TDAtools

TDAtools provides many functions to help data scientists using TDA.

Installation

You can install the development version of TDAtools from GitHub with:

devtools::install_github("vituri/TDAtools")

Notation

Let’s fix some notation:

• X is a data.frame with numeric and, possibly, factor columns. When needed, we select only the numeric columns (like when calculating the distance matrix of X) and denote it by X. The rows of X are called observations, and the columns are called variables;

• f_X is a vector with one number for each observation of X. That is: f_X is the result of applying a filter function f : X → ℝ to X. We provide many filter functions;

• distance_matrix is a matrix of distances calculated with X OR a function that when applied to X results in such a matrix

Graph-reducing algorithms

We provide the Mapper algorithm and the Ball-Mapper algorithm. Both return a list consisting of:

• a graph with weighted vertices;

• a list showing which points of X are in each vertex.

See the vignettes for more examples. (to-do)

Examples

Let X be a sample of random points in a noisy circle:

library(TDAtools)
#> Carregando pacotes exigidos: shiny
#> Carregando pacotes exigidos: dplyr
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
#> Carregando pacotes exigidos: purrr
#> Carregando pacotes exigidos: ggplot2

X = data.noisy_circle()

Let the filter function be the projetion on the x-axis and let color X using it:

f_X = X$x

color_band = ggplot2::cut_interval(f_X, n = 50)
col_vector = viridis::viridis(nlevels(color_band))[as.integer(color_band)]
plot(X, col = col_vector)

Now we embed X in R⁴:

X$z = 0
X$w = 0

and calculate its Mapper Graph:

mp =
  mapper(
    X = X
    ,f_X = f_X
  )
#> Clustering pullback 1...
#> Clustering pullback 2...
#> Clustering pullback 3...
#> Clustering pullback 4...
#> Clustering pullback 5...
#> Clustering pullback 6...
#> Clustering pullback 7...
#> Clustering pullback 8...
#> Clustering pullback 9...
#> Clustering pullback 10...

The result is a list with many objects. For example, the pullback of each interval in the covering:

mp$pullback |> str()
#> List of 10
#>  $ 1 : int [1:77] 7 39 58 62 67 68 76 86 89 100 ...
#>  $ 2 : int [1:256] 1 2 5 7 10 16 18 19 21 25 ...
#>  $ 3 : int [1:303] 1 2 5 9 10 16 17 18 19 21 ...
#>  $ 4 : int [1:199] 9 17 23 24 31 33 36 37 41 44 ...
#>  $ 5 : int [1:164] 20 29 35 36 37 41 42 43 44 46 ...
#>  $ 6 : int [1:180] 3 4 6 11 20 26 29 30 35 42 ...
#>  $ 7 : int [1:194] 3 4 6 11 12 15 26 27 30 34 ...
#>  $ 8 : int [1:272] 8 12 15 22 27 32 34 38 40 48 ...
#>  $ 9 : int [1:262] 8 13 14 22 28 32 38 40 47 49 ...
#>  $ 10: int [1:93] 13 14 28 47 61 91 105 108 111 126 ...
#>  - attr(*, "class")= chr "AsIs"

Let’s plot the mapper graph:

mp$graph %>% plot()

Or, for a better visualization, we use the networkVis package and color the nodes using the mean value of the x variable of X:

mp %>% plot_mapper()

Or color it by y:

mp %>% plot_mapper(data_column = 'y')

To do

• Vignettes using mapper with factor variables
• Ball Mapper documentation
• Persistent homology examples
• Data analysis using some vertices of the mapper + machine learning