Insightful dimensionality reduction with very low rank variable subsets

Bruno Ordozgoiti, Sachith Pai, Marta Kolczynska

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Abstract

Dimensionality reduction techniques can be employed to produce robust, cost-effective predictive models, and to enhance interpretability in exploratory data analysis. However, the models produced by many of these methods are formulated in terms of abstract factors or are too high-dimensional to facilitate insight and fit within low computational budgets. In this paper we explore an alternative approach to interpretable dimensionality reduction. Given a data matrix, we study the following question: are there subsets of variables that can be primarily explained by a single factor? We formulate this challenge as the problem of finding submatrices close to rank one. Despite its potential, this topic has not been sufficiently addressed in the literature, and there exist virtually no algorithms for this purpose that are simultaneously effective, efficient and scalable. We formalize the task as two problems which we characterize in terms of computational complexity, and propose efficient, scalable algorithms with approximation guarantees. Our experiments demonstrate how our approach can produce insightful findings in data, and show our algorithms to be superior to strong baselines.

Original languageEnglish
Title of host publicationProceedings of the Web Conference, WWW 2021
PublisherACM
Pages3066-3075
Number of pages10
ISBN (Electronic)9781450383127
DOIs
Publication statusPublished - 3 Jun 2021
MoE publication typeA4 Article in a conference publication
EventThe Web Conference - Ljubljana, Slovenia
Duration: 19 Apr 202123 Apr 2021

Conference

ConferenceThe Web Conference
Abbreviated titleWWW
Country/TerritorySlovenia
CityLjubljana
Period19/04/202123/04/2021

Keywords

  • Data mining
  • Dimensionality reduction
  • Explainability
  • Variable selection

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