examples/mnist_example.md

In CamaraLab/RayleighSelection: An R package for feature selection in topological spaces.

MNIST Example

Calculate the Combinatorial Laplacian score of pixels on a nerve complex created by TDA mapper run on the MNIST dataset

library(RayleighSelection)

Load the mnist dataset

data("mnist")

Compute reduced representation

Using Laplacian eigenmap of pixels with high variance

library(dimRed)

## Loading required package: DRR

## Loading required package: kernlab

## Loading required package: CVST

## Loading required package: Matrix

## 
## Attaching package: 'dimRed'

## The following object is masked from 'package:stats':
## 
##     embed

## The following object is masked from 'package:base':
## 
##     as.data.frame

leim <- LaplacianEigenmaps()
mnist_top <- mnist[apply(mnist, 1, var) > 10000,]
emb <- leim@fun(as(t(mnist_top), "dimRedData"), leim@stdpars)

## 2018-11-05 22:18:10: Creating weight matrix

## 2018-11-05 22:18:34: Eigenvalue decomposition

## Eigenvalues: 6.178736e-02 4.905515e-02 1.200168e-15

## 2018-11-05 22:19:15: DONE

Compute Mapper representation

Using the Laplacian eigenmap as an auxiliary function and correlation distance as metric

library(TDAmapper)
mnist_distances <- (1.0 - cor(mnist_top))
m2 <- mapper2D(distance_matrix = mnist_distances,
                filter_values = list(emb@data@data[,1], emb@data@data[,2]),
                num_intervals = c(30,30),
                percent_overlap = 35,
                num_bins_when_clustering = 10);

Compute the nerve complex

gg <- nerve_complex(m2$points_in_vertex)

Compute 0-form and 1-form Comb. Lap. scores, p-value, and q-value

For the 301st through 305th pixels

rayleigh_selection(gg, mnist[301:305,])

##             R0    p0    q0       R1    p1      q1
## X301 0.2230237 0.000 0.000 1.526852 0.278 0.69500
## X302 0.2348739 0.000 0.000 1.498672 0.187 0.69500
## X303 0.2596099 0.000 0.000 1.560080 0.531 0.88500
## X304 0.3348691 0.000 0.000 1.631599 0.739 0.92375
## X305 0.4394595 0.001 0.001 1.903140 0.950 0.95000

CamaraLab/RayleighSelection documentation built on Aug. 16, 2021, 12:01 p.m.