Related papers: Diversity maximization in doubling metrics
Multiple importance sampling (MIS) is an indispensable tool in rendering that constructs robust sampling strategies by combining the respective strengths of individual distributions. Its efficiency can be greatly improved by carefully…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
Numerous genotypic diversity measures (GDMs) are available in the literature to assess the convergence status of an evolutionary algorithm (EA) or describe its search behavior. In a recent study, the authors of this paper drew attention to…
Diverse planning approaches are utilised in real-world applications like risk management, automated streamed data analysis, and malware detection. The current diverse planning formulations encode the diversity model as a distance function,…
We consider a facility location problem, where the objective is to ``disperse'' a number of facilities, i.e., select a given number k of locations from a discrete set of n candidates, such that the average distance between selected…
Collaborative Metric Learning (CML) has recently emerged as a popular method in recommendation systems (RS), closing the gap between metric learning and collaborative filtering. Following the convention of RS, existing practices exploit…
Many clustering applications in machine learning and data mining rely on solving metric-constrained optimization problems. These problems are characterized by $O(n^3)$ constraints that enforce triangle inequalities on distance variables…
We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we…
Personalized recommender systems are playing an increasingly important role as more content and services become available and users struggle to identify what might interest them. Although matrix factorization and deep learning based methods…
In previous work cite{Ha98:Towards} we presented a case-based approach to eliciting and reasoning with preferences. A key issue in this approach is the definition of similarity between user preferences. We introduced the probabilistic…
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
In this paper we generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the "closeness" between two nodes. The calculation of the measure is linear in the number of edges in the graph and…
The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…
Motivated by applications in redistricting, we consider the uniform capacitated k-median and uniform capacitated k-means problems in bounded doubling metrics. We provide the first QPTAS for both problems and the first PTAS for the uniform…
Quality diversity is a recent family of evolutionary search algorithms which focus on finding several well-performing (quality) yet different (diversity) solutions with the aim to maintain an appropriate balance between divergence and…
In the metric distortion problem, a set of voters and candidates lie in a common metric space, and a committee of $k$ candidates must be elected. The objective is to minimize a social cost, defined as a function of the distances between…
Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. We present mixed-integer optimization approaches to find optimal distance metrics that generalize the Mahalanobis…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across…