基于感知器系数绘制分类决策边界线

Question

这实际上是this question 的重复。但是，我想问一个非常具体的问题，关于根据我通过基本的“手动”编码实验获得的感知器系数绘制决策边界线。如您所见，从逻辑回归中提取的系数会产生一条不错的决策边界线：

基于glm() 结果：

(Intercept)       test1       test2 
   1.718449    4.012903    3.743903 

感知器实验的系数完全不同：

     bias     test1     test2 
 9.131054 19.095881 20.736352 

为了方便回答，here is the data，这里是代码：

# DATA PRE-PROCESSING:
dat = read.csv("perceptron.txt", header=F)
dat[,1:2] = apply(dat[,1:2], MARGIN = 2, FUN = function(x) scale(x)) # scaling the data
data = data.frame(rep(1,nrow(dat)), dat) # introducing the "bias" column
colnames(data) = c("bias","test1","test2","y")
data$y[data$y==0] = -1 # Turning 0/1 dependent variable into -1/1.
data = as.matrix(data) # Turning data.frame into matrix to avoid mmult problems.

# PERCEPTRON:
set.seed(62416)
no.iter = 1000                           # Number of loops
theta = rnorm(ncol(data) - 1)            # Starting a random vector of coefficients.
theta = theta/sqrt(sum(theta^2))         # Normalizing the vector.
h = theta %*% t(data[,1:3])              # Performing the first f(theta^T X)

for (i in 1:no.iter){                    # We will recalculate 1,000 times
  for (j in 1:nrow(data)){               # Each time we go through each example.
      if(h[j] * data[j, 4] < 0){         # If the hypothesis disagrees with the sign of y,
      theta = theta + (sign(data[j,4]) * data[j, 1:3]) # We + or - the example from theta.
      }
      else
      theta = theta                      # Else we let it be.
  }
  h = theta %*% t(data[,1:3])            # Calculating h() after iteration.
}
theta                                    # Final coefficients
mean(sign(h) == data[,4])                # Accuracy

问题：如果我们只有感知器系数，如何绘制边界线（就像我上面使用逻辑回归系数所做的那样）？

Answer 1

嗯...事实证明它与case of logistic regression中的完全一样，尽管系数有很大不同：选择横坐标的最小值和最大值（测试1），添加一点边距，然后计算在决策边界（0 = theta_o + theta_1 test1 + theta_2 test2时）对应的测试2值，并在点之间画线：

palette(c("tan3","purple4"))
plot(test2 ~ test1, col = as.factor(y), pch = 20, data=data,
     main="College admissions")
(x = c(min(data[,2])-.2,  max(data[,2])+ .2))
(y = c((-1/theta[3]) * (theta[2] * x + theta[1])))
lines(x, y, lwd=3, col=rgb(.7,0,.2,.5))

Answer 2

计算感知器权重，以便当 theta^T X > 0 时将其分类为正，当 theta^T X

除了现在的 sigmoid(theta^T X) > 0.5 之外，逻辑回归也适用相同的逻辑。