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Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
We study (Euclidean) $k$-median and $k$-means with constraints in the streaming model. There have been recent efforts to design unified algorithms to solve constrained $k$-means problems without using knowledge of the specific constraint at…
Active learning is increasingly adopted for expensive multi-objective combinatorial optimization problems, but it involves a challenging subset selection problem, optimizing the batch acquisition score that quantifies the goodness of a…
Motivated by an application from geodesy, we introduce a novel clustering problem which is a $k$-center (or k-diameter) problem with a side constraint. For the side constraint, we are given an undirected connectivity graph $G$ on the input…
This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…
In this work we propose a simple and easily parallelizable algorithm for multiway graph partitioning. The algorithm alternates between three basic components: diffusing seed vertices over the graph, thresholding the diffused seeds, and then…
Combining kernel-based collocation methods with time-stepping methods to solve parabolic partial differential equations can potentially introduce challenges in balancing temporal and spatial discretization errors. Typically, using kernels…
Fueled by massive data, important decision making is being automated with the help of algorithms, therefore, fairness in algorithms has become an especially important research topic. In this work, we design new streaming and distributed…
Classical clustering problems such as \emph{Facility Location} and \emph{$k$-Median} aim to efficiently serve a set of clients from a subset of facilities -- minimizing the total cost of facility openings and client assignments in Facility…
The $k$-means algorithm is a prevalent clustering method due to its simplicity, effectiveness, and speed. However, its main disadvantage is its high sensitivity to the initial positions of the cluster centers. The global $k$-means is a…
Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier…
The taxing computational effort that is involved in solving some high-dimensional statistical problems, in particular problems involving non-convex optimization, has popularized the development and analysis of algorithms that run…
Assisting end users to identify desired results from a large dataset is an important problem for multi-criteria decision making. To address this problem, top-k and skyline queries have been widely adopted, but they both have inherent…
We propose a randomized greedy search algorithm to find a point estimate for a random partition based on a loss function and posterior Monte Carlo samples. Given the large size and awkward discrete nature of the search space, the…
Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta…
The $k$-center problem is a central optimization problem with numerous applications for machine learning, data mining, and communication networks. Despite extensive study in various scenarios, it surprisingly has not been thoroughly…
A coreset is a point set containing information about geometric properties of a larger point set. A series of previous works show that in many machine learning problems, especially in clustering problems, coreset could be very useful to…
In discrete k-center and k-median clustering, we are given a set of points P in a metric space M, and the task is to output a set C \subseteq ? P, |C| = k, such that the cost of clustering P using C is as small as possible. For k-center,…
$k$-means and $k$-median clustering are powerful unsupervised machine learning techniques. However, due to complicated dependences on all the features, it is challenging to interpret the resulting cluster assignments. Moshkovitz, Dasgupta,…
Clustering is a fundamental problem in many areas, which aims to partition a given data set into groups based on some distance measure, such that the data points in the same group are similar while that in different groups are dissimilar.…