Topological Data Analysis: Mapper Algorithm

Document

For a more detailed explanation for this package, this document will keep update for better understanding the source code. I've written some articles on Medium, which you can find here to get familiar with topological data analysis.

Get started quickly

Step visualize from Skaf et al.

Mapper is basically a three-step process:

1. Cover: This step splits the data into overlapping intervals and creates a cover for the data.

2. Cluster: This step clusters the data points in each interval the cover creates.

3. Simplicial Complex: This step combines the two steps above, which connects the data points in the cover to create a simplicial complex.

you can know more about the basic here: Chazal, F., & Michel, B. (2021). An introduction to topological data analysis: fundamental and practical aspects for data scientists. Frontiers in artificial intelligence, 4, 667963.

Example

data <- get(data("iris"))

Mapper <- MapperAlgo(
  data[,1:4],
  filter_values = data[,1:3],
  percent_overlap = 30,
  methods = "kmeans",
  method_params = list(max_kmeans_clusters = 2),
  cover_type = 'stride',
  interval_width = 1,
  num_cores = 12
  )

MapperPlotter(Mapper, label=data$Species, original_data=data, avg=FALSE, use_embedding=FALSE)

Figure 1

Figure 2

Playground (Frontend Beta)

The frontend is still under testing but has been deployed to tda frontend. By integrating webR, it executes the R-based MapperAlgo algorithm directly in the browser via the package.

To visualize your own data, upload a JSON file formatted as shown below. The cc is optional; you can ignore it unless you have pre-calculated labels. The iris example may take a moment to load, so feel free to upload your own file without waiting!

library(jsonlite)

export_data <- list(
  adjacency = Mapper$adjacency,
  num_vertices = Mapper$num_vertices,
  level_of_vertex = Mapper$level_of_vertex,
  points_in_vertex = Mapper$points_in_vertex,
  original_data = as.data.frame(all_features),
  # This is the label that already calculated for each node
  cc = tibble(
    eigen_centrality = e_scores,
    betweenness = b_scores
  )
)
write(toJSON(export_data, auto_unbox = TRUE), "~/desktop/mnist.json")