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Fuzzy clustering is a famous unsupervised learning method used to collecting similar data elements within cluster according to some similarity measurement. But, clustering algorithms suffer from some drawbacks. Among the main weakness…
We study the regimes in which Hamiltonian simulation benefits from randomization. We introduce a sparse-QSVT construction based on composite stochastic decompositions, where dominant terms are treated deterministically and smaller…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…
Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…
This paper is about variable selection, clustering and estimation in an unsupervised high-dimensional setting. Our approach is based on fitting constrained Gaussian mixture models, where we learn the number of clusters $K$ and the set of…
We analyze online \cite{BottouBengio} and mini-batch \cite{Sculley} $k$-means variants. Both scale up the widely used $k$-means algorithm via stochastic approximation, and have become popular for large-scale clustering and unsupervised…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
The solution space of a K-satisfiability (K-SAT) formula is a collection of solution clusters, each of which contains all the solutions that are mutually reachable through a sequence of single-spin flips. Knowledge of the statistical…
We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior combinatorial optimization…
Understanding how evolutionary algorithms perform on constrained problems has gained increasing attention in recent years. In this paper, we study how evolutionary algorithms optimize constrained versions of the classical LeadingOnes…
We study two generalizations of classic clustering problems called dynamic ordered $k$-median and dynamic $k$-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between…
In recent years, crowdsourcing, aka human aided computation has emerged as an effective platform for solving problems that are considered complex for machines alone. Using human is time-consuming and costly due to monetary compensations.…
We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering…
We study a simple model of algorithmic collusion in which Q-learning algorithms are designed in a strategic fashion. We let players (\textit{designers}) choose their exploration policy simultaneously prior to letting their algorithms…
With the rapid advancement of next-generation satellite networks, addressing clustering tasks, user grouping, and efficient link management has become increasingly critical to optimize network performance and reduce interference. In this…
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible…
Periodic orbits in chaotic systems form clusters, whose elements traverse approximately the same points of the phase space. The distribution of cluster sizes depends on the length n of orbits and the parameter p which controls closeness of…
We introduce and benchmark a stochastic local search heuristic for the NP-complete satisfiability problem 3-SAT that drastically outperforms existing solvers in the notoriously difficult realm of critically hard instances. Our construction…
Many studies in heuristic search suggest that the accuracy of the heuristic used has a positive impact on improving the performance of the search. In another direction, historical research perceives that the performance of heuristic search…