Package 'MapperAlgo'

Cut the hierarchical clustering tree to define clusters

Description

Cut the hierarchical clustering tree to define clusters

Usage

cluster_cutoff_at_first_empty_bin(heights, diam, num_bins_when_clustering)

Arguments

heights	Heights of the clusters.
diam	Diameter of the clusters.
num_bins_when_clustering	Number of bins when clustering.

Value

The cutoff height for the clusters.

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Cover points based on intervals and overlap

Description

Cover points based on intervals and overlap

Usage

cover_points(
  lsfi,
  filter_min,
  interval_width,
  percent_overlap,
  filter_values,
  num_intervals
)

Arguments

lsfi	Level set flat index.
filter_min	Minimum filter value.
interval_width	Width of the interval.
percent_overlap	Percentage overlap between intervals.
filter_values	The filter values to be analyzed.
num_intervals	Number of intervals.

Value

Indices of points in the range.

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Find the optimal number of clusters for k-means

Description

This function calculates the total within-cluster sum of squares (WSS) for a range of cluster numbers and identifies the best number of clusters (k) based on the elbow method.

Usage

find_best_k_for_kmeans(dist_object, max_clusters = 10)

Arguments

dist_object	A distance matrix or data frame containing the data to be clustered.
max_clusters	The maximum number of clusters to test for k-means. Default is 10.

Value

The optimal number of clusters (k) based on the elbow method.

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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, methods)

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.
methods	A character string specifying the clustering method to use. The default is "hierarchical".

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.

Author(s)

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)
library(networkD3)

data("iris")

mapper <- MapperAlgo(
  filter_values = iris[,1:4],
  intervals = 4,
  percent_overlap = 50,
  num_bins_when_clustering = 30,
  methods = "hierarchical")
    
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)
forceNetwork(Nodes = MapperNodes, Links = MapperLinks, Target = "Linktarget",
             Value = "Linkvalue", NodeID = "Nodename", Nodesize = "Nodesize",
             Group = "var.maj.vertex", opacity = 1, zoom = TRUE,
             linkDistance = 10, charge = -10, legend = TRUE)

---

Create Mapper Edges

Description

This function generates the edges of the Mapper graph by analyzing the adjacency matrix. It returns a data frame with source and target vertices that are connected by edges.

Usage

mapperEdges(m)

Arguments

m	The Mapper output object that contains the adjacency matrix and other graph components.

Value

A data frame containing the source (Linksource), target (Linktarget), and edge values (Linkvalue) for the graph's edges.

---

Create Mapper Vertices

Description

This function generates the vertices of the Mapper graph, including their labels and groupings. It returns a data frame with the vertex names, the group each vertex belongs to, and the size of each vertex.

Usage

mapperVertices(m, pt_labels)

Arguments

m	The Mapper output object that contains information about the vertices and level sets.
pt_labels	A vector of point labels to be assigned to the points in each vertex.

Value

A data frame containing the vertex names (Nodename), group information (Nodegroup), and vertex sizes (Nodesize).

---

Perform clustering within a level set

Description

Perform clustering within a level set

Usage

perform_clustering(
  points_in_this_level,
  filter_values,
  num_bins_when_clustering,
  methods,
  max_kmeans_clusters = 10,
  eps = 0.5,
  minPts = 5,
  num_clusters = 5
)

Arguments

points_in_this_level	Points in the current level set.
filter_values	The filter values.
num_bins_when_clustering	Number of bins when clustering.
methods	Specify the clustering method to be used, e.g., "hclust" or "kmeans".
max_kmeans_clusters	Maximum number of clusters when using k-means clustering.
eps	The maximum distance between two samples for one to be considered as in the neighborhood of the other.
minPts	The number of samples in a neighborhood for a point to be considered as a core point.
num_clusters	Number of clusters when using PAM clustering.

Value

A list containing the number of vertices, external indices, and internal indices.

---

Construct adjacency matrix of the simplicial complex

Description

Construct adjacency matrix of the simplicial complex

Usage

simplcial_complex(
  filter_values,
  vertex_index,
  num_levelsets,
  num_intervals,
  vertices_in_level_set,
  points_in_vertex
)

Arguments

filter_values	A matrix of filter values.
vertex_index	The number of vertices.
num_levelsets	The total number of level sets.
num_intervals	A vector representing the number of intervals for each filter.
vertices_in_level_set	A list where each element contains the vertices corresponding to each level set.
points_in_vertex	A list where each element contains the points corresponding to each vertex.

Value

An adjacency matrix representing the simplicial complex.

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Convert level set multi-index (lsmi) to flat index (lsfi)

Description

Convert level set multi-index (lsmi) to flat index (lsfi)

Usage

to_lsfi(lsmi, num_intervals)

Arguments

lsmi	Level set multi-index.
num_intervals	Number of intervals.

Value

A flat index corresponding to the multi-index.

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Convert level set flat index (lsfi) to multi-index (lsmi)

Description

Convert level set flat index (lsfi) to multi-index (lsmi)

Usage

to_lsmi(lsfi, num_intervals)

Arguments

lsfi	Level set flat index.
num_intervals	Number of intervals.

Value

A multi-index corresponding to the flat index.

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