构造感知机模型

动手实现感知机模型

1 PLA

library(tidyverse)
theme_set(theme_minimal())
knitr::opts_chunk$set(
  out.width = "80%",
  fig.align = "center",
  dev = "ragg_png"
)

生成线性可分的数据

set.seed(123)
n = 2000
df <- tibble(
  id = 1:n,
  x1 = rnorm(n),
  x2 = rnorm(n),
  y = if_else(2*x1 + 3*x2 >= 0, "A", "B")
) %>% 
  arrange(id)
df

# A tibble: 2,000 × 4
      id      x1     x2 y    
   <int>   <dbl>  <dbl> <chr>
 1     1 -0.560  -0.512 B    
 2     2 -0.230   0.237 A    
 3     3  1.56   -0.542 A    
 4     4  0.0705  1.22  A    
 5     5  0.129   0.174 A    
 6     6  1.72   -0.615 A    
 7     7  0.461  -1.81  B    
 8     8 -1.27   -0.644 B    
 9     9 -0.687   2.05  A    
10    10 -0.446  -0.561 B    
# ℹ 1,990 more rows

df %>% 
  ggplot(aes(x1, x2, color = as_factor(y))) +
  geom_point(alpha = 0.5) +
  labs(
    x = latex2exp::TeX("$x_1$"),
    y = latex2exp::TeX("$x_2$"),
    color = "y"
  ) +
  scale_color_brewer(palette = "Set2")

ml_pla <- function(data, formula, max_time, W = 1) {
  time <- 0 # 记录运行了几次
  model_frame <- model.frame(formula, data)

  # 查看Y的分类
  Y_class <- model.response(model_frame) %>%
    unique()
  Y_class_to_number <- c(1, -1)
  names(Y_class_to_number) <- Y_class


  X_matrix <- model.matrix(formula, model_frame)
  X_ncol <- ncol(X_matrix)
  W <- rep(W, X_ncol)

  n_errors <- 11111 # 设置一个初始的错误数量，触发下面的条件
  log_errors <- c() # 记录错误数量



  while (n_errors > 0 && time < max_time) {
    # 生成Y的预测值
    Y_pred <- if_else(sign(X_matrix %*% W) == 1,
      Y_class[[1]],
      Y_class[[2]]
    )
    
    # 筛选出分类不正确的数据
    errors_dt <- model_frame[Y_pred != model_frame[, 1], ]
    n_errors <- nrow(errors_dt)
    log_errors <- c(log_errors, n_errors) # 记录错误的数据有多少
    time <- time + 1

    # 有错误就更新W
    if (n_errors > 0) {
      # 随机选出一个错误的点
      errors_sample_id <- rownames(errors_dt) %>%
        sample(size = 1)
      x <- X_matrix[errors_sample_id, ]
      y <- model_frame[errors_sample_id, 1] %>%
        as.character() %>%
        Y_class_to_number[.]
      
      # 更新W
      W <- W + y * x
    } 
  }

  return(list(
    pred = Y_pred,
    "W" = W,
    time = time,
    log_errors = log_errors
  ))
}

看一下效果

pla <- ml_pla(df, y ~ x1 + x2, max_time = 10000)
str(pla)

List of 4
 $ pred      : chr [1:2000] "B" "A" "A" "A" ...
 $ W         : Named num [1:3] 0 -26.1 -39.2
  ..- attr(*, "names")= chr [1:3] "(Intercept)" "x1" "x2"
 $ time      : num 1736
 $ log_errors: int [1:1736] 1442 1428 1199 364 449 98 429 368 482 243 ...

df %>% 
  bind_cols(pred = pla$pred) %>% 
  filter(y != pred)

# A tibble: 0 × 5
# ℹ 5 variables: id <int>, x1 <dbl>, x2 <dbl>, y <chr>, pred <chr>