, #. Hidden = 2"

[1] "Train Error: 0.0857, Test Error: 0.6, #. Hidden = 2"

它给出的过拟合结果很差。但是，当我在同一个数据集上构建了一个简单的随机森林时。我得到的火车和测试错误为 - 0

# # Build a Random Forest
trainRF = train
trainRF$Y = as.factor(trainRF$Y)
testRF = test

library(randomForest)
rf = randomForest(Y ~ ., data = trainRF, mtry = 2)

# Calculate Mean Squared Error for Train and Test
trainMSE = mean((round(rf$votes[,2]) - as.numeric(as.character(trainRF$Y)))^2)
testMSE = mean((round(predict(rf, testRF, type = "prob")[,2]) - as.numeric(as.character(testRF$Y)))^2)

print(paste("Train Error: " , round(trainMSE, 4), ", Test Error: ", round(testMSE, 4), sep = ""))

[1] "Train Error: 0, Test Error: 0"

请帮助我理解为什么神经网络在随机森林以 100% 准确率工作的简单情况下失败。

注:我只使用了一个隐藏层(假设一个隐藏层足以进行这种简单的分类)并迭代隐藏层中的神经元数量。

另外，如果我对神经网络参数的理解有误，请帮助我。

完整代码可见 here

Answer 1

一个类似的问题一直在追捕我一段时间，所以我尝试了解您的数据和问题并将它们与我的进行比较。不过，最后，这只是这一行中的一个小错误:

testPred = round(compute(nn,test[-length(ncol(test))])$net.result)

您选择 B , C和 Y用于预测，而不是 A , B和 C , 因为 length(ncol(something))将始终返回 1。您只需要 test[-ncol(test)] .

> summary(test[-length(ncol(test))])

          B              C             Y            
 Min.   :0.00   Min.   :0.0   Min.   :0.0000000  
 1st Qu.:0.00   1st Qu.:0.0   1st Qu.:0.0000000  
 Median :0.00   Median :0.5   Median :0.0000000  
 Mean   :0.48   Mean   :0.5   Mean   :0.3766667  
 3rd Qu.:1.00   3rd Qu.:1.0   3rd Qu.:1.0000000  
 Max.   :1.00   Max.   :1.0   Max.   :1.0000000