Semantic distillation: a method for clustering objects by their contextual specificity

Techniques for data-mining, latent semantic analysis, contextual search of databases, etc. have long ago been developed by computer scientists working on information retrieval (IR). Experimental scientists, from all disciplines, having to analyse large collections of raw experimental data (astronomical, physical, biological, etc.) have developed powerful methods for their statistical analysis and for clustering, categorising, and classifying objects. Finally, physicists have developed a theory of quantum measurement, unifying the logical, algebraic, and probabilistic aspects of queries into a single formalism. The purpose of this paper is twofold: first to show that when formulated at an abstract level, problems from IR, from statistical data analysis, and from physical measurement theories are very similar and hence can profitably be cross-fertilised, and, secondly, to propose a novel method of fuzzy hierarchical clustering, termed \textit{semantic distillation} -- strongly inspired from the theory of quantum measurement --, we developed to analyse raw data coming from various types of experiments on DNA arrays. We illustrate the method by analysing DNA arrays experiments and clustering the genes of the array according to their specificity.Comment: Accepted for publication in Studies in Computational Intelligence, Springer-Verla

Graph Analysis Using a GPU-based Parallel Algorithm: Quantum Clustering

The article introduces a new method for applying Quantum Clustering to graph structures. Quantum Clustering (QC) is a novel density-based unsupervised learning method that determines cluster centers by constructing a potential function. In this method, we use the Graph Gradient Descent algorithm to find the centers of clusters. GPU parallelization is utilized for computing potential values. We also conducted experiments on five widely used datasets and evaluated using four indicators. The results show superior performance of the method. Finally, we discuss the influence of $\sigma$ on the experimental results

Quantum Motif Clustering

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 them obtain square-root like speedups over the fastest classical algorithms in various settings. In order to use approximate counting in the context of clustering, we show that for general weighted graphs the performance of spectral clustering is mostly left unchanged by the presence of constant (relative) errors on the edge weights. Finally, we extend the original analysis of motif clustering in order to better understand the role of multiple `anchor nodes' in motifs and the types of relationships that this method of clustering can and cannot capture.Comment: 51 pages, 11 figure

Microscopic approach to the spectator matter fragmentation from 400 to 1000 AMeV

A study of multifragmentation of gold nuclei is reported at incident energies of 400, 600 and 1000 MeV/nucleon using microscopic theory. The present calculations are done within the framework of quantum molecular dynamics (QMD) model. The clusterization is performed with advanced sophisticated algorithm namely \emph{simulated annealing clusterization algorithm} (SACA) along with conventional spatial correlation method. A quantitative comparison of mean multiplicity of intermediate mass fragments with experimental findings of ALADiN group gives excellent agreement showing the ability of SACA method to reproduce the fragment yields. It also emphasizes the importance of clustering criterion in describing the fragmentation process within semi-classical model

Variational Quantum and Quantum-Inspired Clustering

Here we present a quantum algorithm for clustering data based on a variational quantum circuit. The algorithm allows to classify data into many clusters, and can easily be implemented in few-qubit Noisy Intermediate-Scale Quantum (NISQ) devices. The idea of the algorithm relies on reducing the clustering problem to an optimization, and then solving it via a Variational Quantum Eigensolver (VQE) combined with non-orthogonal qubit states. In practice, the method uses maximally-orthogonal states of the target Hilbert space instead of the usual computational basis, allowing for a large number of clusters to be considered even with few qubits. We benchmark the algorithm with numerical simulations using real datasets, showing excellent performance even with one single qubit. Moreover, a tensor network simulation of the algorithm implements, by construction, a quantum-inspired clustering algorithm that can run on current classical hardware.Comment: 5 pages, 3 figures, revised versio