no code implementations • 18 Aug 2023 • Mieczysław A. Kłopotek, Bartłmiej Starosta, Sławomir T. Wierzchoń
Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian.
no code implementations • 7 Aug 2023 • Mieczysław A. Kłopotek
We hypothesise that this clash is due to the not explicated expectation that the data themselves should have the property of being clusterable in order to expect the algorithm clustering hem to fit a clustering axiomatic system.
no code implementations • 2 Aug 2023 • Mieczysław A. Kłopotek
This paper investigates the capability of correctly recovering well-separated clusters by various brands of the $k$-means algorithm.
no code implementations • 1 Aug 2023 • Bartłomiej Starosta, Mieczysław A. Kłopotek, Sławomir T. Wierzchoń
It is based on showing (approximate) equivalence of combinatorial Laplacian embedding, $K$-embedding (proposed in this paper) and term vector space embedding.
no code implementations • 30 Nov 2022 • Mieczysław A. Kłopotek
Kleinberg's axioms for distance based clustering proved to be contradictory.
no code implementations • 27 Oct 2022 • Mieczysław A. Kłopotek, Robert A. Kłopotek
The paper points at the grieving problems implied by the richness axiom in the Kleinberg's axiomatic system and suggests resolutions.
no code implementations • 19 Feb 2022 • Mieczysław A. Kłopotek
This note introduces a novel clustering preserving transformation of cluster sets obtained from $k$-means algorithm.
no code implementations • 15 Jun 2020 • Mieczysław A. Kłopotek
It is demonstrated that the p-d-separation within the pog is equivalent to d-separation in all derived dags.
no code implementations • 25 May 2020 • Mieczysław A. Kłopotek
It applies general conditional belief functions.
no code implementations • 28 Sep 2019 • Mieczysław A. Kłopotek
It is proven, by example, that the version of $k$-means with random initialization does not have the property probabilistic k-richness.
no code implementations • 26 Sep 2019 • Mieczysław A. Kłopotek, Sławomir T. Wierzchoń
Valuation-Based~System can represent knowledge in different domains including probability theory, Dempster-Shafer theory and possibility theory.
no code implementations • 14 Dec 2018 • Andrzej Matuszewski, Mieczysław A. Kłopotek
One important obstacle in applying Dempster-Shafer Theory (DST) is its relationship to frequencies.
no code implementations • 7 Dec 2018 • Mieczysław A. Kłopotek, Sławomir T. Wierzchoń
Mathematical Theory of Evidence (MTE), a foundation for reasoning under partial ignorance, is blamed to leave frequencies outside (or aside of) its framework.
no code implementations • 30 Nov 2018 • Mieczysław A. Kłopotek
The paper gives an overview of the problems and methods of recovery of structure and motion parameters of rigid bodies from multiframes.
no code implementations • 6 Jun 2018 • Mieczysław A. Kłopotek
A number of algorithms exists for decomposition of probabilistic joint belief distribution into a bayesian (belief) network from data.
no code implementations • 30 May 2018 • Mieczysław A. Kłopotek
Fundamental reason for failure of this algorithm is the temporary introduction of non-real links between nodes of the network with the intention of later removal.
no code implementations • 13 Jul 2017 • Mieczysław A. Kłopotek
Hidden variables are well known sources of disturbance when recovering belief networks from data based only on measurable variables.
no code implementations • 13 Jul 2017 • Mieczysław A. Kłopotek
It excludes especially so-called probabilistic belief functions.
no code implementations • 12 Jul 2017 • Mieczysław A. Kłopotek
On the other hand, though Shenoy and Shafer's hypergraphs can explicitly represent bayesian network factorization of bayesian belief functions, they disclaim any need for representation of independence of variables in belief functions.
no code implementations • 12 Jul 2017 • Mieczysław A. Kłopotek
One of the most important open questions seems to be the relationship between frequencies and the Mathematical Theory of Evidence.
no code implementations • 30 Jun 2017 • Mieczysław A. Kłopotek
This paper proposes a new algorithm for recovery of belief network structure from data handling hidden variables.
no code implementations • 8 Jun 2017 • Mieczysław A. Kłopotek, Andrzej Matuszewski
Weaknesses of various proposals of probabilistic interpretation of MTE belief functions are demonstrated.
no code implementations • 8 Jun 2017 • Andrzej Matuszewski, Mieczysław A. Kłopotek
The conditioning in the Dempster-Shafer Theory of Evidence has been defined (by Shafer \cite{Shafer:90} as combination of a belief function and of an "event" via Dempster rule.
no code implementations • 11 May 2017 • Mieczysław A. Kłopotek
It is demonstrated that no increase in the number of points may lead to recovery of structure and motion parameters from two frames only.
no code implementations • 24 Apr 2017 • Mieczysław A. Kłopotek
We define the notion of a well-clusterable data set combining the point of view of the objective of $k$-means clustering algorithm (minimising the centric spread of data elements) and common sense (clusters shall be separated by gaps).
no code implementations • 18 Apr 2017 • Mieczysław A. Kłopotek
In this paper we would like to deny the results of Wang et al. raising two fundamental claims: * A line does not contribute anything to recognition of motion parameters from two images * Four traceable points are not sufficient to recover motion parameters from two perspective To be constructive, however, we show that four traceable points are sufficient to recover motion parameters from two frames under orthogonal projection and that five points are sufficient to simplify the solution of the two-frame problem under orthogonal projection to solving a linear equation system.
no code implementations • 12 Apr 2017 • Mieczysław A. Kłopotek
This paper is devoted to expressiveness of hypergraphs for which uncertainty propagation by local computations via Shenoy/Shafer method applies.
no code implementations • 11 Apr 2017 • Mieczysław A. Kłopotek
Fundamental discrepancy between first order logic and statistical inference (global versus local properties of universe) is shown to be the obstacle for integration of logic and probability in L. p. logic of Bacchus.
no code implementations • 11 Apr 2017 • Mieczysław A. Kłopotek
It discusses also possibility of simplification of reconstruction of flat curves moving free for prospective projections.
no code implementations • 8 Apr 2017 • Mieczysław A. Kłopotek, Sławomir T. Wierzchoń
The interpretation has the property that Given a definition of the belief measure of objects in the interpretation domain we can perform operations in this domain and the measure of the resulting object is derivable from measures of component objects via belief operator.
no code implementations • 4 Mar 2017 • Mieczysław A. Kłopotek
We define also conditions for which clusterability property of the original space is transmitted to the projected space, so that special case algorithms for the original space are also applicable in the projected space.
no code implementations • 20 Feb 2017 • Mieczysław A. Kłopotek
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.
no code implementations • 19 Jan 2017 • Mieczysław A. Kłopotek
This paper corrects the proof of the Theorem 2 from the Gower's paper \cite[page 5]{Gower:1982} as well as corrects the Theorem 7 from Gower's paper \cite{Gower:1986}.
no code implementations • 16 Jan 2017 • Piotr Borkowski, Krzysztof Ciesielski, Mieczysław A. Kłopotek
In this paper we propose a new document classification method, bridging discrepancies (so-called semantic gap) between the training set and the application sets of textual data.
no code implementations • 10 May 2016 • Paweł Łoziński, Dariusz Czerski, Mieczysław A. Kłopotek
Pattern-based methods of IS-A relation extraction rely heavily on so called Hearst patterns.