Genetic Programming for Evolving Similarity Functions for Clustering: Representations and Analysis

Kernel representations for evolving continuous functions

To parameterize continuous functions for evolutionary learning, we use kernel expansions in nested sequences of function spaces of growing complexity. This approach is particularly powerful when dealing with non-convex constraints and discontinuous objective functions. Kernel methods offer a number of beneficial properties for parameterizing continuous functions, such as smoothness and locality...

Evolving Fuzzy Decision Trees with Genetic Programming and Clustering

On the Analysis of Simple Genetic Programming for Evolving Boolean Functions

This work presents a first step towards a systematic time and space complexity analysis of genetic programming (GP) for evolving functions with desired input/output behaviour. Two simple GP algorithms, called (1+1) GP and (1+1) GP*, equipped with minimal function (F) and terminal (L) sets are considered for evolving two standard classes of Boolean functions. It is rigorously proved that both al...

Evolving Kernel Functions with Particle Swarms and Genetic Programming

The Support Vector Machine has gained significant popularity over recent years as a kernel-based supervised learning technique. However, choosing the appropriate kernel function and its associated parameters is not a trivial task. The kernel is often chosen from several widely-used and general-purpose functions, and the parameters are then empirically tuned for the best results on a specific da...

A Theory of Similarity Functions for Clustering

Problems of clustering data from pairwise similarity information are ubiquitous in Computer Science.Theoretical treatments typically view the similarity information as ground-truth and then design algorithmsto (approximately) optimize various graph-based objective functions. However, in most applications, thissimilarity information is merely based on some heuristic: the true goal is...