7 citations · 28 across the 48 of their papers we have counts for
53 papers
Eigenvalue-based Incremental Spectral Clustering
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 comb…
Wide Gaps and Clustering Axioms
Mieczysław A. Kłopotek
The widely applied k-means algorithm produces clusterings that violate our expectations with respect to high/low similarity/density and is in conflict with Kleinberg's axiomatic sy…
Are Easy Data Easy (for K-Means)
Mieczysław A. Kłopotek
This paper investigates the capability of correctly recovering well-separated clusters by various brands of the -means algorithm. The concept of well-separatedness used here is…
Explainable Graph Spectral Clustering of Text Documents
Bartłomiej Starosta, Mieczysław A. Kłopotek, Sławomir T. Wierzchoń
Spectral clustering methods are known for their ability to represent clusters of diverse shapes, densities etc. However, results of such algorithms, when applied e.g. to text docum…
High-Dimensional Wide Gap -Means Versus Clustering Axioms
Mieczysław A. Kłopotek
Kleinberg's axioms for distance based clustering proved to be contradictory. Various efforts have been made to overcome this problem. Here we make an attempt to handle the issue by…
How To Overcome Richness Axiom Fallacy
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. The richness induces learnability problem in g…
Towards Continuous Consistency Axiom
Mieczyslaw A. Klopotek, Robert A. Klopotek
Development of new algorithms in the area of machine learning, especially clustering, comparative studies of such algorithms as well as testing according to software engineering pr…
A Clustering Preserving Transformation for k-Means Algorithm Output
Mieczysław A. Kłopotek
This note introduces a novel clustering preserving transformation of cluster sets obtained from -means algorithm. This transformation may be used to generate new labeled data{}s…
p-d-Separation -- A Concept for Expressing Dependence/Independence Relations in Causal Networks
Mieczysław A. Kłopotek
Spirtes, Glymour and Scheines formulated a Conjecture that a direct dependence test and a head-to-head meeting test would suffice to construe directed acyclic graph decompositions…
On Irrelevance of Attributes in Flexible Prediction
Mieczyslaw A. Klopotek, Andrzej Matuszewski
This paper analyses properties of conceptual hierarchy obtained via incremental concept formation method called "flexible prediction" in order to determine what kind of "relevance"…
Non-Destructive Sample Generation From Conditional Belief Functions
Mieczysław A. Kłopotek
This paper presents a new approach to generate samples from conditional belief functions for a restricted but non trivial subset of conditional belief functions. It assumes the fac…
A Note On k-Means Probabilistic Poverty
Mieczysław A. Kłopotek
It is proven, by example, that the version of -means with random initialization does not have the property probabilistic k-richness.
Query Optimization Properties of Modified VBS
Mieczysław A. Kłopotek, Sławomir T. Wierzchoń
Valuation-Based~System can represent knowledge in different domains including probability theory, Dempster-Shafer theory and possibility theory. More recent studies show that the f…
Reasoning and Facts Explanation in Valuation Based Systems
S. T. Wierzchoń, M. A. Kłopotek, M. Michalewicz
In the literature, the optimization problem to identify a set of composite hypotheses H, which will yield the largest where a composite hypothesis is an instantiatio…
Factorization of Dempster-Shafer Belief Functions Based on Data
Andrzej Matuszewski, Mieczysław A. Kłopotek
One important obstacle in applying Dempster-Shafer Theory (DST) is its relationship to frequencies. In particular, there exist serious difficulties in finding factorizations of bel…
Rigid Body Structure and Motion From Two-Frame Point-Correspondences Under Perspective Projection
Mieczysław A. Kłopotek
This paper is concerned with possibility of recovery of motion and structure parameters from multiframes under perspective projection when only points on a rigid body are traced. F…
On Marginally Correct Approximations of Dempster-Shafer Belief Functions from Data
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. The seriousness of th…
Structure and Motion from Multiframes
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.
Reasoning From Data in the Mathematical Theory of Evidence
Mieczysław Kłopotek
Mathematical Theory of Evidence (MTE) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed…
Mathematical Theory of Evidence Versus Evidence
Mieczysław Kłopotek
This paper is concerned with the apparent greatest weakness of the Mathematical Theory of Evidence (MTE) of Shafer \cite{Shafer:76}, which has been strongly criticized by Wasserman…
Dempsterian-Shaferian Belief Network From Data
Mieczysław A. Kłopotek
Shenoy and Shafer {Shenoy:90} demonstrated that both for Dempster-Shafer Theory and probability theory there exists a possibility to calculate efficiently marginals of joint belief…
Too Fast Causal Inference under Causal Insufficiency
Mieczysław A. Kłopotek
Causally insufficient structures (models with latent or hidden variables, or with confounding etc.) of joint probability distributions have been subject of intense study not only i…
Fast Restricted Causal Inference
Mieczysław A. Kłopotek
Hidden variables are well known sources of disturbance when recovering belief networks from data based only on measurable variables. Hence models assuming existence of hidden varia…
On (Anti)Conditional Independence in Dempster-Shafer Theory
Mieczysław A. Kłopotek
This paper verifies a result of {Shenoy:94} concerning graphoidal structure of Shenoy's notion of independence for Dempster-Shafer theory of belief functions. Shenoy proved that hi…