Related papers: An efficient volume-preserving MBO scheme for data…

Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…

We consider the problem of clustering in the learning-augmented setting, where we are given a data set in $d$-dimensional Euclidean space, and a label for each data point given by an oracle indicating what subsets of points should be…

Traditional clustering algorithms often struggle with high-dimensional and non-uniformly distributed data, where low-density boundary samples are easily disturbed by neighboring clusters, leading to unstable and distorted clustering…

In stochastic optimisation, the large number of scenarios required to faithfully represent the underlying uncertainty is often a barrier to finding efficient numerical solutions. This motivates the scenario reduction problem: by find a…

We introduce two practical properties of hierarchical clustering methods for (possibly asymmetric) network data: excisiveness and linear scale preservation. The latter enforces imperviousness to change in units of measure whereas the former…

We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the…

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment.…

This paper addresses the limitations of conventional vector quantization algorithms, particularly K-Means and its variant K-Means++, and investigates the Stochastic Quantization (SQ) algorithm as a scalable alternative for high-dimensional…

We develop a general framework to significantly reduce the degree of sum-of-squares proofs by introducing new variables. To illustrate the power of this framework, we use it to speed up previous algorithms based on sum-of-squares for two…

Clustering functional data is a challenging task due to intrinsic infinite-dimensionality and the need for stable, data-adaptive partitioning. In this work, we propose a clustering framework based on Random Projections, which simultaneously…

Clustering is a widely used technique in data mining applications for discovering patterns in underlying data. Most traditional clustering algorithms are limited to handling datasets that contain either numeric or categorical attributes.…

Clustering is inherently ill-posed: there often exist multiple valid clusterings of a single dataset, and without any additional information a clustering system has no way of knowing which clustering it should produce. This motivates the…

We propose an online data compression approach for efficiently solving distributionally robust optimization (DRO) problems with streaming data while maintaining out-of-sample performance guarantees. Our method dynamically constructs…

Consensus-based optimization (CBO) is a versatile multi-particle optimization method for performing nonconvex and nonsmooth global optimizations in high dimensions. Proofs of global convergence in probability have been achieved for a broad…

In our latest studies, by introducing the novel order-preserving (OP) criterion, we have successfully addressed the widely concerned issue of the previously published mapped weighted essentially non-oscillatory (WENO) schemes that it is…

Indexing is an effective way to support efficient query processing in large databases. Recently the concept of learned index, which replaces or complements traditional index structures with machine learning models, has been actively…

Clustering consists of grouping together samples giving their similar properties. The problem of modeling simultaneously groups of samples and features is known as Co-Clustering. This paper introduces ROCCO - a Robust Continuous…

In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…

This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…

Estimation of interface curvature in surface-tension dominated flows is a remaining challenge in Volume of Fluid (VOF) methods. Data-driven methods are recently emerging as a promising alternative in this domain. They outperform…