Related papers: Maximizing diversity over clustered data
Traditional optimization algorithms search for a single global optimum that maximizes (or minimizes) the objective function. Multimodal optimization algorithms search for the highest peaks in the search space that can be more than one.…
Numerous algorithms have been produced for the fundamental problem of clustering under many different notions of fairness. Perhaps the most common family of notions currently studied is group fairness, in which proportional group…
Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize the value of the ranking? These applications exhibit strong diminishing returns: Redundancy…
Given an $n$-point metric space $(\mathcal{X},d)$ where each point belongs to one of $m=O(1)$ different categories or groups and a set of integers $k_1, \ldots, k_m$, the fair Max-Min diversification problem is to select $k_i$ points…
The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a $1-1/e$ factor. Although it is well known that this guarantee is essentially…
Quality-Diversity (QD) algorithms are a new type of Evolutionary Algorithms (EAs), aiming to find a set of high-performing, yet diverse solutions. They have found many successful applications in reinforcement learning and robotics, helping…
We propose an algorithm for clustering high dimensional data. If $P$ features for $N$ objects are represented in an $N\times P$ matrix ${\bf X}$, where $N\ll P$, the method is based on exploiting the cluster-dependent structure of the…
This paper introduces the equiwide clustering problem, where valid partitions must satisfy intra-cluster dissimilarity constraints. Unlike most existing clustering algorithms, equiwide clustering relies neither on density nor on a…
We provide simple and fast polynomial time approximation schemes (PTASs) for several variants of the max-sum diversification problem which, in its most basic form, is as follows: Given n points p_1,...,p_n in R^d and an integer k, select k…
We study the probabilistic assignment of items to platforms that satisfies both group and individual fairness constraints. Each item belongs to specific groups and has a preference ordering over platforms. Each platform enforces group…
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that…
In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…
A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances…
Co-clustering, that is, partitioning a numerical matrix into homogeneous submatrices, has many applications ranging from bioinformatics to election analysis. Many interesting variants of co-clustering are NP-hard. We focus on the basic…
Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent…
In Evolutionary Robotics a population of solutions is evolved to optimize robots that solve a given task. However, in traditional Evolutionary Algorithms, the population of solutions tends to converge to local optima when the problem is…
Recommender systems use data on past user preferences to predict possible future likes and interests. A key challenge is that while the most useful individual recommendations are to be found among diverse niche objects, the most reliably…
One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic…
The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…
When forming a team or group of individuals, we often seek a balance of expertise in a particular task while at the same time maintaining diversity of skills within each group. Here, we view the problem of finding diverse and experienced…