Related papers: Ranking Vectors Clustering: Theory and Application…
The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the…
In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…
Rank fusion is a powerful technique that allows multiple sources of information to be combined into a single result set. However, to date fusion has not been regarded as being cost-effective in cases where strict per-query efficiency…
Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications…
Given a set V of n elements on m attributes, we want to find a partition of V on the minimum number of clusters such that the associated R-squared ratio is at least a given threshold. We denote this problem as Goal Clustering (GC). This…
Clustering is a hard discrete optimization problem. Nonconvex approaches such as low-rank semidefinite programming (SDP) have recently demonstrated promising statistical and local algorithmic guarantees for cluster recovery. Due to the…
Clustering is a fundamental problem in unsupervised learning, and has been studied widely both as a problem of learning mixture models and as an optimization problem. In this paper, we study clustering with respect the emph{k-median}…
We develop new algorithmic methods with provable guarantees for feature selection in regard to categorical data clustering. While feature selection is one of the most common approaches to reduce dimensionality in practice, most of the known…
We consider robust clustering problems in $\mathbb{R}^d$, specifically $k$-clustering problems (e.g., $k$-Median and $k$-Means with $m$ outliers, where the cost for a given center set $C \subset \mathbb{R}^d$ aggregates the distances from…
Clustering is a fundamental machine learning task and can be used in many applications. With the development of deep neural networks (DNNs), combining techniques from DNNs with clustering has become a new research direction and achieved…
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
Load shapes derived from smart meter data are frequently employed to analyze daily energy consumption patterns, particularly in the context of applications like Demand Response (DR). Nevertheless, one of the most important challenges to…
Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some…
Consider a problem where 4k given vectors need to be partitioned into k clusters of four vectors each. A cluster of four vectors is called a quad, and the cost of a quad is the sum of the component-wise maxima of the four vectors in the…
We consider a collection of prediction experiments, which are clustered in the sense that groups of experiments ex- hibit similar relationship between the predictor and response variables. The experiment clusters as well as the regres- sion…
Learning augmented is a machine learning concept built to improve the performance of a method or model, such as enhancing its ability to predict and generalize data or features, or testing the reliability of the method by introducing noise…
We study a variant of classical clustering formulations in the context of algorithmic fairness, known as diversity-aware clustering. In this variant we are given a collection of facility subsets, and a solution must contain at least a…
The nearest prototype classification is a less computationally intensive replacement for the $k$-NN method, especially when large datasets are considered. In metric spaces, centroids are often used as prototypes to represent whole clusters.…
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…
In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from…