English
Related papers

Related papers: Limitations of Clustering Using Quantum Persistent…

200 papers

One of the most prominent challenges in clustering is "the user's dilemma," which is the problem of selecting an appropriate clustering algorithm for a specific task. A formal approach for addressing this problem relies on the…

Machine Learning · Computer Science 2016-10-05 Margareta Ackerman , Shai Ben-David , Simina Brânzei , David Loker

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

Geometric Topology · Mathematics 2012-06-06 Jesse Johnson

Quantum computers promise polynomial or exponential speed-up in solving certain problems compared to classical computers. However, in practical use, there are currently a number of fundamental technical challenges. One of them concerns the…

Emerging Technologies · Computer Science 2024-03-20 Markus Zajac , Uta Störl

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

Applications · Statistics 2016-11-30 Matthew Pietrosanu

Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Alexandre H. Abdo , A. P. S. de Moura

Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…

Data Structures and Algorithms · Computer Science 2018-07-17 Vaggos Chatziafratis , Rad Niazadeh , Moses Charikar

Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with non convex or nested structures. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a…

Quantum Physics · Physics 2021-06-15 Iordanis Kerenidis , Jonas Landman

We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…

Machine Learning · Computer Science 2016-09-20 Vincent Roulet , Fajwel Fogel , Alexandre d'Aspremont , Francis Bach

Extracting useful information from large data sets can be a daunting task. Topological methods for analyzing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying…

Quantum Physics · Physics 2015-12-17 Seth Lloyd , Silvano Garnerone , Paolo Zanardi

This paper proposes a new method for similarity analysis and, consequently, a new algorithm for clustering different types of random attributes, both numerical and nominal. However, in order for nominal attributes to be clustered, their…

Machine Learning · Computer Science 2024-12-16 Zenon Gniazdowski

We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use of quantum approximate counting, and all of…

Quantum Physics · Physics 2023-07-05 Chris Cade , Farrokh Labib , Ido Niesen

Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario,…

Machine Learning · Computer Science 2019-09-13 Tim Jaschek , Marko Bucyk , Jaspreet S. Oberoi

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…

Machine Learning · Computer Science 2025-05-23 Yun-Cheng Tsai , Samuel Yen-Chi Chen

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…

Databases · Computer Science 2020-03-11 Mujahid Sultan

Hierarchical clustering is a stronger extension of one of today's most influential unsupervised learning methods: clustering. The goal of this method is to create a hierarchy of clusters, thus constructing cluster evolutionary history and…

Data Structures and Algorithms · Computer Science 2021-01-14 MohammadTaghi Hajiaghayi , Marina Knittel

Despite the widespread use of Clustering, there is distressingly little general theory of clustering available. Questions like "What distinguishes a clustering of data from other data partitioning?", "Are there any principles governing all…

Machine Learning · Computer Science 2012-05-14 Reza Bosagh Zadeh , Shai Ben-David

We introduce Qlustering, a quantum-inspired algorithm for unsupervised learning that leverages network-based quantum transport to perform data clustering. In contrast to traditional distance-based methods, Qlustering treats the steady-state…

Quantum Physics · Physics 2025-10-28 Shmuel Lorber , Yonatan Dubi

We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…

Data Structures and Algorithms · Computer Science 2018-05-15 Dorit S. Hochbaum

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…

Computational Geometry · Computer Science 2013-10-03 Ulrich Bauer , Michael Kerber , Jan Reininghaus

We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris , Shi Li , Thomas Pensyl , Aravind Srinivasan , Khoa Trinh