submit hw7

hw7/hw7-wenqi.Rmd

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+---
+title: "hw7-wenqi"
+output: html_document
+---
+
+```{r setup, include=FALSE}
+knitr::opts_chunk$set(echo = TRUE)
+```
+
+
+```{r}
+library(keras)
+library('rgl')
+library('ElemStatLearn')
+library('nnet')
+library('dplyr')
+
+## load binary classification example data
+data("mixture.example")
+dat <- mixture.example
+
+```
+
+```{r}
+img_dat <- matrix(nrow=200,ncol=2)
+img_dat[,1]<- dat$x[,1]
+img_dat[,2]<- dat$x[,2]
+```
+
+
+```{r}
+model <- keras_model_sequential()
+
+model <- model %>%
+  layer_flatten(input_shape = c(2, 200)) %>%
+  layer_dense(units = 128, activation = 'relu') %>%
+  layer_dense(units = 10, activation = 'softmax')
+
+model <- model %>% compile(
+  optimizer = 'adam', 
+  loss = 'sparse_categorical_crossentropy',
+  metrics = c('accuracy')
+)
+
+```
+
+
+
+
+
+```{r}
+
+## create 3D plot of mixture data
+plot_mixture_data <- function(dat=mixture.example, showtruth=FALSE) {
+  ## create 3D graphic, rotate to view 2D x1/x2 projection
+  par3d(FOV=1,userMatrix=diag(4))
+  plot3d(dat$xnew[,1], dat$xnew[,2], dat$prob, type="n",
+         xlab="x1", ylab="x2", zlab="",
+         axes=FALSE, box=TRUE, aspect=1)
+  ## plot points and bounding box
+  x1r <- range(dat$px1)
+  x2r <- range(dat$px2)
+  pts <- plot3d(dat$x[,1], dat$x[,2], 1,
+                type="p", radius=0.5, add=TRUE,
+                col=ifelse(dat$y, "orange", "blue"))
+  lns <- lines3d(x1r[c(1,2,2,1,1)], x2r[c(1,1,2,2,1)], 1)
+  
+  if(showtruth) {
+    ## draw Bayes (True) classification boundary
+    probm <- matrix(dat$prob, length(dat$px1), length(dat$px2))
+    cls <- contourLines(dat$px1, dat$px2, probm, levels=0.5)
+    pls <- lapply(cls, function(p) 
+      lines3d(p$x, p$y, z=1, col='purple', lwd=3))
+    ## plot marginal probability surface and decision plane
+    sfc <- surface3d(dat$px1, dat$px2, dat$prob, alpha=1.0,
+      color="gray", specular="gray")
+    qds <- quads3d(x1r[c(1,2,2,1)], x2r[c(1,1,2,2)], 0.5, alpha=0.4,
+      color="gray", lit=FALSE)
+  }
+}
+
+## compute and plot predictions
+plot_nnet_predictions <- function(fit, dat=mixture.example) {
+  
+  ## create figure
+  plot_mixture_data()
+
+  ## compute predictions from nnet
+  preds <- predict(fit, dat$xnew, type="class")
+  probs <- predict(fit, dat$xnew, type="raw")[,1]
+  probm <- matrix(probs, length(dat$px1), length(dat$px2))
+  cls <- contourLines(dat$px1, dat$px2, probm, levels=0.5)
+
+  ## plot classification boundary
+  pls <- lapply(cls, function(p) 
+    lines3d(p$x, p$y, z=1, col='purple', lwd=2))
+  
+  ## plot probability surface and decision plane
+  sfc <- surface3d(dat$px1, dat$px2, probs, alpha=1.0,
+                   color="gray", specular="gray")
+  qds <- quads3d(x1r[c(1,2,2,1)], x2r[c(1,1,2,2)], 0.5, alpha=0.4,
+                 color="gray", lit=FALSE)
+}
+
+## plot data and 'true' probability surface
+plot_mixture_data(showtruth=TRUE)
+
+## fit single hidden layer, fully connected NN 
+## 10 hidden nodes
+fit <- nnet(x=dat$x, y=dat$y, size=10, entropy=TRUE, decay=0) 
+```
+