Quantum Clustering with k-Means: a Hybrid Approach

2020 International Joint Conference on Neural Networks (IJCNN), 2020

Recently, more researchers are interested in the domain of quantum machine learning as it can manipulate and classify large numbers of vectors in high dimensional space in reasonable time. In this paper, we propose a new approach called Quantum Collaborative K-means which is based on combining several clustering models based on quantum K-means. This collaboration consists of exchanging the information of each algorithm locally in order to find a common underlying structure for clustering. Comparing the classical version of collaborative clustering to our approach, we notice that we have an exponential speed up: while the classical version takes O(K × L × M × N), the quantum version takes only O(K×L×log(M ×N)). And comparing to the quantum version of K-means, we get a better solution in terms of the criteria of validation which means in terms of clustering. The empirical evaluations validate the benefits of the proposed approach.

arXiv (Cornell University), 2023

In this paper, two novel measurement-based clustering algorithms are proposed based on quantum parallelism and entanglement. The Euclidean distance metric is used as a measure of 'similarity' between the data points. The first algorithm follows a divisive approach and the bound for each cluster is determined based on the number of ancillae used to label the clusters. The second algorithm is based on unsharp measurements where we construct the set of effect operators with a gaussian probability distribution to cluster similar data points. We specifically implemented the algorithm on a concentric circle data set for which the classical clustering approach fails. It is found that the presented clustering algorithms perform better than the classical divisive one; both in terms of clustering and time complexity which is found to be O(kN logN) for the first and O(N 2) for the second one. Along with that we also implemented the algorithm on the Churrtiz data set of cities and the Wisconsin breast cancer dataset where we found an accuracy of approximately 97.43% which For the later case is achieved by the appropriate choice of the variance of the gaussian window.

arXiv: Quantum Physics, 2018

We present an algorithm for quantum-assisted cluster analysis (QACA) that makes use of the topological properties of a D-Wave 2000Q quantum processing unit (QPU). Clustering is a form of unsupervised machine learning, where instances are organized into groups whose members share similarities. The assignments are, in contrast to classification, not known a priori, but generated by the algorithm. We explain how the problem can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that the introduced quantum-assisted clustering algorithm is, regarding accuracy, equivalent to commonly used classical clustering algorithms. Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology&...

arXiv: Computational Physics, 2020

Matrix product state has become the algorithm of choice when studying one-dimensional interacting quantum many-body systems, which demonstrates to be able to explore the most relevant portion of the exponentially large quantum Hilbert space and find accurate solutions. Here we propose a quantum inspired K-means clustering algorithm which first maps the classical data into quantum states represented as matrix product states, and then minimize the loss function using the variational matrix product states method in the enlarged space. We demonstrate the performance of this algorithm by applying it to several commonly used machine learning datasets and show that this algorithm could reach higher prediction accuracies and that it is less likely to be trapped in local minima compared to the classical K-means algorithm.

pre-print, 2019

Real-time clustering of big performance data generated by the telecommunication networks requires domain-specific high performance compute infrastructure to detect anomalies. In this paper, we evaluate noisy intermediate-scale quantum (NISQ) computers characterized by low decoherence times, for K-means clustering and propose three strategies to generate shorter-depth quantum circuits needed to overcome the limitation of NISQ computers. The strategies are based on exploiting; i) quantum interference, ii) negative rotations and iii) destructive interference. By comparing our implementations on IBMQX2 machine for representative data sets, we show that NISQ computers can solve the K-means clustering problem with the same level of accuracy as that of classical computers.

ArXiv, 2018

Clustering is a complex process in finding the relevant hidden patterns in unlabeled datasets, broadly known as unsupervised learning. Support vector clustering algorithm is a well-known clustering algorithm based on support vector machines and Gaussian kernels. In this paper, we have investigated the support vector clustering algorithm in quantum paradigm. We have developed a quantum algorithm which is based on quantum support vector machine and the quantum kernel (Gaussian kernel and polynomial kernel) formulation. The investigation exhibits approximately exponential speed up in the quantum version with respect to the classical counterpart.

Machine Learning, 2013

We show how the quantum paradigm can be used to speed up unsupervised learning algorithms. More precisely, we explain how it is possible to accelerate learning algorithms by quantizing some of their subroutines. Quantization refers to the process that partially or totally converts a classical algorithm to its quantum counterpart in order to improve performance. In particular, we give quantized versions of clustering via minimum spanning tree, divisive clustering and k-medians that are faster than their classical analogues. We also describe a distributed version of k-medians that allows the participants to save on the global communication cost of the protocol compared to the classical version. Finally, we design quantum algorithms for the construction of a neighbourhood graph, outlier detection as well as smart initialization of the cluster centres. Keywords Unsupervised learning • Clustering • Quantum learning • Quantum information processing • Grover's algorithm 1 Introduction Consider the following scenario, which illustrates a highly challenging clustering task. Imagine that you are an employee of the Department of Statistics of the United Nations. Your boss gives you the demographic data of all the Earth inhabitants and asks you to anal

Machine-learning tasks frequently involve problems of manipulating and classifying large numbers of vectors in high-dimensional spaces. Classical algorithms for solving such problems typically take time polynomial in the number of vectors and the dimension of the space. Quantum computers are good at manipulating high-dimensional vectors in large tensor product spaces. This paper provides supervised and unsupervised quantum machine learning algorithms for cluster assignment and cluster finding. Quantum machine learning can take time logarithmic in both the number of vectors and their dimension, an exponential speed-up over classical algorithms. In machine learning, information processors perform tasks of sorting, assembling, assimilating, and classifying information [1-2]. In supervised learning, the machine infers a function from a set of training examples. In unsupervised learning the machine tries to find hidden structure in unlabeled data. Recent studies and applications focus in particular on the problem of large-scale machine learning [2]-big data-where the training set and/or the number of features is large. Various results on quantum machine learning investigate the use of quantum information processors to perform machine learning tasks [3-9], including pattern matching [3], Probably Approximately Correct learning [4], feedback learning for quantum measurement [5], binary classifiers [6-7], and quantum support vector machines [8].

2001

We propose a novel clustering method that is based on physical intuition derived from quantum mechanics. Starting with given data points, we construct a scale-space probability function. Viewing the latter as the lowest eigenstate of a Schrodinger equation, we use simple analytic operations to derive a potential function whose minima determine cluster centers. The method has one parameter, determining the

arXiv: Quantum Physics, 2020

Quantum machine learning, though in its initial stage, has demonstrated its potential to speed up some of the costly machine learning calculations when compared to the existing classical approaches. Among the challenging subroutines, computing distance between with the large and high-dimensional data sets by the classical k-medians clustering algorithm is one of them. To tackle this challenge, this paper proposes an efficient quantum k-medians clustering algorithm using the powerful quantum Euclidean estimator algorithm. The proposed quantum k-medians algorithm has provided an exponential speed up as compared to the classical version of it. If and only if we allow the input and the output vectors to be quantum states. The proposed algorithm implementation handled in python with the help of third-party module known as QISKit. The implemented quantum algorithm was executed on the IBM Quantum simulators through cloud. The results from the experiment and simulation suggest that quantum ...