English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Even with the rise in popularity of over-parameterized models, simpledimensionality reduction and clustering methods, such as PCA and k-means, arestill routinely used in an amazing variety of settings. A primary reason is thecombination of simplicity, interpretability and computational efficiency. Thefocus of this article is on improving upon PCA and k-means, by allowingnon-linear relations in the data and more flexible cluster shapes, withoutsacrificing the key advantages. The key contribution is a new framework forPrincipal Elliptical Analysis (PEA), defining a simple and computationallyefficient alternative to PCA that fits the best elliptical approximationthrough the data. We provide theoretical guarantees on the proposed PEAalgorithm using Vapnik-Chervonenkis (VC) theory to show strong consistency anduniform concentration bounds. Toy experiments illustrate the performance ofPEA, and the ability to adapt to non-linear structure and complex clustershapes. In a rich variety of real data clustering applications, PEA is shown todo as well as k-means for simple datasets, while dramatically improvingperformance in more complex settings.

Principal Ellipsoid Analysis (PEA): Efficient non-linear dimension reduction & clustering