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,
  type = "stride"
)

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.
type	Type of interval, either 'stride' or 'extension'.

Value

Indices of points in the range.

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Conditional Probability Embedding for Mapper Nodes

Description

The origin Mapper includes mean and majority label embeddings. And this function provides another way to color the Mapper nodes. The function is useful to connect original data for color labeling, especially if you're interested in characteristic attributes.

Usage

CPEmbedding(
  mapper,
  original_data,
  columns = list(),
  a_level = NULL,
  b_level = NULL
)

Arguments

mapper	A Mapper object created by the MapperAlgo function.
original_data	Original dataframe, not the filter values.
columns	Two columns in original_data to compute conditional probability.
a_level	The level (attribute) of column A to condition on. If NULL, the first level is used.
b_level	The level (attribute) of column B for which the conditional probability is computed. If NULL, the first level is used.

Value

A list of conditional probabilities value for each Mapper node.

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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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Fuzzy Mapper Algorithm (Fixed Adjacency Calculation)

Description

Implements a variant of the Mapper algorithm using Fuzzy C-Means (FCM) clustering for the level sets.

Usage

FuzzyMapperAlgo(
  original_data,
  filter_values,
  cluster_n = 5,
  fcm_threshold = NULL,
  methods,
  method_params = list(),
  num_cores = 1
)

Arguments

original_data	Original dataframe, not the filter values.
filter_values	A data frame or matrix of the data to be analyzed.
cluster_n	Number of fuzzy clusters (c in FCM). Default is 5.
fcm_threshold	Membership threshold (tau). Points with u > tau are included in the interval.
methods	Specify the clustering method to be used, e.g., "hclust" or "kmeans".
method_params	A list of parameters for the clustering method.
num_cores	Number of cores to use for parallel computing.

Value

A MapperAlgo object same as MapperAlgo output

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G-Mapper Algorithm

Description

Implements a Mapper algorithm using Anderson-Darling tests and Gaussian Mixture Models (GMM) to automatically learn the cover.

Usage

GMapperAlgo(
  original_data,
  filter_values,
  AD_threshold = 10,
  g_overlap = 0.1,
  methods,
  method_params = list(),
  num_cores = 1
)

Arguments

original_data	Original dataframe, not the filter values.
filter_values	A data frame or matrix of the data to be analysed (1-D).
AD_threshold	Critical value for the Anderson-Darling test
g_overlap	The geometric overlap percentage when splitting an interval
methods	Specify the clustering method to be used, e.g., "hclust" or "kmeans".
method_params	A list of parameters for the clustering method.
num_cores	Number of cores to use for parallel computing.

Value

A MapperAlgo object same as MapperAlgo output

---

GridSearch searched over a list of interval width and overlap, useful for visualizing the convergence of the Mapper.

Description

GridSearch searched over a list of interval width and overlap, useful for visualizing the convergence of the Mapper.

Usage

GridSearch(
  original_data,
  filter_values,
  label,
  column = "label",
  cover_type = "stride",
  width_vec = c(0.5, 1, 1.5),
  overlap_vec = c(10, 20, 30, 40),
  num_cores = 12,
  out_dir = "mapper_grid_outputs",
  avg = FALSE,
  use_embedding = NULL
)

Arguments

original_data	Original dataframe, not the filter values.
filter_values	A numeric matrix or data frame of filter values (rows are samples, columns are filter dimensions).
label	A vector of labels for coloring the Mapper nodes.
column	The original column name (use when use_embedding=TRUE).
cover_type	The type of cover to use "stride" or "extension".
width_vec	A vector of interval widths.
overlap_vec	A vector of percent overlaps.
num_cores	Number of cores to use for parallel computing.
out_dir	Directory to save the output.
avg	Whether coloring the nodes by average label or majority label.
use_embedding	Whether to use embedding for coloring (NULL or embedding vector).

Value

A folder containing the PNG files of the Mapper visualizations.

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Mapper Algorithm

Description

Implements the Mapper algorithm for Topological Data Analysis (TDA). It divides data into intervals, applies clustering within each interval, and constructs a simplicial complex representing the structure of the data.

Usage

MapperAlgo(
  original_data,
  filter_values,
  percent_overlap,
  methods,
  method_params = list(),
  cover_type = "extension",
  intervals = NULL,
  interval_width = NULL,
  num_cores = 1
)

Arguments

original_data	Original dataframe, not the filter values.
filter_values	A data frame or matrix of the data to be analysed.
percent_overlap	Percentage of overlap between consecutive intervals.
methods	Specify the clustering method to be used, e.g., "hclust" or "kmeans".
method_params	A list of parameters for the clustering method.
cover_type	Type of interval, either 'stride' or 'extension'.
intervals	An integer specifying the number of intervals.
interval_width	The width of each interval.
num_cores	Number of cores to use for parallel computing.

Value

A list containing the Mapper graph components:

adjacency

The 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.

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Visualizes the correlation between two Mapper colorings.

Description

Visualizes the correlation between two Mapper colorings.

Usage

MapperCorrelation(
  mapper,
  original_data,
  labels = list(),
  use_embedding = list(FALSE, FALSE)
)

Arguments

mapper	A Mapper object created by the MapperAlgo function.
original_data	Original dataframe, not the filter values.
labels	List of two Mapper color.
use_embedding	List of two booleans indicating whether to use original data or embedding data.

Value

Plot of the correlation between two Mapper.

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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.

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Plot Mapper Result

Description

Visualizes the Mapper output using either networkD3.

Usage

MapperPlotter(Mapper, original_data, label, avg = FALSE, use_embedding = FALSE)

Arguments

Mapper	Mapper object.
original_data	Original dataframe, not the filter values.
label	Label of the data.
avg	Whether coloring the nodes by average label or majority label.
use_embedding	Whether to use original data for coloring (TRUE or FALSE).

Value

Plot of the Mapper.

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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).

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Perform clustering within a level set

Description

Perform clustering within a level set

Usage

perform_clustering(
  original_data,
  filter_values,
  points_in_this_level,
  methods,
  method_params = list()
)

Arguments

original_data	Original dataframe, not the filter values.
filter_values	The filter values.
points_in_this_level	Points in the current level set.
methods	Specify the clustering method to be used, e.g., "hclust" or "kmeans".
method_params	A list of parameters for the clustering method.

Value

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

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Helper function to recursively split data until it is Gaussian The function now takes geometric boundaries (a, b) instead of indices

Description

Helper function to recursively split data until it is Gaussian The function now takes geometric boundaries (a, b) instead of indices

Usage

recursive_gaussian_split(a, b, vals, AD_threshold, g_overlap, depth = 1)

Arguments

a	Left boundary of the interval
b	Right boundary of the interval
vals	The original filter values (1D vector)
AD_threshold	The threshold for the Anderson-Darling test to determine Gaussian
g_overlap	The geometric overlap percentage when splitting an interval
depth	Current depth of recursion to prevent infinite loops

Value

A list of geometric intervals that are Gaussian

---

GridSearch searched over a list of interval width and overlap, useful for visualizing the convergence of the Mapper.

Description

GridSearch searched over a list of interval width and overlap, useful for visualizing the convergence of the Mapper.

Usage

save_mapper_png(
  widget,
  png_path,
  vwidth = 1200,
  vheight = 900,
  zoom = 2,
  delay = 0.5
)

Arguments

widget	The htmlwidget object to be saved as PNG.
png_path	The file path to save the PNG image.
vwidth	The viewport width for the webshot.
vheight	The viewport height for the webshot.
zoom	The zoom factor for the webshot.
delay	The delay in seconds before taking the snapshot. Useful for allowing time for the widget to fully render.

Value

The snapshot is saved to the specified path.

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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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