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quollr

Nonlinear dimension reduction (NLDR) techniques provide a low-dimensional representation of high-dimensional data by applying a non-linear transformation. The complexity of the transformations and data structure can create wildly different representations depending on the method and parameter choices. It is difficult to determine whether any are accurate, which is best, or whether they have missed structure. To help assess the NLDR and decide on which, if any, is best, we have developed an algorithm to create a model that is then used to display as a wireframe in high dimensions. The quollr package provides functions to implement the algorithm.

For a thorough background and discussion on this work, please read our paper https://arxiv.org/abs/2506.22051.

Installation

You can install the released version of quollr from CRAN with:

install.packages("quollr")

The development version from GitHub with:

install.packages("pak")
pak::pak("JayaniLakshika/quollr")

Usage

Our approach involves dividing the high-dimensional data set into two parts: a training set to construct the model and a test set to generate model summaries. To implement our approach, first we use a 2-D embedding data set as the initial point. The output of our algorithm is a tour that displays the model overlaid on high-dimensional data. Our algorithm comprises two main phases: (1) generate the model in the 2-D space, and (2) lift the model into high-dimensional space. This methodology is available in this package.

About the name

questioning how a high-dimensional object looks in low-dimensions using r

Roadmap

Quick start guide: 1. Quick start
To learn more about the data preprocessing: 2. Data preprocessing
To create the full hexagonal grid: 3. Algorithm for binning data
To learn more about the main steps of the algorithm: 4. Algorithm for visualising the model overlaid on high-dimensional data
To generate model summaries: 5. Generating model summaries
To select the optimal bin width: 6. Selecting the best bin width
To select the most reasonable NLDR layout: 7. Selecting the best fit

Copyright

This package is licensed under the MIT license.

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Version

Install

install.packages('quollr')

Monthly Downloads

312

Version

0.3.7

License

MIT + file LICENSE

Maintainer

Jayani P. G. Lakshika

Last Published

July 22nd, 2025

Functions in quollr (0.3.7)

Find points in hexagonal bins

fit_highd_model

Construct the 2-D model and lift into high-dimensions

gen_scaled_data

Scaling the NLDR data

Generate evaluation metrics

Create a trimesh plot

scurve_model_obj

Object for S-curve dataset

S-curve dataset with noise dimensions

Compute Projection for High-Dimensional Data

Generate a design to layout 2-D representations

Generate edge information

show_link_plots

Visualise the model overlaid on high-dimensional data along with 2-D wireframe model.

plot_rmse_layouts

Arrange RMSE plot and 2-D layouts

Plot Projected Data with Axes and Circles

Create a hexgrid plot

scurve_umap_rmse

Summary with different number of bins for `scurve_umap`

Predict 2-D embeddings

Solve Quadratic Equation for Positive Real Roots

Generate hexagonal polygon coordinates

scurve_umap_rmse2

Summary with different number of bins for `scurve_umap2`

scurve_umap_predict

Predicted UMAP embedding for `scurve` data

show_error_link_plots

Visualise the model overlaid on high-dimensional data along with 2-D wireframe model and error.

show_langevitour

Visualise the model overlaid on high-dimensional data

update_trimesh_index

Update from and to values in trimesh data

UMAP embedding for `scurve` with n_neighbors = 10 and min_dist = 0.4

UMAP embedding for `scurve` with n_neighbors = 30 and min_dist = 0.5

UMAP embedding for `scurve` with n_neighbors = 62 and min_dist = 0.1

gen_diffbin1_errors

Generate erros and MSE for different bin widths

stat_hexgrid Custom Stat for hexagonal grid plot

stat_trimesh Custom Stat for trimesh plot

tri_bin_centroids

Triangulate bin centroids

UMAP embedding for `scurve` with n_neighbors = 15 and min_dist = 0.1

scurve_umap_rmse3

Summary with different number of bins for `scurve_umap3`

scurve_umap_rmse4

Summary with different number of bins for `scurve_umap4`

Calculate 2-D Euclidean distances between vertices

GeomHexgrid: A Custom ggplot2 Geom for Hexagonal Grid

Assign data to hexagons

comb_all_data_model

Create a tibble with averaged high-dimensional data and high-dimensional data, non-linear dimension reduction data

Create a tibble with averaged high-dimensional data

Calculate the effective number of bins along x-axis and y-axis

Augment Data with Predictions and Error Metrics

Generate centroid coordinate

Generate Axes for Projection

comb_data_model

Create a tibble with averaged high-dimensional data and high-dimensional data

comb_all_data_model_error

Create a tibble with averaged high-dimensional data and high-dimensional data, non-linear dimension reduction data, model error data

extract_hexbin_mean

Extract hexagonal bin mean coordinates and the corresponding standardize counts.

GeomTrimesh: A Custom ggplot2 Geom for Triangular Meshes

extract_hexbin_centroids

Extract hexagonal bin centroids coordinates and the corresponding standardise counts.

find_low_dens_hex

Find low-density Hexagons

compute_mean_density_hex

Compute mean density of hexagonal bins

compute_std_counts

Compute standardise counts in hexagons

find_non_empty_bins

Find the number of bins required to achieve required number of non-empty bins.

Hexagonal binning