Related papers: Consistent $k$-Median: Simpler, Better and Robust

We study the problem of $k$-means clustering in the space of straight-line segments in $\mathbb{R}^{2}$ under the Hausdorff distance. For this problem, we give a $(1+\epsilon)$-approximation algorithm that, for an input of $n$ segments, for…

Recent spectral clustering methods are a propular and powerful technique for data clustering. These methods need to solve the eigenproblem whose computational complexity is $O(n^3)$, where $n$ is the number of data samples. In this paper, a…

We consider the model introduced by Bilu and Linial (2010), who study problems for which the optimal clustering does not change when distances are perturbed. They show that even when a problem is NP-hard, it is sometimes possible to obtain…

The presence of outliers can potentially significantly skew the parameters of machine learning models trained via stochastic gradient descent (SGD). In this paper we propose a simple variant of the simple SGD method: in each step, first…

We provide an approximation algorithm for k-means clustering in the one-round (aka non-interactive) local model of differential privacy (DP). This algorithm achieves an approximation ratio arbitrarily close to the best non private…

Many algorithms for approximate nearest neighbor search in high-dimensional spaces partition the data into clusters. At query time, in order to avoid exhaustive search, an index selects the few (or a single) clusters nearest to the query…

The k-median problem is a well-known strongly NP-hard combinatorial optimization problem of both theoretical and practical significance. The previous best approximation ratio for this problem is 2.611+\epsilon (Bryka et al. 2014) based on…

We study the Ordered k-Median problem, in which the solution is evaluated by first sorting the client connection costs and then multiplying them with a predefined non-increasing weight vector (higher connection costs are taken with larger…

$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…

Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of $n$ agents located in an underlying metric space, our goal is to partition them into $k$ clusters,…

In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the…

Plain vanilla K-means clustering has proven to be successful in practice, yet it suffers from outlier sensitivity and may produce highly unbalanced clusters. To mitigate both shortcomings, we formulate a joint outlier detection and…

There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between…

We show that both clustering and subspace embeddings can be performed in the streaming model with the same asymptotic efficiency as in the central/offline setting. For $(k, z)$-clustering in the streaming model, we achieve a number of words…

K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a…

We give the first outlier-robust efficient algorithm for clustering a mixture of $k$ statistically separated d-dimensional Gaussians (k-GMMs). Concretely, our algorithm takes input an $\epsilon$-corrupted sample from a $k$-GMM and whp in…

Although numerous clustering algorithms have been developed, many existing methods still leverage k-means technique to detect clusters of data points. However, the performance of k-means heavily depends on the estimation of centers of…

This paper presents fast, distributed, $O(1)$-approximation algorithms for metric facility location problems with outliers in the Congested Clique model, Massively Parallel Computation (MPC) model, and in the $k$-machine model. The paper…

In data summarization we want to choose $k$ prototypes in order to summarize a data set. We study a setting where the data set comprises several demographic groups and we are restricted to choose $k_i$ prototypes belonging to group $i$. A…

Traditional online continual learning (OCL) research has primarily focused on mitigating catastrophic forgetting with fixed and limited storage allocation throughout an agent's lifetime. However, a broad range of real-world applications are…