Related papers: Finding Clustering Algorithms in the Transformer A…
We consider the problem of clustering in the learning-augmented setting, where we are given a data set in $d$-dimensional Euclidean space, and a label for each data point given by an oracle indicating what subsets of points should be…
One iteration of standard $k$-means (i.e., Lloyd's algorithm) or standard EM for Gaussian mixture models (GMMs) scales linearly with the number of clusters $C$, data points $N$, and data dimensionality $D$. In this study, we explore whether…
The widely applied k-means algorithm produces clusterings that violate our expectations with respect to high/low similarity/density and is in conflict with Kleinberg's axiomatic system for distance based clustering algorithms that…
Center-based clustering algorithms (e.g., K-means) are popular for clustering tasks, but they usually struggle to achieve high accuracy on complex datasets. We believe the main reason is that traditional center-based clustering algorithms…
The introduction of Transformers architecture has brought about significant breakthroughs in Deep Learning (DL), particularly within Natural Language Processing (NLP). Since their inception, Transformers have outperformed many traditional…
Self-attention, as the key block of transformers, is a powerful mechanism for extracting features from the inputs. In essence, what self-attention does is to infer the pairwise relations between the elements of the inputs, and modify the…
Transformers have emerged as a widely used neural network model for various natural language processing tasks. Previous research explored their relationship with constant-depth threshold circuits, making two assumptions: average-hard…
Blockchain transaction data exhibits high dimensionality, noise, and intricate feature entanglement, presenting significant challenges for traditional clustering algorithms. In this study, we conduct a comparative analysis of three…
We study the capabilities of the transformer architecture with varying depth. Specifically, we designed a novel set of sequence learning tasks to systematically evaluate and comprehend how the depth of transformer affects its ability to…
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…
This paper investigates the computational and statistical limits in clustering matrix-valued observations. We propose a low-rank mixture model (LrMM), adapted from the classical Gaussian mixture model (GMM) to treat matrix-valued…
Clustering is an unsupervised learning method that constitutes a cornerstone of an intelligent data analysis process. It is used for the exploration of inter-relationships among a collection of patterns, by organizing them into homogeneous…
AI-enabled precision medicine promises a transformational improvement in healthcare outcomes by enabling data-driven personalized diagnosis, prognosis, and treatment. However, the well-known "curse of dimensionality" and the clustered…
In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…
The rapid progress seen in terms of large-scale generative AI is largely based on the attention mechanism. It is conversely non-trivial to conceive small-scale applications for which attention-based architectures outperform traditional…
A clustering outcome for high-dimensional data is typically interpreted via post-processing, involving dimension reduction and subsequent visualization. This destroys the meaning of the data and obfuscates interpretations. We propose…
Transformer networks have seen great success in natural language processing and machine vision, where task objectives such as next word prediction and image classification benefit from nuanced context sensitivity across high-dimensional…
Vision Transformers can achieve high accuracy and strong generalization across various contexts, but their practical applicability on real-world robotic systems is limited due to their quadratic attention complexity. Recent works have…
The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been…
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…