Awesome

Dimensionality Reduction Metrics

This repository contains R functions to evaluate the quality of projections obtained after using dimensionality reduction techniques. A nextjournal notebook is associated to this repository and uses the functions described in this README file to evaluate the quality of a molecular map of lung neuroendocrine tumors produced using the UMAP algorithm.

Sequence difference view (SD) metric

SD metric calculation for one sample compute_SD

Description

This function computes the sequence difference (SD) view metric value for a single given sample (i), following the equation 3 described by Martins et al. in 2015. This dissimilarity metric compares the k-neighborhood of a given sample in two different dimensional spaces. The lower is the SD value, the better is the neighborhood preservation.

Usage

compute_SD(dist_space1,dist_space2,k)

Arguments

• dist_space1: vector containing the distances of sample i to all samples in space1

• dist_space2: vector containing the distances of sample i to all samples in space2

• k: number of neighbors considered

Value

A numeric value corresponding to the SD value is returned.

SD metric calculation for all samples compute_SD_allSamples

Description

This function computes the SD metric for all samples included in the dimensionality reduction. The metric is computed to compare one or multiple comparison reduced spaces to a the reference space. The SD values are computed for several k values (number of neighbors to consider).

Usage

compute_SD_allSamples(distRef,List_projection,k_values,colnames_res_df, threads=2)

Arguments

• distRef: vector containing the distances of sample i to all samples in the reference space

• List_projection: list of data frames where each data frame contains the coordinates of all samples in each reduced space for which the SD metric needs to be calculated.

• k_values: vector listing the k values corresponding to the number of neighbors considered

• colnames_res_df: vector specifying the colnames associated to the computed SD values in the returned data frame. The vector should have the same length as List_projection

Value

• Data frame containing a column with the samples IDs, a column correspoding to the k values, and n colunms containing the SD values, n corresponding to the number of data frames listed in List_projection.

Visualizing the SD metric in a two dimensional map SD_map_f

Description

This function allows to display, on a two dimensional projection, the samples SD values averaged over different values of k (number of neighbors considered to compute the SD metric).

Usage

SD_map_f(SD_df, Coords_df, legend_pos = "right")

Arguments

• SD_df: a data frame resulting from the call to the function compute_SD_allSamples. The data frame contains the following columns: i) the samples IDs, ii) k values, the number of neighbors considered to compute the SD metric, and iii) the SD values

• Coords_df: data frame containing the coordinates of each sample in the projection to use for the representation of the samples

• legend_pos: Optional argument to define the position of the legend

Value

A list containing:

• A data frame containing the same columns as Coords_df and a column corresponding to the averaged SD values over k.
• The plot representing all samples in a two dimensional space. A color gradient is used to represent the SD values averaged over the k levels.

Spatial autocorrelation

Moran's Index (MI) computation moran_I_knn

Description

This function allows to compute the Moran’s Index autocorrelation coefficient for a given feature used in the dimensionality reduction technique, for different levels of the parameter k which corresponds to the number of samples to consider for the samples neighborhood definition. The MI values are computed using the Moran.I function from the R package ape.

Usage

moran_I_knn(expr_data , spatial_data, listK)

Arguments

• expr_data: matrix containing, for each sample (in rows), the values of the features (in columns) for which the MI values will be calculated

• spatial_data: matrix containing the coordinates of each sample in the projection used to define the samples neighborhood

• listK: vector listing the k values corresponding to the number of samples considered to define samples neighborhood

Value

• MI_array: 3D array containing the MI values and their associated p-values for each feature (in columns), and each k level (in rows).