Related papers: k-Means Clustering Is Matrix Factorization

The number of accidents and health diseases which are increasing at an alarming rate are resulting in a huge increase in the demand for blood. There is a necessity for the organized analysis of the blood donor database or blood banks…

Motivated by the needs of estimating the proximity clustering with partial distance measurements from vantage points or landmarks for remote networked systems, we show that the proximity clustering problem can be effectively formulated as…

One key use of k-means clustering is to identify cluster prototypes which can serve as representative points for a dataset. However, a drawback of using k-means cluster centers as representative points is that such points distort the…

K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a…

Determining the correct number of clusters (CNC) is an important task in data clustering and has a critical effect on finalizing the partitioning results. K-means is one of the popular methods of clustering that requires CNC. Validity index…

This paper considers $k$-means clustering in the presence of noise. It is known that $k$-means clustering is highly sensitive to noise, and thus noise should be removed to obtain a quality solution. A popular formulation of this problem is…

The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown…

Over the last three decades, researchers have intensively explored various clustering tools for categorical data analysis. Despite the proposal of various clustering algorithms, the classical k-modes algorithm remains a popular choice for…

Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically…

The k-means algorithm is one of the most common clustering algorithms and widely used in data mining and pattern recognition. The increasing computational requirement of big data applications makes hardware acceleration for the k-means…

We revisit the $(f,g)$-clustering problem that we introduced in a recent work [SODA'25], and which subsumes fundamental clustering problems such as $k$-Center, $k$-Median, Min-Sum of Radii, and Min-Load $k$-Clustering. This problem assigns…

We consider the problem of data clustering with unidentified feature quality and when a small amount of labelled data is provided. An unsupervised sparse clustering method can be employed in order to detect the subgroup of features…

Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of $n$ agents located in an underlying metric space, our goal is to partition them into $k$ clusters,…

In a real-world data set there is always the possibility, rather high in our opinion, that different features may have different degrees of relevance. Most machine learning algorithms deal with this fact by either selecting or deselecting…

There has been much interest recently in developing fair clustering algorithms that seek to do justice to the representation of groups defined along sensitive attributes such as race and gender. We observe that clustering algorithms could…

Clustering is a long-standing problem area in data mining. The centroid-based classical approaches to clustering mainly face difficulty in the case of high dimensional inputs such as images. With the advent of deep neural networks, a common…

Deep learning models have become widely adopted in various domains, but their performance heavily relies on a vast amount of data. Datasets often contain a large number of irrelevant or redundant samples, which can lead to computational…

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…

Text clustering is arguably one of the most important topics in modern data mining. Nevertheless, text data require tokenization which usually yields a very large and highly sparse term-document matrix, which is usually difficult to process…

The fuzzy $K$-means problem is a popular generalization of the well-known $K$-means problem to soft clusterings. We present the first coresets for fuzzy $K$-means with size linear in the dimension, polynomial in the number of clusters, and…