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Computer Science > Machine Learning

arXiv:2309.01030 (cs)
[Submitted on 2 Sep 2023 (v1), last revised 30 Dec 2023 (this version, v2)]

Title:Online Adaptive Mahalanobis Distance Estimation

Authors:Lianke Qin, Aravind Reddy, Zhao Song
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Abstract:Mahalanobis metrics are widely used in machine learning in conjunction with methods like $k$-nearest neighbors, $k$-means clustering, and $k$-medians clustering. Despite their importance, there has not been any prior work on applying sketching techniques to speed up algorithms for Mahalanobis metrics. In this paper, we initiate the study of dimension reduction for Mahalanobis metrics. In particular, we provide efficient data structures for solving the Approximate Distance Estimation (ADE) problem for Mahalanobis distances. We first provide a randomized Monte Carlo data structure. Then, we show how we can adapt it to provide our main data structure which can handle sequences of \textit{adaptive} queries and also online updates to both the Mahalanobis metric matrix and the data points, making it amenable to be used in conjunction with prior algorithms for online learning of Mahalanobis metrics.
Comments: IEEE BigData 2023
Subjects: Machine Learning (cs.LG)
Cite as: arXiv:2309.01030 [cs.LG]
  (or arXiv:2309.01030v2 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2309.01030

Submission history

From: Lianke Qin [view email]
[v1] Sat, 2 Sep 2023 22:19:24 UTC (109 KB)
[v2] Sat, 30 Dec 2023 03:11:25 UTC (190 KB)
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