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.

Hierarchical clustering techniques can reveal nested structures within data by representing patterns in a tree-like form. However, when dealing with complex data, many traditional hierarchical methods produce cluttered and hard-to-interpret trees. To address this, we propose a novel hierarchical clustering method called Discovery of Multi-Density Hierarchical Cluster structures (DMDHC), which introduces a new type of cluster tree to represent hierarchical information more effectively. Our approach automatically generates hierarchical local cuts along the tree structure. In contrast to state-of-the-art methods like PEARCH, which typically apply only a single cut across the hierarchy, DMDHC takes advantage of density-based insights to perform multiple cuts at different levels. This results in a more compact and comprehensible representation of intricate hierarchical structures. Extensive experiments on real- world datasets demonstrate that DMDHC, along with its newly introduced tree structure, outperforms existing methods.

Detecting arbitrarily shaped clusters in high-dimensional noisy data is challenging for current clustering methods. We introduce SHADE, the first deep clustering algorithm that incorporates density-connectivity into its loss function. Similar to existing deep clustering algorithms, SHADE supports high-dimensional and large data sets with the expressive power of a deep autoencoder. In contrast to most existing deep clustering methods that rely on a centroid-based clustering objective, SHADE incorporates a novel loss function that captures density-connectivity. It thereby learns a representation that enhances the separation of density-connected clusters. SHADE detects a stable clustering and noise points fully automatically without any user input. It outperforms existing methods in clustering quality, especially on data that contain non-Gaussian clusters, such as video data. Moreover, the embedded space of SHADE is suitable for visualization and interpretation of the clustering results as the individual shapes of the clusters are preserved.

A major challenge in cluster analysis is the discovery of clusters with widely varying sizes, densities, and shapes. Most clustering algorithms lack the ability to detect heterogeneous clusters that differ greatly in all three properties simultaneously. In this work, we propose the Density Clustering for Highly varying Density algorithm (DBHD). DBHD uses a novel approach that considers local density information and introduces two new conditions to distinguish between different types of data points. Based on this and the adaptively computed density information, DBHD can detect the clusters described above and is robust to noise. Moreover, DBHD has intuitive and robust parameters. In extensive experiments, we show that our technique is considerably more effective in detecting clusters of different shapes, sizes, and densities than well-known (DBSCAN or OPTICS) and recently proposed algorithms such as DPC, SNN-DPC, or LSDBC.

The field of deep clustering combines deep learning and clustering to learn representations that improve both the learned representation and the performance of the considered clustering method. Most existing deep clustering methods are designed for a single clustering method, e.g., k-means, spectral clustering, or Gaussian mixture models, but it is well known that no clustering algorithm works best in all circumstances. Consensus clustering tries to alleviate the individual weaknesses of clustering algorithms by building a consensus between members of a clustering ensemble. Currently, there is no deep clustering method that can include multiple heterogeneous clustering algorithms in an ensemble to update representations and clusterings together. To close this gap, we introduce the idea of a consensus representation that maximizes the agreement between ensemble members. Further, we propose DECCS (Deep Embedded Clustering with Consensus representationS), a deep consensus clustering method that learns a consensus representation by enhancing the embedded space to such a degree that all ensemble members agree on a common clustering result. Our contributions are the following: (1) We introduce the idea of learning consensus representations for heterogeneous clusterings, a novel notion to approach consensus clustering. (2) We propose DECCS, the first deep clustering method that jointly improves the representation and clustering results of multiple heterogeneous clustering algorithms. (3) We show in experiments that learning a consensus representation with DECCS is outperforming several relevant baselines from deep clustering and consensus clustering.