Hierarchical clustering with maximum density paths and mixture models

Hierarchical clustering is an effective and interpretable technique for analyzing structure in data, offering a nuanced understanding by revealing insights at multiple scales and resolutions. It is particularly helpful in settings where the exact number of clusters is unknown, and provides a robust framework for exploring complex datasets. Additionally, hierarchical clustering can uncover inner structures within clusters, capturing subtle relationships and nested patterns that may be obscured by traditional flat clustering methods. However, existing hierarchical clustering methods struggle with high-dimensional data, especially when there are no clear density gaps between modes. Our method addresses this limitation by leveraging a two-stage approach, first employing a Gaussian or Student's t mixture model to overcluster the data, and then hierarchically merging clusters based on the induced density landscape. This approach yields state-of-the-art clustering performance while also providing a meaningful hierarchy, making it a valuable tool for exploratory data analysis. Code is available at https://github.com/ecker-lab/tneb clustering.

MNIST-Nd: a set of naturalistic datasets to benchmark clustering across dimensions

Driven by advances in recording technology, large-scale high-dimensional datasets have emerged across many scientific disciplines. Especially in biology, clustering is often used to gain insights into the structure of such datasets, for instance to understand the organization of different cell types. However, clustering is known to scale poorly to high dimensions, even though the exact impact of dimensionality is unclear as current benchmark datasets are mostly two-dimensional. Here we propose MNIST-Nd, a set of synthetic datasets that share a key property of real-world datasets, namely that individual samples are noisy and clusters do not perfectly separate. MNIST-Nd is obtained by training mixture variational autoencoders with 2 to 64 latent dimensions on MNIST, resulting in six datasets with comparable structure but varying dimensionality. It thus offers the chance to disentangle the impact of dimensionality on clustering. Preliminary common clustering algorithm benchmarks on MNIST-Nd suggest that Leiden is the most robust for growing dimensions.