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Random generation of plots and data, but we only create data sets with 3 points of data. You will notice the linear classifier (logistic regression, which has a linear combination of coefficients), perfectly shatters the data in all cases, as number of points of data is within d+1 (the dimensionality of the data is 2, n = 3). Regarding the possi…
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| # author: matthew skiffington | |
| # purpose: plain viz of vc3 for linear classifiers to go in dissertation - 16 plots | |
| # randomly generates 3 points and fits a glm + plots decision boundary | |
| # original source: glm code adapted from: | |
| # glm code adapted from : https://stats.stackexchange.com/questions/6206/how-to-plot-decision-boundary-in-r-for-logistic-regression-model/6207 | |
| # plot code apated from: https://www.r-bloggers.com/beyond-basic-r-plotting-with-ggplot2-and-multiple-plots-in-one-figure/ | |
| library(ggplot2) # viz | |
| library(cowplot) # multi-viz | |
| # randomised plot generator | |
| vc_3.func <- function(x) { | |
| rand_points.vec <- runif(n = 6,min = 0,max = 6) | |
| class_labels.vec <- c( | |
| "Class 1", | |
| "Class 1", | |
| "Class 2" | |
| ) | |
| vc_ex.df <- data.frame( | |
| x = rand_points.vec[1:3], | |
| y = rand_points.vec[4:6], | |
| Class = class_labels.vec | |
| ) | |
| model <- glm(Class ~.,family=binomial(link='logit'),data = vc_ex.df) | |
| slope.num <- coef(model)[2]/(-coef(model)[3]) | |
| intercept.num <- coef(model)[1]/(-coef(model)[3]) | |
| g <- ggplot(data = vc_ex.df) + | |
| geom_point(mapping = aes(x = x,y = y,fill = Class),colour = 'black',size = 2,shape=21 ,stroke = 0.5,) + | |
| geom_abline(intercept = intercept.num, slope = slope.num, linetype, colour='black', size = 1) + | |
| #labs(title = "Illustration of the VC Dimension of a Linear Classifier",subtitle = "Points randomly generated; GLM logistic decision boundary") + | |
| #scale_fill_manual(values = c("black","white"), | |
| # labels = c("Class 1","Class 2")) + | |
| ylim(0,6) + | |
| xlim(0,6) + | |
| theme_light() + | |
| theme(axis.title=element_blank(), | |
| axis.text=element_blank()) + | |
| theme(legend.position = 'none') + | |
| theme(axis.ticks = element_blank()) | |
| return(g) | |
| } | |
| vc_3_plots.ls <- suppressWarnings(lapply(FUN = vc_3.func,1:16)) # create plot list | |
| title <- ggdraw() + | |
| draw_label("Vapnik Chervonenkis Dimension \n of a Linear Classifier", | |
| fontface='bold', | |
| size = 10) | |
| sub <- ggdraw() + | |
| draw_label("Binary data randomly generated. Logistic regression classifier \n fitted with decision boundary plotted in black.", | |
| size = 8) | |
| plots.grid <- plot_grid(plotlist = vc_3_plots.ls,nrow = 4,ncol = 4) # create plot grid | |
| plot_grid(title,plots.grid,sub,ncol = 1, rel_heights = c(0.1,0.9,0.1)) |
Author
MattSkiff
commented
Mar 11, 2020
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