Geometric insights into support vector machine behavior using the KKT conditions Article Swipe
Iain Carmichael
,
J. S. Marron
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1214/21-ejs1902
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1214/21-ejs1902
The support vector machine (SVM) is a powerful and widely used classification algorithm. This paper uses the Karush-Kuhn-Tucker conditions to provide rigorous mathematical proof for new insights into the behavior of SVM. These insights provide unexpected relationships between SVM and two other linear classifiers: the mean difference and the maximal data piling direction. For example, we show that in many cases SVM can be viewed as a cropped version of these classifiers. By carefully exploring these connections we show how SVM tuning behavior is affected by data characteristics including: balanced vs. unbalanced classes, low vs. high dimension, separable vs. non-separable data. These results provide further insights into tuning SVM via cross-validation by explaining observed pathological behavior and motivating improved cross-validation methodology.
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Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1214/21-ejs1902
- https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-15/issue-2/Geometric-insights-into-support-vector-machine-behavior-using-the-KKT/10.1214/21-EJS1902.pdf
- OA Status
- gold
- Cited By
- 7
- References
- 41
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2605494714
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2605494714Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1214/21-ejs1902Digital Object Identifier
- Title
-
Geometric insights into support vector machine behavior using the KKT conditionsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-01-01Full publication date if available
- Authors
-
Iain Carmichael, J. S. MarronList of authors in order
- Landing page
-
https://doi.org/10.1214/21-ejs1902Publisher landing page
- PDF URL
-
https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-15/issue-2/Geometric-insights-into-support-vector-machine-behavior-using-the-KKT/10.1214/21-EJS1902.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-15/issue-2/Geometric-insights-into-support-vector-machine-behavior-using-the-KKT/10.1214/21-EJS1902.pdfDirect OA link when available
- Concepts
-
Karush–Kuhn–Tucker conditions, Mathematics, Support vector machine, Artificial intelligence, Machine learning, Mathematical optimization, Computer scienceTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
7Total citation count in OpenAlex
- Citations by year (recent)
-
2022: 2, 2021: 2, 2020: 1, 2019: 1, 2017: 1Per-year citation counts (last 5 years)
- References (count)
-
41Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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