相关论文: Mini-batch $k$-means terminates within $O(d/\epsil…

This paper presents a comparative analysis of different optimization techniques for the K-means algorithm in the context of big data. K-means is a widely used clustering algorithm, but it can suffer from scalability issues when dealing with…

Given a set of points in a metric space, the $(k,z)$-clustering problem consists of finding a set of $k$ points called centers, such that the sum of distances raised to the power of $z$ of every data point to its closest center is…

We study $k$-means clustering in a semi-supervised setting. Given an oracle that returns whether two given points belong to the same cluster in a fixed optimal clustering, we investigate the following question: how many oracle queries are…

This paper considers $k$-means clustering in the presence of noise. It is known that $k$-means clustering is highly sensitive to noise, and thus noise should be removed to obtain a quality solution. A popular formulation of this problem is…

A celebrated result of Pollard proves asymptotic consistency for $k$-means clustering when the population distribution has finite variance. In this work, we point out that the population-level $k$-means clustering problem is, in fact,…

The $k$-$\mathtt{means}$++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the $k$-means clustering problem where the goal is to cluster a dataset $\mathcal{X} \subset \mathbb{R} ^d$ into $k$ clusters. The…

We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this…

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…

The incremental K-means clustering algorithm has already been proposed and analysed in paper [Chakraborty and Nagwani, 2011]. It is a very innovative approach which is applicable in periodically incremental environment and dealing with a…

The paper is focused on the forecasting method for time series groups with the use of algorithms for cluster analysis. $K$-means algorithm is suggested to be a basic one for clustering. The coordinates of the centers of clusters have been…

We investigate the complexity of solving stable or perturbation-resilient instances of $k$-Means and $k$-Median clustering in fixed dimension Euclidean metrics (more generally doubling metrics). The notion of stable (perturbation resilient)…

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…

We study in this paper the problem of jointly clustering and learning representations. As several previous studies have shown, learning representations that are both faithful to the data to be clustered and adapted to the clustering…

We define the notion of a well-clusterable data set combining the point of view of the objective of $k$-means clustering algorithm (minimising the centric spread of data elements) and common sense (clusters shall be separated by gaps). We…

We study the classic $k$-means/median clustering, which are fundamental problems in unsupervised learning, in the setting where data are partitioned across multiple sites, and where we are allowed to discard a small portion of the data by…

Center-based clustering is a fundamental primitive for data analysis and becomes very challenging for large datasets. In this paper, we focus on the popular $k$-median and $k$-means variants which, given a set $P$ of points from a metric…

We consider the problem of explainable $k$-medians and $k$-means introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian~(ICML 2020). In this problem, our goal is to find a threshold decision tree that partitions data into $k$ clusters…

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…

We theoretically explore the relationship between sample-efficiency and adaptivity in reinforcement learning. An algorithm is sample-efficient if it uses a number of queries $n$ to the environment that is polynomial in the dimension $d$ of…

We study the generalization performance of $\text{full-batch}$ optimization algorithms for stochastic convex optimization: these are first-order methods that only access the exact gradient of the empirical risk (rather than gradients with…