Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Region of Convergence01:17

Region of Convergence

The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write numerous physical laws...
Central Limit Theorem01:14

Central Limit Theorem

The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
Convergence of Fourier Series01:21

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...
Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Curvature and tangential deflection of discrete arcs: a theory based on the commutator of scatter matrix pairs and its application to vertex detection in planar shape data.

IEEE transactions on pattern analysis and machine intelligence·2011
Same author

Efficient Implementation of the Fuzzy c-Means Clustering Algorithms.

IEEE transactions on pattern analysis and machine intelligence·2011
Same author

Some new indexes of cluster validity.

IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society·2008
Same author

Presupervised and post-supervised prototype classifier design.

IEEE transactions on neural networks·2008
Same author

Dynamic image sequence analysis using fuzzy measures.

IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society·2008
Same author

Fuzzy c-means clustering of incomplete data.

IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society·2008
Same journal

HardFlow: Hard-Constrained Sampling for Flow-Matching Models Via Trajectory Optimization.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Industrial Brain: Self-Evolving Neuro-Symbolic Autonomy with Causal Resilience for Cyber-Physical Systems.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Adaptive Hardness-Driven Dictionary Distillation for Incomplete Streaming View Clustering.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Mixture of Global and Local Experts with Diffusion Transformer for Controllable Face Generation.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Task-KV: Task-aware KV Cache Optimization via Semantic Differentiation of Attention Heads.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Achieving Text-based Person Retrieval with Any Granularity.

IEEE transactions on pattern analysis and machine intelligence·2026
See all related articles

Related Experiment Video

Updated: May 23, 2026

Determination of Aggregate Surface Morphology at the Interfacial Transition Zone (ITZ)
08:59

Determination of Aggregate Surface Morphology at the Interfacial Transition Zone (ITZ)

Published on: December 16, 2019

A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms.

J C Bezdek1

  • 1Department of Mathematics, Utah State University, Logan, UT 84322.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|April 14, 2012
PubMed
Summary
This summary is machine-generated.

This study establishes the convergence of fuzzy ISODATA clustering algorithms. These algorithms are proven to reliably converge to a local minimum for generalized least squares objective functions.

More Related Videos

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Related Experiment Videos

Last Updated: May 23, 2026

Determination of Aggregate Surface Morphology at the Interfacial Transition Zone (ITZ)
08:59

Determination of Aggregate Surface Morphology at the Interfacial Transition Zone (ITZ)

Published on: December 16, 2019

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Area of Science:

  • Computer Science
  • Data Science
  • Machine Learning

Background:

  • Clustering algorithms are fundamental in data analysis.
  • Fuzzy ISODATA algorithms are widely used but their convergence properties require rigorous proof.
  • Understanding convergence is crucial for reliable data partitioning.

Purpose of the Study:

  • To establish the convergence of fuzzy ISODATA clustering algorithms.
  • To provide theoretical guarantees for the termination of these iterative procedures.
  • To analyze the convergence behavior concerning the generalized least squares objective functional.

Main Methods:

  • Utilizing Zangwill's convergence theory.
  • Applying Picard iteration analysis to fuzzy ISODATA sequences.
  • Examining the properties of the generalized least squares objective functional.

Main Results:

  • The convergence of fuzzy ISODATA algorithms is mathematically established.
  • Arbitrary sequences generated by these algorithms are proven to terminate at a local minimum.
  • Guaranteed convergence to a local minimum of the objective functional is demonstrated.

Conclusions:

  • Fuzzy ISODATA algorithms offer reliable convergence properties.
  • The theoretical framework confirms the stability and predictability of these clustering methods.
  • This work provides a foundational understanding for the application of fuzzy ISODATA in complex datasets.