Algorithms for approximate subtropical matrix factorization Article Swipe
Sanjar Karaev
,
Pauli Miettinen
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1007/s10618-018-0599-1
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1007/s10618-018-0599-1
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for finding patterns from the data. Rather than using the standard algebra—and the summation of the rank-1 components to build the approximation of the original matrix—we use the subtropical algebra, which is an algebra over the nonnegative real values with the summation replaced by the maximum operator. Subtropical matrix factorizations allow "winner-takes-it-all" interpretations of the rank-1 components, revealing different structure than the normal (nonnegative) factorizations. We study the complexity and sparsity of the factorizations, and present a framework for finding low-rank subtropical factorizations. We present two specific algorithms, called Capricorn and Cancer, that are part of our framework. They can be used with data that has been corrupted with different types of noise, and with different error metrics, including the sum-of-absolute differences, Frobenius norm, and Jensen–Shannon divergence. Our experiments show that the algorithms perform well on data that has subtropical structure, and that they can find factorizations that are both sparse and easy to interpret.
Related Topics
Concepts
Matrix decomposition
Matrix (chemical analysis)
Non-negative matrix factorization
Factorization
Matrix norm
Dimensionality reduction
Rank (graph theory)
Mathematics
Computer science
Algebra over a field
Algorithm
Artificial intelligence
Eigenvalues and eigenvectors
Combinatorics
Pure mathematics
Physics
Composite material
Materials science
Quantum mechanics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1007/s10618-018-0599-1
- https://link.springer.com/content/pdf/10.1007/s10618-018-0599-1.pdf
- OA Status
- hybrid
- Cited By
- 8
- References
- 68
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2740287343
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2740287343Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1007/s10618-018-0599-1Digital Object Identifier
- Title
-
Algorithms for approximate subtropical matrix factorizationWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2018Year of publication
- Publication date
-
2018-12-18Full publication date if available
- Authors
-
Sanjar Karaev, Pauli MiettinenList of authors in order
- Landing page
-
https://doi.org/10.1007/s10618-018-0599-1Publisher landing page
- PDF URL
-
https://link.springer.com/content/pdf/10.1007/s10618-018-0599-1.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
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hybridOpen access status per OpenAlex
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https://link.springer.com/content/pdf/10.1007/s10618-018-0599-1.pdfDirect OA link when available
- Concepts
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Matrix decomposition, Matrix (chemical analysis), Non-negative matrix factorization, Factorization, Matrix norm, Dimensionality reduction, Rank (graph theory), Mathematics, Computer science, Algebra over a field, Algorithm, Artificial intelligence, Eigenvalues and eigenvectors, Combinatorics, Pure mathematics, Physics, Composite material, Materials science, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
8Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2024: 1, 2023: 2, 2022: 1, 2021: 1Per-year citation counts (last 5 years)
- References (count)
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68Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| referenced_works | https://openalex.org/W1594270709, https://openalex.org/W1683326984, https://openalex.org/W4230791737, https://openalex.org/W2039455169, https://openalex.org/W2017288758, https://openalex.org/W2133763708, https://openalex.org/W2136787567, https://openalex.org/W2107551402, https://openalex.org/W341186930, https://openalex.org/W2030229879, https://openalex.org/W2509841691, https://openalex.org/W2404400936, https://openalex.org/W4237506113, https://openalex.org/W2152557171, https://openalex.org/W4250661196, https://openalex.org/W2035080386, https://openalex.org/W2087414065, https://openalex.org/W2147152072, https://openalex.org/W4210869902, https://openalex.org/W2000827368, https://openalex.org/W2102760078, https://openalex.org/W2102536337, https://openalex.org/W139983096, https://openalex.org/W1783549032, https://openalex.org/W2089835799, https://openalex.org/W2512031891, https://openalex.org/W2327497498, https://openalex.org/W793192718, https://openalex.org/W1965137541, https://openalex.org/W1902027874, https://openalex.org/W2158146385, https://openalex.org/W2131782448, https://openalex.org/W2035922847, https://openalex.org/W4230289556, https://openalex.org/W2160342152, https://openalex.org/W2056857971, https://openalex.org/W2089079408, https://openalex.org/W2059745395, https://openalex.org/W206759535, https://openalex.org/W1832221731, https://openalex.org/W1998867519, https://openalex.org/W2084532411, https://openalex.org/W2277019236, https://openalex.org/W4229898513, https://openalex.org/W2124172487, https://openalex.org/W802370431, https://openalex.org/W2039127023, https://openalex.org/W2013029404, https://openalex.org/W1587663028, https://openalex.org/W2249347839, https://openalex.org/W1920066055, https://openalex.org/W2028660300, https://openalex.org/W1546001247, https://openalex.org/W2120270169, https://openalex.org/W1557235141, https://openalex.org/W53596869, https://openalex.org/W2122090912, https://openalex.org/W2059120410, https://openalex.org/W2920997011, https://openalex.org/W1643616905, https://openalex.org/W1246381107, https://openalex.org/W2497542973, https://openalex.org/W2798909945, https://openalex.org/W1578332044, https://openalex.org/W1512832987, https://openalex.org/W1506895146, https://openalex.org/W2118718620, https://openalex.org/W1991466857 |
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