Related papers: Theoretical Analysis of the $k$-Means Algorithm - …
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 can be defined as the process of assembling objects into a number of groups whose elements are similar to each other in some manner. As a technique that is used in many domains, such as face clustering, plant categorization,…
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: Pick the…
K-means clustering, a classic and widely-used clustering technique, is known to exhibit suboptimal performance when applied to non-linearly separable data. Numerous adjustments and modifications have been proposed to address this issue,…
This work proposes a clusterization algorithm called k-Morphological Sets (k-MS), based on morphological reconstruction and heuristics. k-MS is faster than the CPU-parallel k-Means in worst case scenarios and produces enhanced…
The incremental K-means clustering algorithm has already been proposed and analysed in paper [Chakraborty and Nagwani, 2011]. It is a very innovative approach which is applicable in periodically incremental environment and dealing with a…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task?…
This paper gives a k-means approximation algorithm that is efficient in the relational algorithms model. This is an algorithm that operates directly on a relational database without performing a join to convert it to a matrix whose rows…
Organizing data into semantically more meaningful is one of the fundamental modes of understanding and learning. Cluster analysis is a formal study of methods for understanding and algorithm for learning. K-mean clustering algorithm is one…
We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…
Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy…
Clustering is a fundamental problem in unsupervised learning, and has been studied widely both as a problem of learning mixture models and as an optimization problem. In this paper, we study clustering with respect the emph{k-median}…
Clustering is a basic task in data analysis and machine learning, and the optimization of clustering objectives are well-studied optimization problems; amongst these, the $k$-Means objective is arguably the most well known. Given a…
The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…
The problem of rapid and automated detection of distinct market regimes is a topic of great interest to financial mathematicians and practitioners alike. In this paper, we outline an unsupervised learning algorithm for clustering financial…
Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…
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 categorical data is an integral part of data mining and has attracted much attention recently. In this paper, we present k-histogram, a new efficient algorithm for clustering categorical data. The k-histogram algorithm extends…
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…