Related papers: Asymptotics for The $k$-means
This paper presents a novel method for clustering surfaces. The proposal involves first using basis functions in a tensor product to smooth the data and thus reduce the dimension to a finite number of coefficients, and then using these…
Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all…
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…
The k-means method is a widely used clustering algorithm. One of its distinguished features is its speed in practice. Its worst-case running-time, however, is exponential, leaving a gap between practical and theoretical performance. Arthur…
In this paper we provide a fully distributed implementation of the k-means clustering algorithm, intended for wireless sensor networks where each agent is endowed with a possibly high-dimensional observation (e.g., position, humidity,…
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…
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…
We present methods for k-means clustering on a stream with a focus on providing fast responses to clustering queries. Compared to the current state-of-the-art, our methods provide substantial improvement in the query time for cluster…
We prove in this paper that the expected value of the objective function of the $k$-means++ algorithm for samples converges to population expected value. As $k$-means++, for samples, provides with constant factor approximation for $k$-means…
The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote…
The paper presents a novel approach for unsupervised techniques in the field of clustering. A new method is proposed to enhance existing literature models using the proper Bayesian bootstrap to improve results in terms of robustness 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…
The $K$-means algorithm remains one of the most widely-used clustering methods due to its simplicity and general utility. The performance of $K$-means depends upon location of minima low in cost function, amongst a potentially vast number…
We devise coresets for kernel $k$-Means with a general kernel, and use them to obtain new, more efficient, algorithms. Kernel $k$-Means has superior clustering capability compared to classical $k$-Means, particularly when clusters are…
In a recent work, [19] studied the following "fair" variants of classical clustering problems such as $k$-means and $k$-median: given a set of $n$ data points in $\mathbb{R}^d$ and a binary type associated to each data point, the goal is to…
In $K$-means classification, a set of data will form clusters, i.e. classes, if the measured distances between data points (or some common point in each class) are below a certain threshold. With the assumption that the data points are…
Existing clustering algorithms such as K-means often need to preset parameters such as the number of categories K, and such parameters may lead to the failure to output objective and consistent clustering results. This paper introduces a…
Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general…
Manifold clustering, with its exceptional ability to capture complex data structures, holds a pivotal position in cluster analysis. However, existing methods often focus only on finding the optimal combination between K-means and manifold…
To cluster data that are not linearly separable in the original feature space, $k$-means clustering was extended to the kernel version. However, the performance of kernel $k$-means clustering largely depends on the choice of kernel…