Assessing the impact of dimensionality reduction on clustering performance -- a systematic study

Dimensionality reduction (DR) techniques are often characterized by whether they preserve global, high-level structures in the data or local, neighborhood structures. This distinction matters in visualization: global methods can obscure clusters while local methods can over-emphasize them. Yet, even when clusters appear distinct, their relative arrangement in the projection may be arbitrary or misleading, a common issue in techniques such as t-SNE and UMAP. Existing cluster quality metrics either only measure cluster separability or assume spherical, globular clusters in the original space. We introduce the Class Angular Distortion Index (CADI), a metric that uses internal angles among point triples to determine the faithfulness of cluster organization in a projection. We show cases on both real and synthetic data where existing cluster metrics fail, but CADI provides an interpretable result. Since it relies on computing angles, CADI is also differentiable, enabling optimization. We demonstrate this with a CADI-based DR technique.

Clustering is a fundamental problem in data science with a long-standing research history, yielding numerous insightful algorithms. Despite this progress, a systematic and large-scale empirical evaluation that jointly considers conventional algorithms, deep learning-based methods, and recent foundation model-based clustering remains largely absent, leading to limited guidance on algorithm selection and deployment. To address this gap, we introduce CLUBench, a comprehensive clustering benchmark comprising 24 algorithms of diverse principles evaluated on 131 datasets across tabular, text, and image data, involving 178,815 experiments. Importantly, our analyses of (i) the impact of hyperparameter tuning,(ii) the impact of data types and characteristics,(iii) the impact of pretrained embeddings,(iv) large language model-based clustering,(v) the similarity of algorithms, and (vi) the low-rank structures of performance matrices, yield meaningful insights and promising pathways for clustering research. For instance, our study reveals that: 1) All evaluated deep clustering methods do not exhibit a significant advantage compared with the top-performing conventional clustering algorithms (e.g., KMeans, SpeClu) in terms of average performance; 2) For image and text clustering tasks, combining pretrained embeddings with conventional clustering algorithms (e.g., KMeans, SpeClu) offers effective and efficient clustering; 3) Clustering remains a challenging and nontrivial problem, even in the era of increasingly dominant foundation models. Moreover, we propose to use the low-rank structure in cross-model performance matrices to efficiently approximate the overall performance evaluation in practical applications. We further demonstrate the feasibility of model selection based on the performance matrices across all hyperparameter configurations.

Clustering is a cornerstone of modern data analysis. Detecting clusters in exploratory data analyses (EDA) requires algorithms that make few assumptions about the data. Density-based clustering algorithms are particularly well-suited for EDA because they describe high-density regions, assuming only that a density exists. Applying density-based clustering algorithms in practice, however, requires selecting appropriate hyperparameters, which is difficult without prior knowledge of the data distribution. For example, DBSCAN requires selecting a density threshold, and HDBSCAN* relies on a minimum cluster size parameter. In this work, we propose Persistent Leaves Spatial Clustering for Applications with Noise (PLSCAN), a multiscale density-based clustering algorithm that replaces HDBSCAN*'s fixed minimum cluster size pruning of a mutual-reachability linkage hierarchy with a persistence-based cluster selection procedure. Effectively, PLSCAN identifies all minimum cluster sizes for which HDBSCAN* produces stable (leaf) clusters. In concept, PLSCAN applies scale-space clustering principles and is equivalent to persistent homology on a novel metric space. We compare its performance to HDBSCAN* on several real-world datasets, demonstrating that it achieves a higher median ARI, is less sensitive to changes in the number of mutual reachability neighbours, and has higher stability under resampling. Additionally, we compare PLSCAN's computational costs to $k$-Means++, demonstrating competitive run-times on low-dimensional datasets. At higher dimensions, run times scale more similarly to HDBSCAN*.