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Clustering is a core task in machine learning with wide-ranging applications in data mining and pattern recognition. However, its unsupervised nature makes it inherently challenging. Many existing clustering algorithms suffer from critical…

Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a…

This note introduces a novel clustering preserving transformation of cluster sets obtained from $k$-means algorithm. This transformation may be used to generate new labeled data{}sets from existent ones. It is more flexible that Kleinberg…

Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…

$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are…

We consider $K$-means clustering in networked environments (e.g., internet of things (IoT) and sensor networks) where data is inherently distributed across nodes and processing power at each node may be limited. We consider a clustering…

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…

Lloyd's k-means algorithm is one of the most widely used clustering methods. We prove that in high-dimensional, high-noise settings, the algorithm exhibits catastrophic failure: with high probability, essentially every partition of the data…

A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and…

Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…

Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise. The main interest of Bregman divergences is that the standard Lloyd algorithm adapts to…

Clustering problems have numerous applications and are becoming more challenging as the size of the data increases. In this paper, we consider designing clustering algorithms that can be used in MapReduce, the most popular programming…

Transformers have emerged as a powerful neural network architecture capable of tackling a wide range of learning tasks. In this work, we provide a theoretical analysis of their ability to automatically extract structure from data in an…

Clustering is an unsupervised learning task that aims to partition data into a set of clusters. In many applications, these clusters correspond to real-world constructs (e.g. electoral districts) whose benefit can only be attained by groups…

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…

Mathematical reasoning is one of the most impressive achievements of human intellect but remains a formidable challenge for artificial intelligence systems. In this work we explore whether modern deep learning architectures can learn to…

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…

K-means defines one of the most employed centroid-based clustering algorithms with performances tied to the data's embedding. Intricate data embeddings have been designed to push $K$-means performances at the cost of reduced theoretical…

$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…

We propose a new clustering algorithm that is robust to the presence of outliers in the dataset. We perform Lloyd-type iterations with robust estimates of the centroids. More precisely, we build on the idea of median-of-means statistics to…