Related papers: An initialization method for the k-means using the…
Application of K-Means algorithm is restricted by the fact that the number of clusters should be known beforehand. Previously suggested methods to solve this problem are either ad hoc or require parametric assumptions and complicated…
The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…
The $k$-means clustering algorithm is popular but has the following main drawbacks: 1) the number of clusters, $k$, needs to be provided by the user in advance, 2) it can easily reach local minima with randomly selected initial centers, 3)…
\textit{Clustering problems} often arise in the fields like data mining, machine learning etc. to group a collection of objects into similar groups with respect to a similarity (or dissimilarity) measure. Among the clustering problems,…
This paper proposes an original approach to cluster multi-component data sets, including an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's algorithm, and the assumption that the vertices…
K-Means++ and its distributed variant K-Means$\|$ have become de facto tools for selecting the initial seeds of K-means. While alternatives have been developed, the effectiveness, ease of implementation, and theoretical grounding of the…
In the Euclidean $k$-center problem in sliding window model, input points are given in a data stream and the goal is to find the $k$ smallest congruent balls whose union covers the $N$ most recent points of the stream. In this model, input…
Mining clusters from data is an important endeavor in many applications. The $k$-means method is a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply for categorical-valued…
Pseudo-Centroid Clustering replaces the traditional concept of a centroid expressed as a center of gravity with the notion of a pseudo-centroid (or a coordinate free centroid) which has the advantage of applying to clustering problems where…
The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. In this sense, cluster analysis algorithms are a key element of exploratory data analysis, due to their easiness in the…
We study the complexity of the classic capacitated k-median and k-means problems parameterized by the number of centers, k. These problems are notoriously difficult since the best known approximation bound for high dimensional Euclidean…
We revisit the randomized seeding techniques for k-means clustering and k-GMM (Gaussian Mixture model fitting with Expectation-Maximization), formalizing their three key ingredients: the metric used for seed sampling, the number of…
Due to its simplicity and versatility, k-means remains popular since it was proposed three decades ago. The performance of k-means has been enhanced from different perspectives over the years. Unfortunately, a good trade-off between quality…
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…
Clustering is one of the most fundamental tasks in machine learning, and the k-means clustering algorithm is perhaps one of the most widely used clustering algorithms. However, it suffers from several limitations, such as sensitivity to…
This paper investigates the capability of correctly recovering well-separated clusters by various brands of the $k$-means algorithm. The concept of well-separatedness used here is derived directly from the common definition of clusters,…
Clustering data is a popular feature in the field of unsupervised machine learning. Most algorithms aim to find the best method to extract consistent clusters of data, but very few of them intend to cluster data that share the same…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
We investigate the role of the initialization for the stability of the k-means clustering algorithm. As opposed to other papers, we consider the actual k-means algorithm and do not ignore its property of getting stuck in local optima. We…