# Spectral Clustering of Categorical and Mixed-type Data via Extra Graph Nodes

arXiv: https://arxiv.org/abs/2403.05669 · HTML: https://mlsanity.com/paper/2403.05669/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 48 references that are in the map.
- First posted on arXiv 8 Mar 2024.

## Builds on (most cited first, 7 of 7)

- [Guarantees for Spectral Clustering with Fairness Constraints](https://mlsanity.com/paper/1901.08668/) (2019)
- [A Survey on Multi-View Clustering](https://mlsanity.com/paper/1712.06246/) (2017)
- [Survey of state-of-the-art mixed data clustering algorithms](https://mlsanity.com/paper/1811.04364/) (2018)
- [Model Based Clustering for Mixed Data: clustMD](https://mlsanity.com/paper/1511.01720/) (2015)
- [LIBRE: Learning Interpretable Boolean Rule Ensembles](https://mlsanity.com/paper/1911.06537/) (2019)
- [A Performance Guarantee for Spectral Clustering](https://mlsanity.com/paper/2007.05627/) (2020)
- [Mixed-type Distance Shrinkage and Selection for Clustering via Kernel Metric Learning](https://mlsanity.com/paper/2306.01890/) (2023)

## Built on by (most cited first, 1 of 1)

- [Categorical data clustering: 25 years beyond K-modes](https://mlsanity.com/paper/2408.17244/) (2024)

## Abstract (arXiv)

Clustering data objects into homogeneous groups is one of the most important tasks in data mining. Spectral clustering is arguably one of the most important algorithms for clustering, as it is appealing for its theoretical soundness and is adaptable to many real-world data settings. For example, mixed data, where the data is composed of numerical and categorical features, is typically handled via numerical discretization, dummy coding, or similarity computation that takes into account both data types. This paper explores a more natural way to incorporate both numerical and categorical information into the spectral clustering algorithm, avoiding the need for data preprocessing or the use of sophisticated similarity functions. We propose adding extra nodes corresponding to the different categories the data may belong to and show that it leads to an interpretable clustering objective function. Furthermore, we demonstrate that this simple framework leads to a linear-time spectral clustering algorithm for categorical-only data. Finally, we compare the performance of our algorithms against other related methods and show that it provides a competitive alternative to them in terms of performance and runtime.