Mittal, A.M. orcid.org/0000-0002-8633-3126, Lin, A.C. orcid.org/0000-0001-6310-9765 and Gupta, N. orcid.org/0000-0002-8408-3848 (Submitted: 2021) Pairwise Relative Distance (PRED) is an intuitive and robust metric for assessing vector similarity and class separability. [Preprint - bioRxiv] (Submitted)
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.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 The Author(s). This preprint is made available under a Creative Commons Attribution 4.0 International License. (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | Biotechnology |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Biosciences (Sheffield) |
Funding Information: | Funder Grant number EUROPEAN COMMISSION - HORIZON 2020 639489 BIOTECHNOLOGY AND BIOLOGICAL SCIENCES RESEARCH COUNCIL BB/S016031/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 10 Feb 2023 11:10 |
Last Modified: | 10 Feb 2023 11:10 |
Published Version: | http://dx.doi.org/10.1101/2021.08.13.456194 |
Status: | Submitted |
Publisher: | Cold Spring Harbor Laboratory |
Identification Number: | 10.1101/2021.08.13.456194 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:196145 |