# Wasserstein-based Kernel Principal Component Analysis for Clustering Applications

arXiv: https://arxiv.org/abs/2503.14357 · HTML: https://mlsanity.com/paper/2503.14357/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [Wasserstein Embedding for Graph Learning](https://mlsanity.com/paper/2006.09430/) (2020)
- [Dynamic Clustering in Federated Learning](https://mlsanity.com/paper/2012.03788/) (2020)
- [The Wasserstein-Fourier Distance for Stationary Time Series](https://mlsanity.com/paper/1912.05509/) (2019)
- [Robust clustering tools based on optimal transportation](https://mlsanity.com/paper/1607.01179/) (2016)
- [Wasserstein Exponential Kernels](https://mlsanity.com/paper/2002.01878/) (2020)
- [Hybrid Wasserstein Distance and Fast Distribution Clustering](https://mlsanity.com/paper/1812.11026/) (2018)
- [Clustering performance analysis using a new correlation-based cluster validity index](https://mlsanity.com/paper/2109.11172/) (2021)
- [A Restarted Large-Scale Spectral Clustering with Self-Guiding and Block Diagonal Representation](https://mlsanity.com/paper/2306.15138/) (2023)
- [Kernel Correlation-Dissimilarity for Multiple Kernel k-Means Clustering](https://mlsanity.com/paper/2403.03448/) (2024)
- [Matrix Normal PCA for Interpretable Dimension Reduction and Graphical Noise Modeling](https://mlsanity.com/paper/1911.10796/) (2019)

## Abstract (arXiv)

Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance provides a well-conditioned dissimilarity measure. Kernel methods extend this by embedding distance information into feature spaces that facilitate analysis. However, an unsupervised framework that combines kernels with Wasserstein distances for clustering distributional data is still lacking. We address this gap by introducing a computationally tractable framework that integrates Wasserstein metrics with kernel methods for clustering. The framework can accommodate both vectorial and distributional data, enabling applications in various domains. It comprises three components: (i) an efficient approximation of pairwise Wasserstein distances using multiple reference distributions; (ii) shifted positive definite kernel functions based on Wasserstein distances, combined with kernel principal component analysis for feature mapping; and (iii) scalable, distance-agnostic validity indices for clustering evaluation and kernel parameter optimization. Experiments on power distribution graphs and real-world time series demonstrate the effectiveness and efficiency of the proposed framework.