Deep Learning Excursion 2: ISLR’s CNN for classifying geometric shapes

Vincent J. Carey, stvjc at channing.harvard.edu

July 05, 2023

Introduction

In this vignette we consider how to classify images representing geometric shapes. The idea is that we can produce very large training sets from specified classes and explore relationships between complexity of comparison tasks, training set size, and accuracy.

We’ll work with the image-classifying CNN from ISLR.

Building collections of randomly generated shapes

We have code that situates pixels derived from randomly constructed and positioned circles, triangles, and quadrilaterals in a 32 x 32 plane. We form ImageArray instances for each geometric type.

library(littleDeep)
library(abind)
set.seed(1234)

NIMAGES=2500

build_array = function( shapefun = rancirc, nimages=NIMAGES, sidelength=64, depth=3, npts=90, ... ) {
 tmp = array(1, dim=c(nimages,sidelength,sidelength,depth)) # store images with 0 for dark
 for (i in seq_len(nimages)) {
    z = shapefun(npts=npts, ...)
    p = load_jpeg(z$x, z$y, siz=sidelength, dim=c(sidelength,sidelength,3))
    tmp[i,,,] = p
    }
  tmp
}
 

# training data

circarr = build_array( rancirc, sidelength=32, side_plane=32, npts=120 )
triarr = build_array( rantri, sidelength=32, side_plane=32, npts=40 )
quadarr = build_array( ranbox, sidelength=32, side_plane=32, npts=30 )

allsh = abind(circarr, triarr, along=1)
allsh = abind(allsh, quadarr, along=1)

shapes = ImageArray(allsh, types=rep(c("circle", "triangle", "quad"), each=NIMAGES))

# test data

test_circarr = build_array( rancirc, sidelength=32, side_plane=32, npts=120 )
test_triarr = build_array( rantri, sidelength=32, side_plane=32, npts=40 )
test_quadarr = build_array( ranbox, sidelength=32, side_plane=32, npts=30 )

test_allsh = abind(test_circarr, test_triarr, along=1)
test_allsh = abind(test_allsh, test_quadarr, along=1)

test_shapes = ImageArray(test_allsh, types=rep(c("circle", "triangle", "quad"), each=NIMAGES))
preview(shapes[c(1:3, 2501:2503, 5001:5003)])

## NULL

Fit the ISLR CNN on the training data

We’ll use a small number of epochs as the model seems capable of rapid learning for these inputs.

fit_sh = islr_cnn( shapes, nEpochs=5 )
plot(fit_sh$history)

eval_model(fit_sh$model, test_shapes)

## [1] 1