Related papers: Fully Dynamic Euclidean k-Means
The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial $k$ centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: {quote}…
We present the first (randomized) parallel dynamic algorithm for maximal matching, which can process an arbitrary number of updates simultaneously. Given a batch of edge deletion or insertion updates to the graph, our parallel algorithm…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
The aim of the k-means is to minimize squared sum of Euclidean distance from the mean (SSEDM) of each cluster. The k-means can effectively optimize this function, but it is too sensitive for initial centers (seeds). This paper proposed a…
Effectively applying the K-means algorithm to clustering tasks with incomplete features remains an important research area due to its impact on real-world applications. Recent work has shown that unifying K-means clustering and imputation…
This paper extends k-means algorithms from the Euclidean domain to the domain of graphs. To recompute the centroids, we apply subgradient methods for solving the optimization-based formulation of the sample mean of graphs. To accelerate the…
A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as centers among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized.…
We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. Specifically, we are given a set $T$ of $n$ points in $\mathbb{R}^d$ and a parameter $0< \alpha <\frac 1 2$ such that an…
Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…
We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean…
The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed…
The widely applied k-means algorithm produces clusterings that violate our expectations with respect to high/low similarity/density and is in conflict with Kleinberg's axiomatic system for distance based clustering algorithms that…
We propose a novel method to accelerate Lloyd's algorithm for K-Means clustering. Unlike previous acceleration approaches that reduce computational cost per iterations or improve initialization, our approach is focused on reducing the…
We present a new distance oracle in the fully dynamic setting: given a weighted undirected graph $G=(V,E)$ with $n$ vertices undergoing both edge insertions and deletions, and an arbitrary parameter $\epsilon$ where $\epsilon\in[1/\log^{c}…
In this paper, we give a conditional lower bound of $n^{\Omega(k)}$ on running time for the classic k-median and k-means clustering objectives (where n is the size of the input), even in low-dimensional Euclidean space of dimension four,…
The k-means objective is arguably the most widely-used cost function for modeling clustering tasks in a metric space. In practice and historically, k-means is thought of in a continuous setting, namely where the centers can be located…
The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice. Theoretically, however, the best known upper bound on its…
This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…
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…
Quantum machine learning, though in its initial stage, has demonstrated its potential to speed up some of the costly machine learning calculations when compared to the existing classical approaches. Among the challenging subroutines,…