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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 $2\text{-}D$ 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 $2\text{-}D$ 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
To generate linked plots with detourr: 8. Linked plots with detourr

Copyright

This package is licensed under the MIT license.

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Version

Install

install.packages('quollr')

Monthly Downloads

197

Version

1.0.6

License

MIT + file LICENSE

Maintainer

Jayani P. G. Lakshika

Last Published

December 18th, 2025

Functions in quollr (1.0.6)

Compute Projection for High-Dimensional Data

S-curve dataset with noise dimensions

show_langevitour

Visualise the model overlaid on high-dimensional data

Predict 2-D embeddings

Create a hexgrid plot

Solve Quadratic Equation for Positive Real Roots

Plot Projected Data with Axes and Circles

stat_trimesh Custom Stat for trimesh plot

tri_bin_centroids

Triangulate bin centroids

Generate edge information

scurve_umap_predict

Predicted UMAP embedding for `scurve` data

Generate hexagonal polygon coordinates

plot_hbe_layouts

Arrange HBE plot and 2-D layouts

show_error_link_plots

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

gen_scaled_data

Scaling the NLDR data

show_link_plots

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

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

stat_hexgrid Custom Stat for hexagonal grid plot

scurve_model_obj

Object for S-curve dataset

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

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

S3 generic for glance

scurve_umap_rmse3

Summary with different number of bins for `scurve_umap3`

glance.highd_vis_model

Generate evaluation metrics for a hex_model object

merge_hexbin_mean

Extract hexagonal bin mean coordinates and the corresponding standardize counts.

merge_hexbin_centroids

Extract hexagonal bin centroids coordinates and the corresponding standardise counts.

update_trimesh_index

Update from and to values in trimesh data

Hexagonal binning

scurve_umap_rmse

Summary with different number of bins for `scurve_umap`

Grouped points in each hexagon

Generate Axes for Projection

Generate centroid coordinate

scurve_umap_rmse2

Summary with different number of bins for `scurve_umap2`

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

scurve_umap_rmse4

Summary with different number of bins for `scurve_umap4`

S3 generic for augment

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

comb_all_data_model

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

GeomHexgrid: A Custom ggplot2 Geom for Hexagonal Grid

Create a tibble with averaged high-dimensional data

augment.highd_vis_model

Augment Data with Predictions and Error Metrics for NLDR Models

Calculate 2-D Euclidean distances between vertices

Assign data to hexagons

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

fit_highd_model

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

find_non_empty_bins

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

comb_data_model

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

compute_mean_density_hex

Compute mean density of hexagonal bins

Create a trimesh plot

GeomTrimesh: A Custom ggplot2 Geom for Triangular Meshes

compute_std_counts

Compute standardise counts in hexagons

gen_diffbin1_errors

Generate erros and MSE for different bin widths

Generate a design to layout 2-D representations

find_low_dens_hex

Find low-density Hexagons