Real-world datasets commonly arise from mixtures of multiple, potentially overlapping subdistributions. Traditional anomaly detection methods often use rigid assumptions or global thresholds and, as a result, struggle to identify anomalies within complex multimodal data. We propose ADM-Anomalies Detection through Local Maxima and Mutual Nearest Neighbors-an unsupervised approach that systematically identifies dense, mode-like structures without imposing a single global model. Specifically, ADM constructs a mutual nearest neighbor (MNN) graph and takes its transitive closure to reveal groups of high-density points, which converge to the true modes under mild assumptions. A “double-knee” procedure then refines these groups: (i) it separates large, high-density modes from small, fringe-like clusters, and (ii) within each major mode, it pinpoints local maxima to accommodate internal multimodality. Finally, ADM assigns an anomaly score to every point by calculating its distance to the closest local maxima, thereby identifying both globally isolated anomalies and subtle boundary anomalies. Extensive evaluations on diverse real-world datasets show that ADM consistently outperforms or matches leading baselines, all while requiring only a single hyperparameter k.

Despite the popularity of density-based clustering, its procedural definition makes it difficult to analyze compared to clustering methods that minimize a loss function. In this paper, we reformulate DBSCAN through a clean objective function by introducing the density-connectivity distance (dc-dist), which captures the essence of density-based clusters by endowing the minimax distance with the concept of density. This novel ultrametric allows us to show that DBSCAN, k-center, and spectral clustering are equivalent in the space given by the dc-dist, despite these algorithms being perceived as fundamentally different in their respective literatures. We also verify that finding the pairwise dc-dists gives DBSCAN clusterings across all epsilon-values, simplifying the problem of parameterizing density-based clustering. We conclude by thoroughly analyzing density-connectivity and its properties -- a task that has been elusive thus far in the literature due to the lack of formal tools. Our code recreates every experiment below: https://github.com/Andrew-Draganov/dc_dist

Active learning has the power to significantly reduce the amount of labeled data needed to build strong classifiers. Existing active pseudo-labeling methods show high potential in integrating pseudo-labels within the active learning loop but heavily depend on the prediction accuracy of the model. In this work, we propose VERIPS, an algorithm that significantly outperforms existing pseudo-labeling techniques for active learning. At its core, VERIPS uses a pseudo-label verification mechanism that consists of a second network only trained on data approved by the oracle and helps to discard questionable pseudo-labels. In particular, the verifier model eliminates all pseudo-labels for which it disagrees with the actual task model. VERIPS overcomes the problems of poorly performing initial models, e.g., due to imbalanced or too small initial pools, where previous methods select too many incorrect pseudo-labels and recovering takes long or is not possible. Moreover, VERIPS is particularly insensitive to parameter choices that existing approaches suffer from. Our code is available at https://github.com/lmu-dbs/VERIPS.