Related papers: An Aggregate and Iterative Disaggregate Algorithm …

Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…

Cluster analysis is one of the essential tasks in data mining and knowledge discovery. Each type of data poses unique challenges in achieving relatively efficient partitioning of the data into homogeneous groups. While the algorithms for…

In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number…

Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…

We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…

To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network…

Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…

This paper presents a method for solving the supervised learning problem in which the output is highly nonlinear and discontinuous. It is proposed to solve this problem in three stages: (i) cluster the pairs of input-output data points,…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

We present a technique for clustering categorical data by generating many dissimilarity matrices and averaging over them. We begin by demonstrating our technique on low dimensional categorical data and comparing it to several other…

Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario,…

Designing recommendation systems with limited or no available training data remains a challenge. To that end, a new combinatorial optimization problem is formulated to generate optimized item selection for experimentation with the goal to…

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…

The problem of optimizing a sequence of tasks for a robot, also known as multi-point manufacturing, is a well-studied problem. Many of these solutions use a variant of the Traveling Salesman Problem (TSP) and seek to find the minimum…

We propose an algebraic framework for studying efficient algorithms for query evaluation, aggregation, enumeration, and maintenance under updates, on sparse databases. Our framework allows to treat those problems in a unified way, by…

We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used 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…

With the development of Big data technology, data analysis has become increasingly important. Traditional clustering algorithms such as K-means are highly sensitive to the initial centroid selection and perform poorly on non-convex…

The iteration dynamics of the coupled cluster equations exhibits a synergistic relationship among the cluster amplitudes. The iteration scheme may be viewed as a multivariate discrete-time propagation of nonlinearly coupled equations, which…