Skip to main content
bioRxiv
  • Home
  • About
  • Submit
  • ALERTS / RSS
Advanced Search
New Results

Pairwise Relative Distance (PRED) is an intuitive and robust metric for assessing vector similarity and class separability

View ORCID ProfileAarush Mohit Mittal, View ORCID ProfileAndrew C. Lin, View ORCID ProfileNitin Gupta
doi: https://doi.org/10.1101/2021.08.13.456194
Aarush Mohit Mittal
1Department of Biological Sciences and Bioengineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • ORCID record for Aarush Mohit Mittal
Andrew C. Lin
2Department of Biomedical Science, University of Sheffield, Firth Court, Western Bank, Sheffield S10 2TN, UK
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • ORCID record for Andrew C. Lin
Nitin Gupta
1Department of Biological Sciences and Bioengineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
3Mehta Family Center for Engineering in Medicine, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • ORCID record for Nitin Gupta
  • For correspondence: guptan@iitk.ac.in
  • Abstract
  • Full Text
  • Info/History
  • Metrics
  • Supplementary material
  • Data/Code
  • Preview PDF
Loading

Abstract

Scientific studies often require assessment of similarity between ordered sets of values. Each set, containing one value for every dimension or class of data, can be conveniently represented as a vector. The commonly used metrics for vector similarity include angle-based metrics, such as cosine similarity or Pearson correlation, which compare the relative patterns of values, and distance-based metrics, such as the Euclidean distance, which compare the magnitudes of values. Here we evaluate a newly proposed metric, pairwise relative distance (PRED), which considers both relative patterns and magnitudes to provide a single measure of vector similarity. PRED essentially reveals whether the vectors are so similar that their values across the classes are separable. By comparing PRED to other common metrics in a variety of applications, we show that PRED provides a stable chance level irrespective of the number of classes, is invariant to global translation and scaling operations on data, has high dynamic range and low variability in handling noisy data, and can handle multi-dimensional data, as in the case of vectors containing temporal or population responses for each class. We also found that PRED can be adapted to function as a reliable metric of class separability even for datasets that lack the vector structure and simply contain multiple values for each class.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • https://github.com/neuralsystems/PRED

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
Back to top
PreviousNext
Posted August 15, 2021.
Download PDF

Supplementary Material

Data/Code
Email

Thank you for your interest in spreading the word about bioRxiv.

NOTE: Your email address is requested solely to identify you as the sender of this article.

Enter multiple addresses on separate lines or separate them with commas.
Pairwise Relative Distance (PRED) is an intuitive and robust metric for assessing vector similarity and class separability
(Your Name) has forwarded a page to you from bioRxiv
(Your Name) thought you would like to see this page from the bioRxiv website.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Share
Pairwise Relative Distance (PRED) is an intuitive and robust metric for assessing vector similarity and class separability
Aarush Mohit Mittal, Andrew C. Lin, Nitin Gupta
bioRxiv 2021.08.13.456194; doi: https://doi.org/10.1101/2021.08.13.456194
Digg logo Reddit logo Twitter logo Facebook logo Google logo LinkedIn logo Mendeley logo
Citation Tools
Pairwise Relative Distance (PRED) is an intuitive and robust metric for assessing vector similarity and class separability
Aarush Mohit Mittal, Andrew C. Lin, Nitin Gupta
bioRxiv 2021.08.13.456194; doi: https://doi.org/10.1101/2021.08.13.456194

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
  • Tweet Widget
  • Facebook Like
  • Google Plus One

Subject Area

  • Neuroscience
Subject Areas
All Articles
  • Animal Behavior and Cognition (3683)
  • Biochemistry (7762)
  • Bioengineering (5658)
  • Bioinformatics (21219)
  • Biophysics (10544)
  • Cancer Biology (8151)
  • Cell Biology (11895)
  • Clinical Trials (138)
  • Developmental Biology (6727)
  • Ecology (10385)
  • Epidemiology (2065)
  • Evolutionary Biology (13833)
  • Genetics (9685)
  • Genomics (13047)
  • Immunology (8116)
  • Microbiology (19922)
  • Molecular Biology (7820)
  • Neuroscience (42930)
  • Paleontology (318)
  • Pathology (1276)
  • Pharmacology and Toxicology (2255)
  • Physiology (3346)
  • Plant Biology (7201)
  • Scientific Communication and Education (1309)
  • Synthetic Biology (1998)
  • Systems Biology (5526)
  • Zoology (1126)