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$k$-defective cliques relax cliques by allowing up-to $k$ missing edges from being a complete graph. This relaxation enables us to find larger near-cliques and has applications in link prediction, cluster detection, social network analysis…
In this study, we investigate the application of Semidefinite Programming (SDP) to phylogenetics. SDP is a powerful optimization framework that seeks to optimize a linear objective function over the cone of positive semidefinite matrices.…
Reinforcement learning (RL) is a powerful tool for sequential decision-making, but its application is often hindered by privacy concerns arising from its interaction data. This challenge is particularly acute in advanced networked systems,…
In this work, we study the socially fair $k$-median/$k$-means problem. We are given a set of points $P$ in a metric space $\mathcal{X}$ with a distance function $d(.,.)$. There are $\ell$ groups: $P_1,\dotsc,P_{\ell} \subseteq P$. We are…
Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for $k$-means with a provable guarantee is a simple…
Semidefinite programming (SDP) relaxation has emerged as a promising approach for neural network verification, offering tighter bounds than other convex relaxation methods for deep neural networks (DNNs) with ReLU activations. However, we…
We present a scalable algorithm for the individually fair ($p$, $k$)-clustering problem introduced by Jung et al. and Mahabadi et al. Given $n$ points $P$ in a metric space, let $\delta(x)$ for $x\in P$ be the radius of the smallest ball…
Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…
Given a weighted undirected graph, a number of clusters $k$, and an exponent $z$, the goal in the $(k, z)$-clustering problem on graphs is to select $k$ vertices as centers that minimize the sum of the distances raised to the power $z$ of…
Deep clustering has the potential to learn a strong representation and hence better clustering performance compared to traditional clustering methods such as $k$-means and spectral clustering. However, this strong representation learning…
Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead,…
We present a method for finding lower bounds on the global infima of integral variational problems, wherein $\int_\Omega f(x,u(x),\nabla u(x)){\rm d}x$ is minimized over functions $u\colon\Omega\subset\mathbb{R}^n\to\mathbb{R}^m$ satisfying…
We devise and explore an iterative optimization procedure for controlling particle populations in particle-in-cell (PIC) codes via merging and splitting of computational macro-particles. Our approach, is to compute an optimal representation…
This paper presents a novel centroid-based heuristic algorithm, termed Kempe Swap K-Means, for constrained clustering under rigid must-link (ML) and cannot-link (CL) constraints. The algorithm employs a dual-phase iterative process: an…
Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set…
Recently, methodology was presented to facilitate the incorporation of interim analyses in stepped-wedge (SW) cluster randomised trials (CRTs). Here, we extend this previous discussion. We detail how the stopping boundaries, allocation…
The concept of $k$-defective clique, a relaxation of clique by allowing up-to $k$ missing edges, has been receiving increasing interests recently. Although the problem of finding the maximum $k$-defective clique is NP-hard, several…
Federated clustering, an integral aspect of federated machine learning, enables multiple data sources to collaboratively cluster their data, maintaining decentralization and preserving privacy. In this paper, we introduce a novel federated…
Spectral clustering is one of the most important algorithms in data mining and machine intelligence; however, its computational complexity limits its application to truly large scale data analysis. The computational bottleneck in spectral…
We study the problem of privacy-preserving $k$-means clustering in the horizontally federated setting. Existing federated approaches using secure computation suffer from substantial overheads and do not offer output privacy. At the same…