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Related Experiment Video

Updated: Jun 28, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Convergence properties of a class of learning vector quantization algorithms.

E B Kosmatopoulos¹, M A Christodoulou

¹Dept. of Electron. and Comput. Eng., Tech. Univ. of Crete, Chania.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|January 1, 1996

Summary

This study mathematically proves that Learning Vector Quantization (LVQ) algorithms converge. By transforming LVQ into linear equations, convergence is demonstrated using stochastic Lyapunov stability arguments.

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Area of Science:

Machine Learning
Mathematical Analysis
Algorithm Convergence

Background:

Learning Vector Quantization (LVQ) is a pattern recognition algorithm.
Analyzing LVQ convergence is crucial for its reliable application.

Purpose of the Study:

To provide a rigorous mathematical proof of convergence for a class of LVQ algorithms.
To establish the theoretical underpinnings of LVQ algorithm stability.

Main Methods:

Mathematical analysis of LVQ algorithms.
Time-coordinate transformation to linear time-varying stochastic difference equations.
Application of stochastic Lyapunov stability arguments.

Main Results:

Demonstrated that LVQ algorithms can be represented as linear time-varying stochastic difference equations.
Proved the convergence of these LVQ algorithms under specific conditions.
Established a theoretical framework for understanding LVQ stability.

Conclusions:

The analyzed LVQ algorithms are proven to converge.
The convergence is contingent upon satisfying certain predefined conditions.
This work contributes to the theoretical understanding of LVQ algorithm behavior.