Summary of Canonical Variates in Wasserstein Metric Space, by Jia Li and Lin Lin
Canonical Variates in Wasserstein Metric Space
by Jia Li, Lin Lin
First submitted to arxiv on: 24 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper presents a novel approach to classify instances characterized by distributions on a vector space, rather than singular points. The authors employ the Wasserstein metric to measure distances between these distributions and use distance-based classification algorithms such as k-nearest neighbors, k-means, and pseudo-mixture modeling. To enhance classification accuracy, they introduce dimension reduction within the Wasserstein metric space, grounded in the principle of maximizing Fisher’s ratio. This is achieved through an iterative algorithm that alternates between optimal transport and maximization steps. Experimental results demonstrate that this method outperforms well-established algorithms and exhibits robustness against variations in data representations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us better understand how to group things together based on patterns they follow. Instead of looking at each thing individually, we look at the patterns or distributions they fit into. The authors use a special way of measuring distances between these patterns called Wasserstein metric. They then use this measurement to improve how well things are grouped together. To do this, they shrink down the big pattern space to make it easier to work with. This is done by maximizing something called Fisher’s ratio. The authors tested their method and found that it works better than other methods and can handle different ways of looking at patterns. |
Keywords
» Artificial intelligence » Classification » K means » Vector space
