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We propose a simple, projection-based algorithm for clustering mixtures of discrete (Bernoulli) distributions. Unlike previous approaches that rely on coordinate-specific ``combinatorial projections,'' our algorithm is rotationally…

A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…

We present the first application of the made-to-measure method for modelling dynamical systems to globular clusters. Through the made-to-measure algorithm, the masses of individual particles within a model cluster are adjusted while the…

We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified singular sets. We then apply this…

Recent advances in deep learning have enabled the generation of realistic data by training generative models on large datasets of text, images, and audio. While these models have demonstrated exceptional performance in generating novel and…

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…

Clustering is an important phenomenon in turbulent flows laden with inertial particles. Although this process has been studied extensively, there are still open questions about both the fundamental physics and the reconciliation of…

Structural regularities in man-made environments reflect in the distribution of their surface normals. Describing these surface normal distributions is important in many computer vision applications, such as scene understanding, plane…

We revisit the issue of non-parametric gravitational lens reconstruction and present a new method to obtain the cluster mass distribution using strong lensing data without using any prior information on the underlying mass. The method…

What is the "right" topological invariant of a large point cloud X? Prior research has focused on estimating the full persistence diagram of X, a quantity that is very expensive to compute, unstable to outliers, and far from a sufficient…

Shape-morphing structures possess the ability to change their shapes from one state to another, and therefore, offer great potential for a broad range of applications. A typical paradigm of morphing is transforming from an initial…

We propose a novel clustering approach for point-cloud segmentation based on supervised contrastive metric learning (CML). Rather than predicting cluster assignments or object-centric variables, the method learns a latent representation in…

This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…

We investigate the roles of spin and packing fraction on the dynamics of cratering when a solid projectile impacts a granular bed at different incident angles. For that, we carried out DEM (discrete element method) computations in which we…

Spatial clustering has been widely used for spatial data mining and knowledge discovery. An ideal multivariate spatial clustering should consider both spatial contiguity and aspatial attributes. Existing spatial clustering approaches may…

Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited…

The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance…

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…

We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges…

Granular material in a swirled container exhibits a curious transition as the number of particles is increased: at low densities the particle cluster rotates in the same direction as the swirling motion of the container, while at high…