相关论文: Generalization of k-means Related Algorithms

In this paper, we propose an acceleration of the exact k-means++ algorithm using geometric information, specifically the Triangle Inequality and additional norm filters, along with a two-step sampling procedure. Our experiments demonstrate…

This paper presents a new way of selecting an initial solution for the k-modes algorithm that allows for a notion of mathematical fairness and a leverage of the data that the common initialisations from literature do not. The method, which…

Center-based clustering techniques are fundamental in some areas of machine learning such as data summarization. Generic $k$-center algorithms can produce biased cluster representatives so there has been a recent interest in fair $k$-center…

This paper proposes the use of an optimization algorithm, namely PSO to decide the initial centroids in K-means, to eventually get better accuracy. The vectorized notation of the optimal centroids can be thought of as entities in an…

The fuzzy $K$-means problem is a generalization of the classical $K$-means problem to soft clusterings, i.e. clusterings where each points belongs to each cluster to some degree. Although popular in practice, prior to this work the fuzzy…

We answer the question: "Does local progress (on batches) imply global progress (on the entire dataset) for mini-batch $k$-means?". Specifically, we consider mini-batch $k$-means which terminates only when the improvement in the quality of…

We propose k^2-means, a new clustering method which efficiently copes with large numbers of clusters and achieves low energy solutions. k^2-means builds upon the standard k-means (Lloyd's algorithm) and combines a new strategy to accelerate…

Minimum sum-of-squares clustering (MSSC) is a widely used clustering model, of which the popular K-means algorithm constitutes a local minimizer. It is well known that the solutions of K-means can be arbitrarily distant from the true MSSC…

K-means is one of the most widely used algorithms for clustering in Data Mining applications, which attempts to minimize the sum of the square of the Euclidean distance of the points in the clusters from the respective means of the…

We utilize the PageRank vector to generalize the $k$-means clustering algorithm to directed and undirected graphs. We demonstrate that PageRank and other centrality measures can be used in our setting to robustly compute centrality of nodes…

We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…

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…

We study feature selection for $k$-means clustering. Although the literature contains many methods with good empirical performance, algorithms with provable theoretical behavior have only recently been developed. Unfortunately, these…

We study k-median clustering under the sequential no-substitution setting. In this setting, a data stream is sequentially observed, and some of the points are selected by the algorithm as cluster centers. However, a point can be selected as…

$k$-means algorithm is one of the most classical clustering methods, which has been widely and successfully used in signal processing. However, due to the thin-tailed property of the Gaussian distribution, $k$-means algorithm suffers from…

In the classical NP-hard metric $k$-median problem, we are given a set of $n$ clients and centers with metric distances between them, along with an integer parameter $k\geq 1$. The objective is to select a subset of $k$ open centers that…

We investigate the fine-grained complexity of approximating the classical $k$-median / $k$-means clustering problems in general metric spaces. We show how to improve the approximation factors to $(1+2/e+\varepsilon)$ and…

This study investigates the performance of median-of-means sampling compared to traditional mean-of-means sampling for computing the Keister function integral using Randomized Quasi-Monte Carlo (RQMC) methods. The research tests both…

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…

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…