Confusion matrices and their derived metrics are central to performance evaluation in supervised machine learning. This framework, however, has not been fully explored in the unsupervised domain, particularly within relative clustering validation. This gap was first addressed with the introduction of the AUCC (Area Under the ROC Curve for Clustering) relative index. Despite its solid theoretical foundation and empirical results, AUCC might be misleading in scenarios characterized by significant cluster size imbalance. In this work, we explore the Area Under the Precision-Recall Curve (and related metrics) in the context of clustering validation. We show that these are not only appropriate as clustering validation indices, but should also be preferred in the presence of cluster imbalance. Our observations contribute towards a unified validation framework for both supervised and unsupervised learning models.
We present an overview of our solutions to each of the three 2026 SISAP Challenges. In our solution to the first challenge we create an approximate near-neighbour table over a bitwise encoding of the data, which gives acceptable quality within a very small memory footprint. The bitwise representation is grounded in the high-dimensional geometry of the embedding space used for the challenge. Our solutions to Challenges 2 and 3 are based upon an approach to locality sensitive hashing (LSH) utilising a modified version of FALCONN. These LSH-based solutions accelerate search by incrementally refining a dynamically modified query object, which gives better results for locality sensitive functions than the query itself.
Feature selection is one of the most important and fundamental tasks in data mining, tackled by a family of methods with an established set of evaluation techniques to measure the quality of a specific method. Most of the methods commonly used for the unsupervised evaluation of feature selection algorithms suffer from critical design flaws which question their unsupervised nature. In this paper, we provide a critical discussion on the established allegedly unsupervised evaluation techniques, and shed light on the reasons why they are not truly unsupervised but, at best, supervised evaluation under an unsupervised downstream task. We also propose a novel, truly unsupervised evaluation framework to measure the quality of the feature selection algorithms without any form of information about the labels. The proposed framework utilizes unsupervised Principal Component Analysis, and optimal transport to measure the quality of the feature selection methods in a truly unsupervised manner.
Many iterative algorithms are dynamical systems generated by repeated application of an update map. Classical Lyapunov exponents characterize the stability of such systems by measuring exponential-scale perturbation growth along an ‘orbit’ (state trajectory). For fixed-point iteration with the limit translated to the origin, the convergence order of the system is known to be equivalent to the local intrinsic dimensionality (LID) when the update map is analytic near the fixed point. For univariate fixed-point dynamics, we connect these notions by decomposing the ordinary Lyapunov exponent into error contraction and an orbit average of log-LID values. Normalizing perturbations by the error yields an error-relative Lyapunov exponent equal to the logarithm of the asymptotic LID when this limit is well-defined. We also interpret Lyapunov-type exponents within the LID framework through intrinsic bases, and discuss tracked scalar spectral coordinates and ratio dynamics, distinguishing linear contraction from higher-order convergence behavior.
Proximity measures assign a numerical value quantifying the directed similarity relative to a fixed reference point. Distance and rank can serve as useful proximity measures, each with its own limitations: distance is affected by the curse of dimensionality, while rank is insensitive to changes in the relative positions of neighboring points. We define closeness, a proximity measure that naturally describes the degree of proximity in the context of a probability distribution. We show that closeness is equivalent to distance, yet robust to dimensionality, and it serves as a fundamental value when modeling the distribution of the rank. Moreover, closeness connects the discrete definition of rank with the continuous intuition of proximity in manifolds. We show that closeness is useful for defining a notion of neighborhood, quantifying eccentricity with respect to a dataset, and detecting outliers.
