# Kernel Treelets

## TL;DR

Kernel Treelets (KT) is a novel hierarchical clustering method that integrates multiscale data decomposition with kernel functions, enabling application to non-numeric data and providing multi-resolution analysis.

## Contribution

It introduces Kernel Treelets, combining treelets with kernel methods, allowing hierarchical clustering on general data types in feature space.

## Key findings

- KT effectively clusters non-numeric data.
- KT produces multi-resolution basis sequences.
- Examples demonstrate KT's effectiveness in clustering.

## Abstract

A new method for hierarchical clustering is presented. It combines treelets, a particular multiscale decomposition of data, with a projection on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT), effectively substitutes the correlation coefficient matrix used in treelets with a symmetric, positive semi-definite matrix efficiently constructed from a kernel function. Unlike most clustering methods, which require data sets to be numeric, KT can be applied to more general data and yield a multi-resolution sequence of basis on the data directly in feature space. The effectiveness and potential of KT in clustering analysis is illustrated with some examples.