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pro vyhledávání: '"Mieczyslaw A. Klopotek"'
Autor:
Mieczyslaw A. Klopotek
Publikováno v:
Fundamenta Informaticae. 172:361-377
We prove in this paper that the expected value of the objective function of the $k$-means++ algorithm for samples converges to population expected value. As $k$-means++, for samples, provides with constant factor approximation for $k$-means objective
Autor:
Mieczyslaw A. Klopotek
Publikováno v:
Knowledge and Information Systems. 62:1961-2009
The widely discussed and applied Johnson–Lindenstrauss (JL) Lemma has an existential form saying that for each set of data points Q in n-dimensional space, there exists a transformation f into an $$n'$$n′-dimensional space ($$n'n′
Publikováno v:
Lecture Notes in Computer Science ISBN: 9783030594909
ISMIS
ISMIS
Kleinberg introduced an axiomatic system for clustering functions. Out of three axioms, he proposed two (scale invariance and consistency) are concerned with data transformations that should produce the same clustering under the same clustering funct
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8a275608e85a6f5d9ea574dc97de942b
https://doi.org/10.1007/978-3-030-59491-6_33
https://doi.org/10.1007/978-3-030-59491-6_33
Publikováno v:
IFIP Advances in Information and Communication Technology ISBN: 9783030491604
AIAI (1)
AIAI (1)
We present a novel justification why k-means clusters should be (hyper)ball-shaped ones. We show that the clusters must be ball-shaped to attain motion-consistency. If clusters are ball-shaped, one can derive conditions under which two clusters attai
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d825b5e5c328b68f7acc13a9112f10ce
https://doi.org/10.1007/978-3-030-49161-1_10
https://doi.org/10.1007/978-3-030-49161-1_10
Publikováno v:
Machine Learning, Optimization, and Data Science ISBN: 9783030375980
LOD
LOD
With Kleinberg’s axiomatic system for clustering, a discussion has been initiated, what kind of properties clustering algorithms should have and have not. As Ackerman et al. pointed out, the static properties studied by Kleinberg and other are not
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2b312a5fbc4e7686c88594906cbb8a96
https://doi.org/10.1007/978-3-030-37599-7_22
https://doi.org/10.1007/978-3-030-37599-7_22
Autor:
Mieczyslaw A. Klopotek
Publikováno v:
Lecture Notes in Computer Science ISBN: 9783319604374
ISMIS
ISMIS
This paper corrects the proof of the Theorem 2 from the Gower’s paper [1, p. 5]. The correction is needed in order to establish the existence of the kernel function used commonly in the kernel trick e.g. for k-means clustering algorithm, on the gro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f951199b9b6ed5203330a2e0b181a0b5
https://doi.org/10.1007/978-3-319-60438-1_10
https://doi.org/10.1007/978-3-319-60438-1_10