Best Subset Solution Path for Linear Dimension Reduction Models using Continuous Optimization Article Swipe
Benoît Liquet
,
Sarat Moka
,
Samuel Müller
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2403.20007
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2403.20007
The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper, we focus on two multivariate statistical methods: principal components analysis and partial least squares. Both approaches are popular linear dimension-reduction methods with numerous applications in several fields including in genomics, biology, environmental science, and engineering. In particular, these approaches build principal components, new variables that are combinations of all the original variables. A main drawback of principal components is the difficulty to interpret them when the number of variables is large. To define principal components from the most relevant variables, we propose to cast the best subset solution path method into principal component analysis and partial least square frameworks. We offer a new alternative by exploiting a continuous optimization algorithm for best subset solution path. Empirical studies show the efficacy of our approach for providing the best subset solution path. The usage of our algorithm is further exposed through the analysis of two real datasets. The first dataset is analyzed using the principle component analysis while the analysis of the second dataset is based on partial least square framework.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2403.20007
- https://arxiv.org/pdf/2403.20007
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4393399276
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4393399276Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2403.20007Digital Object Identifier
- Title
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Best Subset Solution Path for Linear Dimension Reduction Models using Continuous OptimizationWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-03-29Full publication date if available
- Authors
-
Benoît Liquet, Sarat Moka, Samuel MüllerList of authors in order
- Landing page
-
https://arxiv.org/abs/2403.20007Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2403.20007Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2403.20007Direct OA link when available
- Concepts
-
Dimension (graph theory), Reduction (mathematics), Path (computing), Dimensionality reduction, Mathematics, Mathematical optimization, Applied mathematics, Algorithm, Computer science, Combinatorics, Artificial intelligence, Geometry, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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