Supervised Kernel PCA For Longitudinal Data Article Swipe
Patrick Staples
,
Min Ouyang
,
Robert F. Dougherty
,
Gregory Ryslik
,
Paul Dagum
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1808.06638
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1808.06638
In statistical learning, high covariate dimensionality poses challenges for robust prediction and inference. To address this challenge, supervised dimension reduction is often performed, where dependence on the outcome is maximized for a selected covariate subspace with smaller dimensionality. Prevalent dimension reduction techniques assume data are $i.i.d.$, which is not appropriate for longitudinal data comprising multiple subjects with repeated measurements over time. In this paper, we derive a decomposition of the Hilbert-Schmidt Independence Criterion as a supervised loss function for longitudinal data, enabling dimension reduction between and within clusters separately, and propose a dimensionality-reduction technique, $sklPCA$, that performs this decomposed dimension reduction. We also show that this technique yields superior model accuracy compared to the model it extends.
Related Topics
Concepts
Dimensionality reduction
Covariate
Sufficient dimension reduction
Dimension (graph theory)
Kernel (algebra)
Artificial intelligence
Subspace topology
Mathematics
Curse of dimensionality
Inference
Pattern recognition (psychology)
Sliced inverse regression
Reduction (mathematics)
Clustering high-dimensional data
Computer science
Statistics
Cluster analysis
Pure mathematics
Combinatorics
Geometry
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1808.06638
- https://arxiv.org/pdf/1808.06638
- OA Status
- green
- Cited By
- 1
- References
- 2
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2888614774
All OpenAlex metadata
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https://openalex.org/W2888614774Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1808.06638Digital Object Identifier
- Title
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Supervised Kernel PCA For Longitudinal DataWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2018Year of publication
- Publication date
-
2018-08-20Full publication date if available
- Authors
-
Patrick Staples, Min Ouyang, Robert F. Dougherty, Gregory Ryslik, Paul DagumList of authors in order
- Landing page
-
https://arxiv.org/abs/1808.06638Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1808.06638Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1808.06638Direct OA link when available
- Concepts
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Dimensionality reduction, Covariate, Sufficient dimension reduction, Dimension (graph theory), Kernel (algebra), Artificial intelligence, Subspace topology, Mathematics, Curse of dimensionality, Inference, Pattern recognition (psychology), Sliced inverse regression, Reduction (mathematics), Clustering high-dimensional data, Computer science, Statistics, Cluster analysis, Pure mathematics, Combinatorics, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
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2019: 1Per-year citation counts (last 5 years)
- References (count)
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2Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.also | 102 |
| abstract_inverted_index.data | 43, 52 |
| abstract_inverted_index.high | 3 |
| abstract_inverted_index.loss | 76 |
| abstract_inverted_index.over | 59 |
| abstract_inverted_index.show | 103 |
| abstract_inverted_index.that | 95, 104 |
| abstract_inverted_index.this | 15, 62, 97, 105 |
| abstract_inverted_index.with | 35, 56 |
| abstract_inverted_index.data, | 80 |
| abstract_inverted_index.model | 109, 114 |
| abstract_inverted_index.often | 21 |
| abstract_inverted_index.poses | 6 |
| abstract_inverted_index.time. | 60 |
| abstract_inverted_index.where | 23 |
| abstract_inverted_index.which | 46 |
| abstract_inverted_index.assume | 42 |
| abstract_inverted_index.derive | 65 |
| abstract_inverted_index.paper, | 63 |
| abstract_inverted_index.robust | 9 |
| abstract_inverted_index.within | 86 |
| abstract_inverted_index.yields | 107 |
| abstract_inverted_index.address | 14 |
| abstract_inverted_index.between | 84 |
| abstract_inverted_index.outcome | 27 |
| abstract_inverted_index.propose | 90 |
| abstract_inverted_index.smaller | 36 |
| abstract_inverted_index.accuracy | 110 |
| abstract_inverted_index.clusters | 87 |
| abstract_inverted_index.compared | 111 |
| abstract_inverted_index.enabling | 81 |
| abstract_inverted_index.extends. | 116 |
| abstract_inverted_index.function | 77 |
| abstract_inverted_index.multiple | 54 |
| abstract_inverted_index.performs | 96 |
| abstract_inverted_index.repeated | 57 |
| abstract_inverted_index.selected | 32 |
| abstract_inverted_index.subjects | 55 |
| abstract_inverted_index.subspace | 34 |
| abstract_inverted_index.superior | 108 |
| abstract_inverted_index.$i.i.d.$, | 45 |
| abstract_inverted_index.$sklPCA$, | 94 |
| abstract_inverted_index.Criterion | 72 |
| abstract_inverted_index.Prevalent | 38 |
| abstract_inverted_index.covariate | 4, 33 |
| abstract_inverted_index.dimension | 18, 39, 82, 99 |
| abstract_inverted_index.learning, | 2 |
| abstract_inverted_index.maximized | 29 |
| abstract_inverted_index.reduction | 19, 40, 83 |
| abstract_inverted_index.technique | 106 |
| abstract_inverted_index.challenge, | 16 |
| abstract_inverted_index.challenges | 7 |
| abstract_inverted_index.comprising | 53 |
| abstract_inverted_index.decomposed | 98 |
| abstract_inverted_index.dependence | 24 |
| abstract_inverted_index.inference. | 12 |
| abstract_inverted_index.performed, | 22 |
| abstract_inverted_index.prediction | 10 |
| abstract_inverted_index.reduction. | 100 |
| abstract_inverted_index.supervised | 17, 75 |
| abstract_inverted_index.technique, | 93 |
| abstract_inverted_index.techniques | 41 |
| abstract_inverted_index.appropriate | 49 |
| abstract_inverted_index.separately, | 88 |
| abstract_inverted_index.statistical | 1 |
| abstract_inverted_index.Independence | 71 |
| abstract_inverted_index.longitudinal | 51, 79 |
| abstract_inverted_index.measurements | 58 |
| abstract_inverted_index.decomposition | 67 |
| abstract_inverted_index.dimensionality | 5 |
| abstract_inverted_index.Hilbert-Schmidt | 70 |
| abstract_inverted_index.dimensionality. | 37 |
| abstract_inverted_index.dimensionality-reduction | 92 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile |