# Cluster-based Kriging Approximation Algorithms for Complexity Reduction

## TL;DR

This paper introduces cluster Kriging, a methodology that partitions data into smaller clusters to build multiple Kriging models, significantly reducing computational complexity while maintaining accuracy.

## Contribution

It proposes a novel cluster-based framework with four new Kriging approximation algorithms that enable handling larger datasets efficiently.

## Key findings

- Proposed algorithms outperform existing Kriging approximations in empirical tests.
- Cluster Kriging reduces computational complexity from cubic to manageable levels.
- Practical guidelines for applying the new algorithms are provided.

## Abstract

Kriging or Gaussian Process Regression is applied in many fields as a non-linear regression model as well as a surrogate model in the field of evolutionary computation. However, the computational and space complexity of Kriging, that is cubic and quadratic in the number of data points respectively, becomes a major bottleneck with more and more data available nowadays. In this paper, we propose a general methodology for the complexity reduction, called cluster Kriging, where the whole data set is partitioned into smaller clusters and multiple Kriging models are built on top of them. In addition, four Kriging approximation algorithms are proposed as candidate algorithms within the new framework. Each of these algorithms can be applied to much larger data sets while maintaining the advantages and power of Kriging. The proposed algorithms are explained in detail and compared empirically against a broad set of existing state-of-the-art Kriging approximation methods on a well-defined testing framework. According to the empirical study, the proposed algorithms consistently outperform the existing algorithms. Moreover, some practical suggestions are provided for using the proposed algorithms.