# Extracting preference relations from data: Clustering with transitive centroids

## TL;DR

This paper introduces a new clustering algorithm called k-orders that extracts transitive relations from data, useful for studying heterogeneous individual preferences.

## Contribution

The paper proposes k-orders with transitive centroid adjustment procedures for clustering transitive relations in preference studies.

## Key findings

- Both versions of k-orders outperform k-modes when centroids are transitive relations.
- TCA performs better than greedy TCA in two-component experimental designs.
- An empirical application demonstrates the usefulness of k-orders in analyzing individual preferences.

## Abstract

A clustering algorithm, named k-orders, is proposed to extract transitive relations from a data set. The k-orders algorithm differs from the original k-modes only in the adjustment step. Two adjustment procedures, named transitive centroid adjustment (TCA) and greedy TCA, are proposed that can be used to find clusters with transitive centroids. The proposed clustering approach finds application, especially in studies on preference, where this last may be heterogeneous across individuals, although transitive. The set of cluster centroids extracted by the algorithm from a data set can then be empirically tested via the estimation of a latent class model. The performance of the two versions of k-orders were compared to one another and with the canonical k-modes, in simulation studies. Results show that when centroids are transitive relations, both versions of k-orders outperform k-modes. Moreover, in experimental designs in which two-component options are considered, the TCA algorithm performs better than the greedy TCA. An empirical application was also carried out for exemplifying how k-orders can be useful for studying individual preferences.