# Mixed-type Distance Shrinkage and Selection for Clustering via Kernel Metric Learning

arXiv: https://arxiv.org/abs/2306.01890 · HTML: https://mlsanity.com/paper/2306.01890/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 76 references that are in the map.
- First posted on arXiv 2 Jun 2023.

## Builds on (most cited first, 3 of 3)

- [Hierarchical Clustering: Objective Functions and Algorithms](https://mlsanity.com/paper/1704.02147/) (2017)
- [An Overview of Distance and Similarity Functions for Structured Data](https://mlsanity.com/paper/2002.07420/) (2020)
- [A general framework for implementing distances for categorical variables](https://mlsanity.com/paper/2301.02190/) (2023)

## Built on by (most cited first, 2 of 2)

- [Spectral Clustering of Categorical and Mixed-type Data via Extra Graph Nodes](https://mlsanity.com/paper/2403.05669/) (2024)
- [A Deterministic Information Bottleneck Method for Clustering Mixed-Type Data](https://mlsanity.com/paper/2407.03389/) (2024)

## Abstract (arXiv)

Distance-based clustering and classification are widely used in various fields to group mixed numeric and categorical data. In many algorithms, a predefined distance measurement is used to cluster data points based on their dissimilarity. While there exist numerous distance-based measures for data with pure numerical attributes and several ordered and unordered categorical metrics, an efficient and accurate distance for mixed-type data that utilizes the continuous and discrete properties simulatenously is an open problem. Many metrics convert numerical attributes to categorical ones or vice versa. They handle the data points as a single attribute type or calculate a distance between each attribute separately and add them up. We propose a metric called KDSUM that uses mixed kernels to measure dissimilarity, with cross-validated optimal bandwidth selection. We demonstrate that KDSUM is a shrinkage method from existing mixed-type metrics to a uniform dissimilarity metric, and improves clustering accuracy when utilized in existing distance-based clustering algorithms on simulated and real-world datasets containing continuous-only, categorical-only, and mixed-type data.