Improving the K-means algorithm using improved downhill simplex search

TL;DR

This paper introduces an improved downhill simplex search method to enhance the initialization of the k-means clustering algorithm, aiming to avoid local optima and improve clustering quality.

Contribution

The paper proposes a novel improved downhill simplex search technique to find better initial partitions for k-means, outperforming existing methods like genetic algorithms.

Findings

The improved method yields better clustering results than traditional k-means.

It outperforms genetic algorithm-based approaches in initial partitioning.

The approach reduces the likelihood of convergence to local optima.

Abstract

The k-means algorithm is one of the well-known and most popular clustering algorithms. K-means seeks an optimal partition of the data by minimizing the sum of squared error with an iterative optimization procedure, which belongs to the category of hill climbing algorithms. As we know hill climbing searches are famous for converging to local optimums. Since k-means can converge to a local optimum, different initial points generally lead to different convergence cancroids, which makes it important to start with a reasonable initial partition in order to achieve high quality clustering solutions. However, in theory, there exist no efficient and universal methods for determining such initial partitions. In this paper we tried to find an optimum initial partitioning for k-means algorithm. To achieve this goal we proposed a new improved version of downhill simplex search, and then we used it in order to find an optimal result for clustering approach and then compare this algorithm with Genetic Algorithm base (GA), Genetic K-Means (GKM), Improved Genetic K-Means (IGKM) and k-means algorithms.