Clustering High-dimensional Data: Balancing Abstraction and Representation Tutorial at AAAI 2026

How to find a natural grouping of a large real data set? Clustering requires a balance between abstraction and representation. To identify clusters, we need to abstract from superfluous details of individual objects. But we also need a rich representation that emphasizes the key features shared by groups of objects that distinguish them from other groups of objects. Each clustering algorithm implements a different trade-off between abstraction and representation. Classical K-means implements a high level of abstraction - details are simply averaged out - combined with a very simple representation - all clusters are Gaussians in the original data space. We will see how approaches to subspace and deep clustering support high-dimensional and complex data by allowing richer representations. However, with increasing representational expressiveness comes the need to explicitly enforce abstraction in the objective function to ensure that the resulting method performs clustering and not just representation learning. We will see how current deep clustering methods define and enforce abstraction through centroid-based and density-based clustering losses. Balancing the conflicting goals of abstraction and representation is challenging. Ideas from subspace clustering help by learning one latent space for the information that is relevant to clustering and another latent space to capture all other information in the data. The tutorial ends with an outlook on future research in clustering. Future methods will more adaptively balance abstraction and representation to improve performance, energy efficiency and interpretability. By automatically finding the sweet spot between abstraction and representation, the human brain is very good at clustering and other related tasks such as single-shot learning. So, there is still much room for improvement.

Extension of the Dip-test Repertoire -- Efficient and Differentiable p-value Calculation for Clustering

Over the last decade, the Dip-test of unimodality has gained increasing interest in the data mining community as it is a parameter-free statistical test that reliably rates the modality in one-dimensional samples. It returns a so called Dip-value and a corresponding probability for the sample's unimodality (Dip-p-value). These two values share a sigmoidal relationship. However, the specific transformation is dependent on the sample size. Many Dip-based clustering algorithms use bootstrapped look-up tables translating Dip- to Dip-p-values for a certain limited amount of sample sizes. We propose a specifically designed sigmoid function as a substitute for these state-of-the-art look-up tables. This accelerates computation and provides an approximation of the Dip- to Dip-p-value transformation for every single sample size. Further, it is differentiable and can therefore easily be integrated in learning schemes using gradient descent. We showcase this by exploiting our function in a novel subspace clustering algorithm called Dip'n'Sub. We highlight in extensive experiments the various benefits of our proposal.