Package 'mappeR' reference manual

Title:	Construct and Visualize TDA Mapper Graphs
Description:	Topological data analysis (TDA) is a method of data analysis that uses techniques from topology to analyze high-dimensional data. Here we implement Mapper, an algorithm from this area developed by Singh, Mémoli and Carlsson (2007) which generalizes the concept of a Reeb graph <https://en.wikipedia.org/wiki/Reeb_graph>. The output graph is able to be visualized in R using 'igraph' or using a free network analysis software called 'Cytoscape', available for download from at <https://cytoscape.org/>.
Authors:	George Clare Kennedy [aut, cre]
Maintainer:	George Clare Kennedy <[email protected]>
License:	MIT + file LICENSE
Version:	1.1.0
Built:	2024-10-17 05:27:58 UTC
Source:	CRAN

Get a tester function for an interval.

Description

Get a tester function for an interval.

Usage

check_in_interval(endpoints)
check_in_interval(endpoints)

Arguments

endpoints

A vector of interval endpoints, namely a left and a right. Must be in order.

Value

A function that eats a data point and outputs TRUE if the datapoint is in the interval and FALSE if not.

Compute dispersion of a single cluster

Description

Compute dispersion of a single cluster

Usage

compute_tightness(dists, cluster)
compute_tightness(dists, cluster)

Arguments

`dists`	A distance matrix for points in the cluster.
`cluster`	A list containing named vectors, whose names are data point names and whose values are cluster labels

Value

A real number in $(0,\infty)$ representing a measure of dispersion of a cluster. This method finds the medoid of the input data set, the point with the smallest sum of distances to all other points, and returns that sum divided by the largest distance from the medoid to another point. Formally, we say the tightness $\tau$ of a cluster $C$ is given by

$\tau(C) = \dfrac{1}{\displaystyle\max_{x_i\in C, i\neq j}{\text{dist}(x_i, x_j)}}\displaystyle\sum_{i}\text{dist}(x_i, x_j)$

where

$x_j = \text{arg}\,\min\limits_{x_j\in C}\, \sum_{x_i \in C, i\neq j}\text{dist}(x_i, x_j)$

A smaller value indicates a tighter cluster based on this metric.

The easiest clustering method

Description

The easiest clustering method

Usage

convert_to_clusters(bins)
convert_to_clusters(bins)

Arguments

bins

A list of bins, each containing names of data from some data frame.

Value

A named vector whose names are data point names and whose values are cluster labels

Run 1D mapper

Description

Run mapper using a one-dimensional filter, a cover of intervals, and a clustering algorithm.

Usage

create_1D_mapper_object(
  data,
  dists,
  filtered_data,
  cover,
  clustering_method = "single"
)
create_1D_mapper_object(
  data,
  dists,
  filtered_data,
  cover,
  clustering_method = "single"
)

Arguments

`data`	A data frame.
`dists`	A distance matrix for the data frame.
`filtered_data`	The result of a function applied to the data frame; there should be one row per observation in the original data frame.
`cover`	A 2D array of interval left and right endpoints.
`clustering_method`	Your favorite clustering algorithm.

Value

A list of two data frames, one with node data containing bin membership, data points per cluster, and cluster dispersion, and one with edge data containing sources, targets, and weights representing overlap strength.

Examples

data = data.frame(x = sapply(1:100, function(x) cos(x)), y = sapply(1:100, function(x) sin(x)))
projx = data$x

num_bins = 10
percent_overlap = 25

cover = create_width_balanced_cover(min(projx), max(projx), num_bins, percent_overlap)

create_1D_mapper_object(data, dist(data), projx, cover, "single")
data = data.frame(x = sapply(1:100, function(x) cos(x)), y = sapply(1:100, function(x) sin(x)))
projx = data$x

num_bins = 10
percent_overlap = 25

cover = create_width_balanced_cover(min(projx), max(projx), num_bins, percent_overlap)

create_1D_mapper_object(data, dist(data), projx, cover, "single")

Run mapper using a trivial filter, a cover of balls, and no clustering algorithm.

Description

Run mapper using an $\varepsilon$ -net cover (greedily generated) and the 2D inclusion function as a filter.

Usage

create_ball_mapper_object(data, dists, eps)
create_ball_mapper_object(data, dists, eps)

Arguments

`data`	A data frame.
`dists`	A distance matrix for the data frame.
`eps`	A positive real number for your desired ball radius.

Value

A list of two data frames, one with node data containing ball size, data points per ball, ball tightness, and one with edge data containing sources, targets, and weights representing overlap strength.

Examples

data = data.frame(x = sapply(1:100, function(x) cos(x)), y = sapply(1:100, function(x) sin(x)))
eps = .5

create_ball_mapper_object(data, dist(data), eps)
data = data.frame(x = sapply(1:100, function(x) cos(x)), y = sapply(1:100, function(x) sin(x)))
eps = .5

create_ball_mapper_object(data, dist(data), eps)

Make a cover of balls

Description

Make a cover of balls

Usage

create_balls(data, dists, eps)
create_balls(data, dists, eps)

Arguments

`data`	A data frame.
`dists`	A distance matrix for the data frame.
`eps`	A positive real number.

Value

A list of vectors of data point names, one list element per ball. The output is such that every data point is contained in a ball of radius $\varepsilon$ , and no ball center is contained in more than one ball. The centers are datapoints themselves.

Examples

num_points = 5000

P.data = data.frame(
  x = sapply(1:num_points, function(x)
    sin(x) * 10) + rnorm(num_points, 0, 0.1),
  y = sapply(1:num_points, function(x)
    cos(x) ^ 2 * sin(x) * 10) + rnorm(num_points, 0, 0.1),
  z = sapply(1:num_points, function(x)
    10 * sin(x) ^ 2 * cos(x)) + rnorm(num_points, 0, 0.1)
)

P.dist = dist(P.data)
balls = create_balls(data = P.data, dists = P.dist, eps = .25)
num_points = 5000

P.data = data.frame(
  x = sapply(1:num_points, function(x)
    sin(x) * 10) + rnorm(num_points, 0, 0.1),
  y = sapply(1:num_points, function(x)
    cos(x) ^ 2 * sin(x) * 10) + rnorm(num_points, 0, 0.1),
  z = sapply(1:num_points, function(x)
    10 * sin(x) ^ 2 * cos(x)) + rnorm(num_points, 0, 0.1)
)

P.dist = dist(P.data)
balls = create_balls(data = P.data, dists = P.dist, eps = .25)

Create bins of data

Description

Create bins of data

Usage

create_bins(data, filtered_data, cover_element_tests)
create_bins(data, filtered_data, cover_element_tests)

Arguments

`data`	A data frame.
`filtered_data`	The result of a function applied to the data frame; there should be one row per observation in the original data frame.
`cover_element_tests`	A list of membership test functions for a list of cover elements. Each member of `cover_element_tests` should be able to identify (return `TRUE` or `FALSE`) if a single input data point is a member of the cover element it represents.

Value

A list of bins, each containing a vector of the names of the data inside it.

Run clusterball mapper

Description

Run ball mapper, but additionally cluster within the balls. Can use two different distance matrices to accomplish this.

Usage

create_clusterball_mapper_object(data, dist1, dist2, eps, clustering_method)
create_clusterball_mapper_object(data, dist1, dist2, eps, clustering_method)

Arguments

`data`	A data frame.
`dist1`	A distance matrix for the data frame; this will be used to ball the data.
`dist2`	Another distance matrix for the data frame; this will be used to cluster the data after balling.
`eps`	A positive real number for your desired ball radius.
`clustering_method`	Your favorite clustering algorithm.

Value

A list of two dataframes, one with node data containing bin membership, datapoints per cluster, and cluster dispersion, and one with edge data containing sources, targets, and weights representing overlap strength.

Examples

data = data.frame(x = sapply(1:100, function(x) cos(x)), y = sapply(1:100, function(x) sin(x)))
data.dists = dist(data)
eps = 1

create_clusterball_mapper_object(data, data.dists, data.dists, eps, "single")
data = data.frame(x = sapply(1:100, function(x) cos(x)), y = sapply(1:100, function(x) sin(x)))
data.dists = dist(data)
eps = 1

create_clusterball_mapper_object(data, data.dists, data.dists, eps, "single")

Create a mapper object

Description

Run the mapper algorithm on a data frame.

Usage

create_mapper_object(
  data,
  dists,
  filtered_data,
  cover_element_tests,
  method = "none"
)
create_mapper_object(
  data,
  dists,
  filtered_data,
  cover_element_tests,
  method = "none"
)

Arguments

`data`	A data frame.
`dists`	A distance matrix for the data frame.
`filtered_data`	The result of a function applied to the data frame; there should be one row per observation in the original data frame.
`cover_element_tests`	A list of membership test functions for a list of cover elements. Each member of `cover_element_tests` should be able to identify (return `TRUE` or `FALSE`) if a single input data point is a member of the cover element it represents.
`method`	The desired clustering method to use. e.g., "single"

Value

A list of two dataframes, one with node data containing bin membership, datapoints per cluster, and cluster dispersion, and one with edge data containing sources, targets, and weights representing overlap strength.

Examples

data = data.frame(x = sapply(1:100, function(x) cos(x)), y = sapply(1:100, function(x) sin(x)))
projx = data$x

num_bins = 10
percent_overlap = 25
xcover = create_width_balanced_cover(min(projx), max(projx), num_bins, percent_overlap)

check_in_interval <- function(endpoints) {
 return(function(x) (endpoints[1] - x <= 0) & (endpoints[2] - x >= 0))
}

# each of the "cover" elements will really be a function that checks if a data point lives in it
xcovercheck = apply(xcover, 1, check_in_interval)

# build the mapper object
xmapper = create_mapper_object(
  data = data,
  dists = dist(data),
  filtered_data = projx,
  cover_element_tests = xcovercheck,
  method = "single"
)
data = data.frame(x = sapply(1:100, function(x) cos(x)), y = sapply(1:100, function(x) sin(x)))
projx = data$x

num_bins = 10
percent_overlap = 25
xcover = create_width_balanced_cover(min(projx), max(projx), num_bins, percent_overlap)

check_in_interval <- function(endpoints) {
 return(function(x) (endpoints[1] - x <= 0) & (endpoints[2] - x >= 0))
}

# each of the "cover" elements will really be a function that checks if a data point lives in it
xcovercheck = apply(xcover, 1, check_in_interval)

# build the mapper object
xmapper = create_mapper_object(
  data = data,
  dists = dist(data),
  filtered_data = projx,
  cover_element_tests = xcovercheck,
  method = "single"
)

Create a bin of data

Description

Create a bin of data

Usage

create_single_bin(data, filtered_data, cover_element_test)
create_single_bin(data, filtered_data, cover_element_test)

Arguments

`data`	A data frame.
`filtered_data`	The result of a function applied to the data frame; there should be one row per observation in the original data frame.
`cover_element_test`	A membership test function for a cover element. It should identify (return `TRUE` or `FALSE`) if a single input data point, is a member of the cover element it represents.

Value

A vector of names of points from the data frame, representing a bin.

Generate an overlapping cover of an interval

Description

This is a function that generates a cover of an interval $[a,b]$ with some number of (possibly) overlapping, evenly spaced, identical width subintervals.

Usage

create_width_balanced_cover(min_val, max_val, num_bins, percent_overlap)
create_width_balanced_cover(min_val, max_val, num_bins, percent_overlap)

Arguments

`min_val`	The left endpoint $a$ . A real number.
`max_val`	The right endpoint $b$ . A real number.
`num_bins`	The number of cover intervals with which to cover the interval. A positive integer.
`percent_overlap`	How much overlap desired between the cover intervals (the percent of the intersection of each interval with its immediate neighbor relative to its length, e.g., $[0,2]$ and $[1,3]$ would have $50\%$ overlap). A real number between 0 and 100, inclusive.

Value

A 2D numeric array.

left_ends - The left endpoints of the cover intervals.
right_ends - The right endpoints of the cover intervals.

Examples

create_width_balanced_cover(min_val=0, max_val=100, num_bins=10, percent_overlap=15)
create_width_balanced_cover(-11.5, 10.33, 100, 2)
create_width_balanced_cover(min_val=0, max_val=100, num_bins=10, percent_overlap=15)
create_width_balanced_cover(-11.5, 10.33, 100, 2)

Cut a dendrogram

Description

Cut a dendrogram

Usage

cut_dendrogram(dend, threshold)
cut_dendrogram(dend, threshold)

Arguments

`dend`	A single dendrogram.
`threshold`	A mininum tallest branch value.

Value

A named vector whose names are data point names and whose values are cluster labels. The number of clusters is determined to be 1 if the tallest branch of the dendrogram is less than the threshold, or if the index of dispersion (standard deviation squared divided by mean) of the branch heights is too low. Otherwise, we cut at the longest branch of the dendrogram to determine the number of clusters.

Compute eccentricity of data points

Description

Compute eccentricity of data points

Usage

eccentricity_filter(dists)
eccentricity_filter(dists)

Arguments

dists

A distance matrix associated to a data frame.

Value

A vector of centrality measures, calcuated per data point as the sum of its distances to every other data point, divided by the number of points.

Examples

num_points = 5000

P.data = data.frame(
  x = sapply(1:num_points, function(x)
    sin(x) * 10) + rnorm(num_points, 0, 0.1),
  y = sapply(1:num_points, function(x)
    cos(x) ^ 2 * sin(x) * 10) + rnorm(num_points, 0, 0.1),
  z = sapply(1:num_points, function(x)
    10 * sin(x) ^ 2 * cos(x)) + rnorm(num_points, 0, 0.1)
)

P.dist = dist(P.data)
eccentricity = eccentricity_filter(P.dist)
num_points = 5000

P.data = data.frame(
  x = sapply(1:num_points, function(x)
    sin(x) * 10) + rnorm(num_points, 0, 0.1),
  y = sapply(1:num_points, function(x)
    cos(x) ^ 2 * sin(x) * 10) + rnorm(num_points, 0, 0.1),
  z = sapply(1:num_points, function(x)
    10 * sin(x) ^ 2 * cos(x)) + rnorm(num_points, 0, 0.1)
)

P.dist = dist(P.data)
eccentricity = eccentricity_filter(P.dist)

Recover bins

Description

Recover bins

Usage

get_bin_vector(binclust_data)
get_bin_vector(binclust_data)

Arguments

binclust_data

A list of bins, each containing named vectors whose names are those of data points and whose values are cluster ids.

Value

A vector of integers equal in length to the number of clusters, whose members identify which bin that cluster belongs to.

Compute cluster sizes

Description

Compute cluster sizes

Usage

get_cluster_sizes(binclust_data)
get_cluster_sizes(binclust_data)

Arguments

binclust_data

A list of bins, each containing named vectors whose names are those of data points and whose values are cluster

Value

A vector of integers representing the lengths of the clusters in the input data.

Compute dispersion measures of a list of clusters

Description

Compute dispersion measures of a list of clusters

Usage

get_cluster_tightness_vector(dists, binclust_data)
get_cluster_tightness_vector(dists, binclust_data)

Arguments

`dists`	A distance matrix for the data points inside the input clusters
`binclust_data`	A list of bins, each containing named vectors whose names are those of data points and whose values are cluster ids

Value

A vector of real numbers in $(0,\infty)$ representing a measure of dispersion of a cluster, calculated according to compute_tightness()

Get data within a cluster

Description

Get data within a cluster

Usage

get_clustered_data(binclust_data)
get_clustered_data(binclust_data)

Arguments

binclust_data

A list of bins, each containing named vectors whose names are those of data points and whose values are cluster ids

Value

A list of strings, each a comma separated list of the toString values of the data point names.

Initate the clustering process

Description

This function processes the binned data and global distance matrix to return freshly clustered data.

Usage

get_clusters(bins, dists, method)
get_clusters(bins, dists, method)

Arguments

`bins`	A list containing "bins" of vectors of names of data points.
`dists`	A distance matrix containing pairwise distances between named data points.
`method`	A clue!

Value

A list containing named vectors (one per bin), whose names are data point names and whose values are cluster labels

Calculate edge weights

Description

Calculate edge weights

Usage

get_edge_weights(overlap_lengths, cluster_sizes, edges)
get_edge_weights(overlap_lengths, cluster_sizes, edges)

Arguments

`overlap_lengths`	A named vector of cluster overlap lengths, obtained by calling `length()` on the output from `[get_overlaps()]`.
`cluster_sizes`	A vector of cluster sizes.
`edges`	A 2D array of source and target nodes, representing an edge list. Should be ordered consistently with the `overlap_lengths` parameter.

Value

A vector of real numbers representing cluster overlap strength. This is calculated per edge by dividing the number of data points in the overlap by the number of points in the cluster on either end, and taking the maximum value.

Obtain edge list from cluster intersections

Description

Obtain edge list from cluster intersections

Usage

get_edgelist_from_overlaps(overlaps, num_vertices)
get_edgelist_from_overlaps(overlaps, num_vertices)

Arguments

`overlaps`	A named list of edges, whose elements contain the names of clusters in the overlap represented by that edge; output of `get_overlaps()`.
`num_vertices`	The number of vertices in the graph.

Value

A 2D array representing the edge list of a graph.

Get cluster overlaps

Description

Get cluster overlaps

Usage

get_overlaps(binclust_data)
get_overlaps(binclust_data)

Arguments

binclust_data

A list of bins, each containing named vectors whose names are those of data points and whose values are cluster ids.

Value

A named list of edges, whose elements contain the names of clusters in the overlap represented by that edge.

Perform single linkage clustering and process dendrograms

Description

Perform single linkage clustering and process dendrograms

Usage

get_single_linkage_clusters(dist_mats)
get_single_linkage_clusters(dist_mats)

Arguments

dist_mats

A list of distance matrices to be used for clustering.

Value

A list containing named vectors (one per dendrogram), whose names are data point names and whose values are cluster labels

Find the tallest branch of a dendrogram

Description

Find the tallest branch of a dendrogram

Usage

get_tallest_branch(dend)
get_tallest_branch(dend)

Arguments

dend

A single dendrogram.

Value

The height of the tallest branch (longest time between merge heights) of the input dendrogram.

Get a tester function for a ball.

Description

Get a tester function for a ball.

Usage

is_in_ball(ball)
is_in_ball(ball)

Arguments

ball

A list of data points.

Value

A function that eats a data point and returns TRUE or FALSE depending if the point is in the ball or not.

make igraph

Description

make igraph

Usage

mapper_object_to_igraph(mapperobject)
mapper_object_to_igraph(mapperobject)

Arguments

mapperobject

mapper object generated by mappeR

Value

an igraph object

Examples

data = data.frame(x = sapply(1:100, function(x) cos(x)), y = sapply(1:100, function(x) sin(x)))

projy = data$y

cover = create_width_balanced_cover(min(projy), max(projy), 10, 25)

mapperobj = create_1D_mapper_object(data, dist(data), data$y, cover, "single")

mapper_object_to_igraph(mapperobj)
data = data.frame(x = sapply(1:100, function(x) cos(x)), y = sapply(1:100, function(x) sin(x)))

projy = data$y

cover = create_width_balanced_cover(min(projy), max(projy), 10, 25)

mapperobj = create_1D_mapper_object(data, dist(data), data$y, cover, "single")

mapper_object_to_igraph(mapperobj)

Find which triangular number you're on

Description

Find which triangular number you're on

Usage

next_triangular(x)
next_triangular(x)

Arguments

`x`	A positive integer.

Value

The index of the next greatest or equal triangular number to $x$ .

Cut many dendrograms

Description

Cut many dendrograms

Usage

process_dendrograms(dends)
process_dendrograms(dends)

Arguments

dends

A list of dendrograms to be cut.

Value

A list of named vectors (one per dendrogram) whose names are data point names and whose values are cluster labels. This function determines a global minimum threshold based on the longest branches in all the input dendrograms, and uses that as a heuristic to gauge if the best number of clusters is 1, or the value obtained by cutting the longest branch.

Ship data off to the clustering goblins

Description

This function tells the computer to look away for a second, so the goblins come and cluster your data while it's not watching.

Usage

run_cluster_machine(dist_mats, method)
run_cluster_machine(dist_mats, method)

Arguments

`dist_mats`	A list of distance matrices of each bin that is to be clustered.
`method`	A string that suggests how the goblins will handle the data.

Value

A list containing named vectors (one per bin), whose names are data point names and whose values are cluster labels (within each bin)

Construct mapper graph from data

Description

Construct mapper graph from data

Usage

run_mapper(binclust_data, dists, binning = TRUE)
run_mapper(binclust_data, dists, binning = TRUE)

Arguments

`binclust_data`	A list of bins, each containing named vectors whose names are those of data points and whose values are cluster ids
`dists`	A distance matrix for the data that has been binned and clustered.
`binning`	Whether the output dataframe should sort vertices into "bins" or not. Should be true if using clustering, leave false otherwise

Value

A list of two dataframes, one with node data containing bin membership, datapoints per cluster, and cluster dispersion, and one with edge data containing sources, targets, and weights representing overlap strength.

Perform single linkage clustering

Description

Perform single linkage clustering

Usage

run_slink(dist)
run_slink(dist)

Arguments

dist

A distance matrix.

Value

A dendrogram generated by fastcluster.

Subset a distance matrix

Description

Subset a distance matrix

Usage

subset_dists(bin, dists)
subset_dists(bin, dists)

Arguments

`bin`	A list of names of data points.
`dists`	A distance matrix for data points in the bin, possibly including extra points.

Value

A distance matrix for only the data points in the input bin.

Package 'mappeR'

Help Index

Get a tester function for an interval.

Description

Usage

Arguments

Value

Compute dispersion of a single cluster

Description

Usage

Arguments

Value

The easiest clustering method

Description

Usage

Arguments

Value

Run 1D mapper

Description

Usage

Arguments

Value

Examples

Run mapper using a trivial filter, a cover of balls, and no clustering algorithm.

Description

Usage

Arguments

Value

Examples

Make a cover of balls

Description

Usage

Arguments

Value

Examples

Create bins of data

Description

Usage

Arguments

Value

Run clusterball mapper

Description

Usage

Arguments

Value

Examples

Create a mapper object

Description

Usage

Arguments

Value

Examples

Create a bin of data

Description

Usage

Arguments

Value

Generate an overlapping cover of an interval

Description

Usage

Arguments

Value

Examples

Cut a dendrogram

Description

Usage

Arguments

Value

Compute eccentricity of data points

Description

Usage

Arguments

Value

Examples

Recover bins

Description

Usage

Arguments

Value

Compute cluster sizes