Related papers: Finding Clustering Algorithms in the Transformer A…

Transformers have transformed modern machine learning, driving breakthroughs in computer vision, natural language processing, and robotics. At the core of their success lies the attention mechanism, which enables the modeling of global…

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…

We present a clustering- and demotion-based algorithm called Kmeans-FOLD to induce nonmonotonic logic programs from positive and negative examples. Our algorithm improves upon-and is inspired by-the FOLD algorithm. The FOLD algorithm itself…

Large language models (LLMs) have recently transformed natural language processing, enabling machines to generate human-like text and engage in meaningful conversations. This development necessitates speed, efficiency, and accessibility in…

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 performs an essential role in many real world applications, such as market research, pattern recognition, data analysis, and image processing. However, due to the high dimensionality of the input feature values, the data being…

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

We design an interpretable clustering algorithm aware of the nonlinear structure of image manifolds. Our approach leverages the interpretability of $K$-means applied in the image space while addressing its clustering performance issues.…

In the context of unsupervised learning, Lloyd's algorithm is one of the most widely used clustering algorithms. It has inspired a plethora of work investigating the correctness of the algorithm under various settings with ground truth…

In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and…

In this paper we initiate a systematic study of exact algorithms for well-known clustering problems, namely $k$-Median and $k$-Means. In $k$-Median, the input consists of a set $X$ of $n$ points belonging to a metric space, and the task is…

Powerful generative artificial intelligence from large language models (LLMs) harnesses extensive computational resources for inference. In this work, we investigate the transformer architecture, a key component of these models, under the…

In this paper a variant of the classical hierarchical cluster analysis is reported. This agglomerative (bottom-up) cluster technique is referred to as the Adaptive Mean-Linkage Algorithm. It can be interpreted as a linkage algorithm where…

The transformer architecture is central to the success of modern Large Language Models (LLMs), in part due to its surprising ability to perform a wide range of tasks - including mathematical reasoning, memorization, and retrieval - using…

Mean shift is a simple interactive procedure that gradually shifts data points towards the mode which denotes the highest density of data points in the region. Mean shift algorithms have been effectively used for data denoising, mode…

This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes…

Gaussian mixture models (GMM) are the most widely used statistical model for the $k$-means clustering problem and form a popular framework for clustering in machine learning and data analysis. In this paper, we propose a natural semi-random…

Scientists study trajectory data to understand trends in movement patterns, such as human mobility for traffic analysis and urban planning. There is a pressing need for scalable and efficient techniques for analyzing this data and…