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

We prove that the dynamics of the MBO scheme for data clustering converge to a viscosity solution to mean curvature flow. The main ingredients are (i) a new abstract convergence result based on quantitative estimates for heat operators and…

Clustering large spatial databases is an important problem, which tries to find the densely populated regions in a spatial area to be used in data mining, knowledge discovery, or efficient information retrieval. However most algorithms have…

Clustering algorithms are at the basis of several technological applications, and are fueling the development of rapidly evolving fields such as machine learning. In the recent past, however, it has become apparent that they face challenges…

In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…

As data sets continue to grow in size and complexity, effective and efficient techniques are needed to target important features in the variable space. Many of the variable selection techniques that are commonly used alongside clustering…

A novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the proposed method through the employment of multiple interacting…

The use of brain images as markers for diseases or behavioral differences is challenged by the small effects size and the ensuing lack of power, an issue that has incited researchers to rely more systematically on large cohorts. Coupled…

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…

Co-clustering simultaneously clusters rows and columns, revealing more fine-grained groups. However, existing co-clustering methods suffer from poor scalability and cannot handle large-scale data. This paper presents a novel and scalable…

Cluster analysis plays an important role in decision making process for many knowledge-based systems. There exist a wide variety of different approaches for clustering applications including the heuristic techniques, probabilistic models,…

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…

The analysis of data streams has received considerable attention over the past few decades due to sensors, social media, etc. It aims to recognize patterns in an unordered, infinite, and evolving stream of observations. Clustering this type…

Clustering is a fundamental task in data mining and machine learning, particularly for analyzing large-scale data. In this paper, we introduce Clust-Splitter, an efficient algorithm based on nonsmooth optimization, designed to solve the…

This paper introduces a novel K-means clustering algorithm, an advancement on the conventional Big-means methodology. The proposed method efficiently integrates parallel processing, stochastic sampling, and competitive optimization to…

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…

One of the most widely used techniques for data clustering is agglomerative clustering. Such algorithms have been long used across many different fields ranging from computational biology to social sciences to computer vision in part…

Recent advancements in Mixed Integer Optimization (MIO) algorithms, paired with hardware enhancements, have led to significant speedups in resolving MIO problems. These strategies have been utilized for optimal subset selection,…

In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…

Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…