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

Conventional dimensionality reduction methods such as Multidimensional Scaling are prone to be sensitive to the presence of orthogonal outliers, leading to significant errors in the embedding. Here, we propose a robust MDS method, based on the geometry and statistics of simplices formed by data points, that allows to detect orthogonal outliers and subsequently reduce dimensionality.

Installation

Development and requirements

DeCOr-MDS has been developed using Python 3.8.

Code structure

DeCOr-MDS procedures are implemented in DeCOr_MDS.py. Experiment scripts are in exp_synthetic/, exp_cells/ and exp_hmp/. Experiment data is in data/.

Commands to regenerate results, figures are saved in outputs/.

Synthetic dataset

python3 exp_synthetic/test_synthetic_outlier_fraction.py

to generate Fig. 5, and

python3 exp_synthetic/test_synthetic_datasets.py

to generate the rest

Cell shape dataset

python3 exp_cells/test_cells_datasets.py 

HMP dataset

python3 exp_hmp/test_hmp_MDS_nSimplices.py 

scRNA-seq dataset

Run the jupyter notebook in exp_genomic/test_scRNAseq_Baron.ipynb