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The density based clustering method {\em Density-Based Spatial Clustering of Applications with Noise (DBSCAN)} is a popular method for outlier recognition and has received tremendous attention from many different areas. A major issue of the…

Brain midline shift (MLS) is one of the most critical factors to be considered for clinical diagnosis and treatment decision-making for intracranial hemorrhage. Existing computational methods on MLS quantification not only require intensive…

Efficient continual learning techniques have been a topic of significant research over the last few years. A fundamental problem with such learning is severe degradation of performance on previously learned tasks, known also as catastrophic…

The problem of inhomogeneous cluster densities has been a long-standing issue for distance-based and density-based algorithms in clustering and anomaly detection. These algorithms implicitly assume that all clusters have approximately the…

Generating graphs with hierarchical structures remains a fundamental challenge due to the limitations of Euclidean geometry in capturing exponential complexity. Here we introduce \textbf{GGBall}, a novel hyperbolic framework for graph…

Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and…

Learning embeddings of entities and relations existing in knowledge bases allows the discovery of hidden patterns in data. In this work, we examine the geometrical space's contribution to the task of knowledge base completion. We focus on…

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input.…

Subspace clustering aims to group data points that lie in a union of low-dimensional subspaces and finds wide application in computer vision, hyperspectral imaging, and recommendation systems. However, most existing methods assume fully…

Clustering aims to divide a set of points into groups. The current paradigm assumes that the grouping is well-defined (unique) given the probability model from which the data is drawn. Yet, recent experiments have uncovered several…

Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…

Linear mixed models are widely used for clustered data, but their reliance on parametric forms limits flexibility in complex and high-dimensional settings. In contrast, gradient boosting methods achieve high predictive accuracy through…

Hyperbolic deep learning has become a growing research direction in computer vision due to the unique properties afforded by the alternate embedding space. The negative curvature and exponentially growing distance metric provide a natural…

We present a new technique for visualizing high-dimensional data called cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality reduction methods: preserving both local and global structures of the original sample in a…

The progress in hyperbolic neural networks (HNNs) research is hindered by their absence of inductive bias mechanisms, which are essential for generalizing to new tasks and facilitating scalable learning over large datasets. In this paper,…

Functional magnetic resonance imaging (fMRI) reveals complex brain functional networks with hierarchical topologies crucial for cognitive processing. Standard Euclidean Graph Neural Networks (GNNs) often struggle to represent these…

Hyperspectral images capture vast amounts of high-dimensional spectral information about a scene, making labeling an intensive task that is resistant to out-of-the-box statistical methods. Unsupervised learning of clusters allows for…

In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the…

A mixture of multiple scaled generalized hyperbolic distributions (MMSGHDs) is introduced. Then, a coalesced generalized hyperbolic distribution (CGHD) is developed by joining a generalized hyperbolic distribution with a multiple scaled…

In this paper we present a novel iterative multiphase clustering technique for efficiently clustering high dimensional data points. For this purpose we implement clustering feature (CF) tree on a real data set and a Gaussian density…