7 citations · 28 across the 48 of their papers we have counts for
11 papers · 1 filter
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…
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…
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.
An Aposteriorical Clusterability Criterion for -Means++ and Simplicity of Clustering
Mieczysław A. Kłopotek
We define the notion of a well-clusterable data set combining the point of view of the objective of -means clustering algorithm (minimising the centric spread of data elements)…
On the Consistency of -means++ algorithm
Mieczysław A. Kłopotek
We prove in this paper that the expected value of the objective function of the -means++ algorithm for samples converges to population expected value. As -means++, for sample…
On the Discrepancy Between Kleinberg's Clustering Axioms and -Means Clustering Algorithm Behavior
Robert Kłopotek, Mieczysław Kłopotek
This paper investigates the validity of Kleinberg's axioms for clustering functions with respect to the quite popular clustering algorithm called -means. While Kleinberg's axiom…
Validity of Clusters Produced By kernel--means With Kernel-Trick
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}. The first co…