nerve_complex: Generates the nerve complex of an open cover.

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

Description

Takes the open cover of a finite set and returns its nerve complex. The output is a nerve complex that can be used by other functions in the RayleighSelection package. The orientation of simplices is based on the order of the points in the point cloud.

Usage

nerve_complex(open_cover)

Arguments

open_cover

a list of open sets with open_cover[[i]] a vector of indices of points corresponding to the i-th open set in the open cover.

Value

An object of the class simplicial. The class simplicial inherits from the class igraph.

Examples

# Example 1
library(RayleighSelection)
gy <- nerve_complex(list(c(1,4,6,10), c(1,2,7), c(2,3,8), c(3,4,9,10), c(4,5)))
plot_skeleton(gy,k=c(0,1,1,0,0,0,0,0,0,1))


# Example 2: MNIST dataset
data("mnist")

# Compute reduced representation using Laplacian eigenmap of pixels with high variance
library(dimRed)
leim <- LaplacianEigenmaps()
mnist_top <- mnist[apply(mnist, 1, var) > 10000,]
emb <- leim@fun(as(t(mnist_top), "dimRedData"), leim@stdpars)

# 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)

# Plots simplicial complex colored by the value of the 301th pixel
plot_skeleton(gg, k=mnist[301,])

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