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Gaussian splatting has emerged as a powerful tool for high-fidelity reconstruction of dynamic scenes. However, existing methods primarily rely on implicit motion representations, such as encoding motions into neural networks or per-Gaussian…
Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the…
Density-based clustering has found numerous applications across various domains. The Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is capable of finding clusters of varied shapes that are not linearly…
We present a Bayesian inference approach to estimating the cumulative mass profile and mean squared velocity profile of a globular cluster given the spatial and kinematic information of its stars. Mock globular clusters with a range of…
High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped…
Clustering analysis is of substantial significance for data mining. The properties of big data raise higher demand for more efficient and economical distributed clustering methods. However, existing distributed clustering methods mainly…
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…
The mean shift (MS) is a non-parametric, density-based, iterative algorithm with prominent usage in clustering and image segmentation. A rigorous proof for the convergence of its mode estimate sequence in full generality remains unknown. In…
K-means plays a vital role in data mining and is the simplest and most widely used algorithm under the Euclidean Minimum Sum-of-Squares Clustering (MSSC) model. However, its performance drastically drops when applied to vast amounts of…
Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this…
Learning the representation of data with hierarchical structures in the hyperbolic space attracts increasing attention in recent years. Due to the constant negative curvature, the hyperbolic space resembles tree metrics and captures the…
Learning fine-grained embeddings from coarse labels is a challenging task due to limited label granularity supervision, i.e., lacking the detailed distinctions required for fine-grained tasks. The task becomes even more demanding when…
Gaussian Boson Sampling (GBS) is a quantum computing concept based on drawing samples from a multimode nonclassical Gaussian state using photon-number resolving detectors. It was initially posed as a near-term approach aiming to achieve…
Accurate boundary detection in high-dimensional data remains a central challenge in unsupervised learning, particularly in the presence of non-linear structures and heterogeneous densities. In this work, we introduce Mean Curvature Boundary…
Gradient Boosting (GB) is a popular methodology used to solve prediction problems by minimizing a differentiable loss function, $L$. GB performs very well on tabular machine learning (ML) problems; however, as a pure ML solver it lacks the…
We propose a robust clustering framework for high-dimensional data with heavy tails and a large fraction of irrelevant variables. The method replaces the mean updates of Lloyd's $K$-means with \emph{spatial medians} to enhance robustness.…
The problem of unsupervised learning and segmentation of hyperspectral images is a significant challenge in remote sensing. The high dimensionality of hyperspectral data, presence of substantial noise, and overlap of classes all contribute…
Recent advances in image clustering typically focus on learning better deep representations. In contrast, we present an orthogonal approach that does not rely on abstract features but instead learns to predict image transformations and…
We investigate a novel non-parametric regression-based clustering algorithm for longitudinal data analysis. Combining natural cubic splines with Gaussian mixture models (GMM), the algorithm can produce smooth cluster means that describe the…
Hierarchical semantic structures, naturally existing in real-world datasets, can assist in capturing the latent distribution of data to learn robust hash codes for retrieval systems. Although hierarchical semantic structures can be simply…