Related papers: Relational Algorithms for k-means Clustering

We consider the problem of approximate $K$-means clustering with outliers and side information provided by same-cluster queries and possibly noisy answers. Our solution shows that, under some mild assumptions on the smallest cluster size,…

Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously…

Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…

The K-means algorithm is a widely used clustering algorithm that offers simplicity and efficiency. However, the traditional K-means algorithm uses the random method to determine the initial cluster centers, which make clustering results…

This paper presents a neural network-based end-to-end clustering framework. We design a novel strategy to utilize the contrastive criteria for pushing data-forming clusters directly from raw data, in addition to learning a feature embedding…

The metric $k$-median problem is a textbook clustering problem. As input, we are given a metric space $V$ of size $n$ and an integer $k$, and our task is to find a subset $S \subseteq V$ of at most $k$ `centers' that minimizes the total…

Ensuring fairness in machine learning algorithms is a challenging and essential task. We consider the problem of clustering a set of points while satisfying fairness constraints. While there have been several attempts to capture group…

The problem of automatically clustering data is an age old problem. People have created numerous algorithms to tackle this problem. The execution time of any of this algorithm grows with the number of input points and the number of cluster…

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes…

We analyze online and mini-batch k-means variants. Both scale up the widely used Lloyd 's algorithm via stochastic approximation, and have become popular for large-scale clustering and unsupervised feature learning. We show, for the first…

Optimization tasks over relational data, such as clustering, often suffer from the prohibitive cost of join operations, which are necessary to access the full dataset. While geometric data structures like BBD trees yield fast approximation…

Clustering is an unsupervised learning technique in which data or objects are grouped into sets based on some similarity measure. Most of the clustering algorithms assume that the main memory is infinite and can accommodate the set of…

Data clustering is an approach to seek for structure in sets of complex data, i.e., sets of "objects". The main objective is to identify groups of objects which are similar to each other, e.g., for classification. Here, an introduction to…

We study $k$-clustering problems with lower bounds, including $k$-median and $k$-means clustering with lower bounds. In addition to the point set $P$ and the number of centers $k$, a $k$-clustering problem with (uniform) lower bounds gets a…

We present a study on how to effectively reduce the dimensions of the $k$-means clustering problem, so that provably accurate approximations are obtained. Four algorithms are presented, two \textit{feature selection} and two \textit{feature…

Clustering categorical data is an integral part of data mining and has attracted much attention recently. In this paper, we present k-ANMI, a new efficient algorithm for clustering categorical data. The k-ANMI algorithm works in a way that…

We consider the $k$-means clustering problem in the dynamic streaming setting, where points from a discrete Euclidean space $\{1, 2, \ldots, \Delta\}^d$ can be dynamically inserted to or deleted from the dataset. For this problem, we…

Ashtiani et al. (NIPS 2016) introduced a semi-supervised framework for clustering (SSAC) where a learner is allowed to make same-cluster queries. More specifically, in their model, there is a query oracle that answers queries of the form…

Clustering data is a popular feature in the field of unsupervised machine learning. Most algorithms aim to find the best method to extract consistent clusters of data, but very few of them intend to cluster data that share the same…

This paper provides new algorithms for distributed clustering for two popular center-based objectives, k-median and k-means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following…