Digital Library of Zielona Góra contains 63 052 digital objects
Object
Title: A feasible k-means kernel trick under non-Euclidean feature space
Contributor:
Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Group publication title:
Abstract:
This paper poses the question of whether or not the usage of the kernel trick is justified. We investigate it for the special case of its usage in the kernel k-means algorithm. Kernel-k-means is a clustering algorithm, allowing clustering data in a similar way to k-means when an embedding of data points into Euclidean space is not provided and instead a matrix of "distances" (dissimilarities) or similarities is available. The kernel trick allows us to by-pass the need of finding an embedding into Euclidean space. ; We show that the algorithm returns wrong results if the embedding actually does not exist. This means that the embedding must be found prior to the usage of the algorithm. If it is found, then the kernel trick is pointless. If it is not found, the distance matrix needs to be repaired. But the reparation methods require the construction of an embedding, which first makes the kernel trick pointless, because it is not needed, and second, the kernel-k-means may return different clusterings prior to repairing and after repairing so that the value of the clustering is questioned. ; In the paper, we identify a distance repairing method that produces the same clustering prior to its application and afterwards and does not need to be performed explicitly, so that the embedding does not need to be constructed explicitly. This renders the kernel trick applicable for kernel-k-means.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Resource Identifier:
DOI:
Pages:
Source:
AMCS, volume 30, number 4 (2020) ; click here to follow the link
Language:
License CC BY 4.0:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Digital Library of Zielona Góra > Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Digital Library of Zielona Góra > Repository > Types of work > Articles
- Digital Library of Zielona Góra > Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2020)
Last modified:
Jul 17, 2025
In our library since:
Jul 17, 2025
Number of object content hits:
9
All available object's versions:
https://zbc.uz.zgora.pl/publication/101261
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 30, number 1 (2020)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 30, number 2 (2020)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 30, number 3 (2020)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 30, number 4 (2020)
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| Edition name | Date |
|---|---|
| A feasible k-means kernel trick under non-Euclidean feature space | Jul 17, 2025 |
Objects Similar
Kłopotek, Mieczysław Korbicz, Józef (1951- ) - red. Uciński, Dariusz - red.
Lucińska, Małgorzata Wierzchoń, Sławomir T. Korbicz, Józef (1951- ) - red. Uciński, Dariusz - red.
Kulczycki, Piotr Charytanowicz, Małgorzata Korbicz, Józef (1951- ) - red. Uciński, Dariusz - red.
Frąckiewicz, Mariusz Palus, Henryk Korbicz, Józef (1951- ) - red. Uciński, Dariusz - red.
Malinowski, Paweł Ziembicki, Piotr Kuczyński, Tadeusz - red.
Hachaj, Tomasz Piekarczyk, Marcin Wąs, Jarosław Campagner, Andrea - ed. Lenz, Oliver Urs - ed. Xia, Shuyin - ed.
Jankowski, Norbert Korbicz, Józef (1951- ) - red. Uciński, Dariusz - red.
Leski, Jacek M. Kotas, Marian P. Korbicz, Józef (1951- ) - red. Uciński, Dariusz - red.
