Metric Multidimensional Scaling for Large Single-Cell Data Sets using Neural Networks

Abstract

Metric multidimensional scaling is one of the classical methods for embedding data into low-dimensional Euclidean space. It creates the low-dimensional embedding by approximately preserving the pairwise distances between the input points. However, current state-of-the-art approaches only scale to a few thousand data points. For larger data sets such as those occurring in single-cell RNA sequencing experiments, the running time becomes prohibitively large and thus alternative methods such as PCA are widely used instead. Here, we propose a neural network based approach for solving the metric multidimensional scaling problem that is orders of magnitude faster than previous state-of-the-art approaches, and hence scales to data sets with up to a few million cells. At the same time, it provides a non-linear mapping between high- and low-dimensional space that can place previously unseen cells in the same embedding.

Orthogonal outlier detection and dimension estimation for improved MDS embedding of biological datasets

“…We further evaluated DeCOr-MDS on single cell RNA-seq (scRNA-seq) data. In general, analyzing scRNA seq data requires dimensionality reduction for visualization (including MDS-based methods Canzar et al (2021) ; Senabouth et al (2019) ), and specific quality control procedures to mitigate various technical artifacts McCarthy et al (2017) ; Luecken and Theis (2019) . We applied our method as a potentially relevant tool for this purpose.…”

Well-Separated Pair Decompositions for High-Dimensional Datasets

“…For the implementation of a function f θ , I will use deep neural networks. The neural network approach for computing the metric MDS mapper has already been used in [9]. Inspired by the work of [5,10,11], I chose the following architecture with L = five fully connected layers of the form below: d − 500 − 500 − 2000 − d and d ∈ {2, 3}.…”