# TiK-means: $K$-means clustering for skewed groups

## TL;DR

TiK-Means extends traditional K-means to effectively cluster skewed data by incorporating skewness transformations and an automatic method for determining the number of clusters, demonstrated on simulated, real, and astronomical data.

## Contribution

The paper introduces TiK-Means, a novel K-means variant that models skewed groups and estimates transformation parameters for improved clustering.

## Key findings

- Successfully clusters skewed data with estimated transformations
- Automatically determines optimal number of clusters using jump statistic
- Effectively applied to astronomical gamma ray burst data

## Abstract

The $K$-means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a $K$-means type algorithm that assigns observations to groups while estimating their skewness-transformation parameters. The resulting groups and transformation reveal general-structured clusters that can be explained by inverting the estimated transformation. Further, a modification of the jump statistic chooses the number of groups. Our algorithm is evaluated on simulated and real-life datasets and then applied to a long-standing astronomical dispute regarding the distinct kinds of gamma ray bursts.