MapperAlgo (version 1.0)

MapperAlgo: Topological data analysis: Mapper algorithm

Description

The Mapper algorithm is a method for topological data analysis that provides a way to visualize the structure of high-dimensional data. The Mapper algorithm is a generalization of the Reeb graph construction, which is a method for visualizing the topology of scalar fields.

Usage

MapperAlgo(filter_values, intervals, percent_overlap, num_bins_when_clustering)

Value

An adjacency matrix and other components of the Mapper graph, including:

adjacency

An adjacency matrix of the Mapper graph.

num_vertices

The number of vertices in the Mapper graph.

level_of_vertex

A vector specifying the level of each vertex.

points_in_vertex

A list of the indices of the points in each vertex.

points_in_level_set

A list of the indices of the points in each level set.

vertices_in_level_set

A list of the indices of the vertices in each level set.

Arguments

filter_values

A data frame or matrix of the data to be analyzed.

intervals

An integer specifying the number of intervals to divide the filter values into.

percent_overlap

An integer specifying the percentage of overlap between consecutive intervals.

num_bins_when_clustering

An integer specifying the number of bins to use when clustering the data.

Author

ChiChien Wang

References

The original paper on the Mapper algorithm is: G. Singh, F. Memoli, G. Carlsson (2007). Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition, Point Based Graphics 2007, Prague, September 2007. This code is based on Paul Pearson's implementation of the Mapper algorithm in R, optimized for speed and memory usage. You can install using the following command: devtools::install_github("paultpearson/TDAmapper")

Examples

library(igraph)

data("iris")

mapper <- MapperAlgo(
  filter_values = iris[,1:4],
  intervals = 4,
  percent_overlap = 50,
  num_bins_when_clustering = 30)
    
graph <- graph.adjacency(mapper$adjacency, mode="undirected")
l = length(V(graph))
Mode <- function(x) {
  ux <- unique(x)
  ux[which.max(tabulate(match(x, ux)))]
}
# Distribution of specific variable in each vertex - Majority vote
var.maj.vertex <- c()
filter.vertex <- c()

for (i in 1:l){
  points.in.vertex <- mapper$points_in_vertex[[i]]
  Mode.in.vertex <- Mode(iris$Species[points.in.vertex])
  var.maj.vertex <- c(var.maj.vertex, as.character(Mode.in.vertex))
}

# Size
vertex.size <- rep(0, l)
for (i in 1:l){
  points.in.vertex <- mapper$points_in_vertex[[i]]
  vertex.size[i] <- length(mapper$points_in_vertex[[i]])
}

MapperNodes <- mapperVertices(mapper, 1:nrow(iris))
MapperNodes$var.maj.vertex <- as.factor(var.maj.vertex)
MapperNodes$Nodesize <- vertex.size
MapperLinks <- mapperEdges(mapper)