A Dynamic Quantum Clustering Approach to Brain Tumor Segmentation

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 (Cornell University), 2022

Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this paper, we design, implement, and evaluate three hybrid quantum k-Means algorithms, exploiting different degree of parallelism. Indeed, each algorithm incrementally leverages quantum parallelism to reduce the complexity of the cluster assignment step up to a constant cost. In particular, we exploit quantum phenomena to speed up the computation of distances. The core idea is that the computation of distances between records and centroids can be executed simultaneously, thus saving time, especially for big datasets. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version, still obtaining comparable clustering results.

IEEE International Conference on Image Processing 2005, 2005

This paper introduces a new nonparametric estimation approach that can be used for data that is not necessarily Gaussian distributed. The proposed approach employs the Shrödinger partial differential equation. We assume that each data sample is associated with a quantum physics particle that has a radial field around its value. We consider a statistical estimation approach for finding the size of the influence field around each data sample. By implementing the Shrödinger equation we obtain a potential field that is assimilated with the data density. The regions of minima in the potential are determined by calculating the local Hessian on the potential hypersurface. The quantum clustering approach is applied for blind separation of signals and for segmenting SAR images of terrain based on surface normal orientation.

Physical Review E, 2009

A given set of data-points in some feature space may be associated with a Schrödinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrödinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition or feature filtering. PACS numbers: 89.75.Fb,89.90.+n,95.75.Pq,89.75.Kd −1/2 i,j

2014 International Conference on Computational Intelligence and Communication Networks, 2014

Clustering is a simple technique to make partition of given data set into number of clusters. This paper presents an quantum inspired algorithm using GA to automatically find the number of clusters for image data set. The advantage lies in this technique is that no previous information about the data set used for classification is required before hand. The method decides the optimum cluster number on run. The popular evolutionary method called genetic algorithm has been used for generation wise improvement of clustering. CS measure is used as a fitness function in clustering. Effectiveness and accuracy of the proposed technique are demonstrated in terms of standard error found in computation. Finally, desired number of threshold values are heuristically taken from the input image to produce the image after thresholding.

ArXiv, 2019

Quantum Clustering is a powerful method to detect clusters in data with mixed density. However, it is very sensitive to a length parameter that is inherent to the Schrodinger equation. In addition, linking data points into clusters requires local estimates of covariance that are also controlled by length parameters. This raises the question of how to adjust the control parameters of the Schrodinger equation for optimal clustering. We propose a probabilistic framework that provides an objective function for the goodness-of-fit to the data, enabling the control parameters to be optimised within a Bayesian framework. This naturally yields probabilities of cluster membership and data partitions with specific numbers of clusters. The proposed framework is tested on real and synthetic data sets, assessing its validity by measuring concordance with known data structure by means of the Jaccard score (JS). This work also proposes an objective way to measure performance in unsupervised learni...

Mathematics

In real-world scenarios, identifying the optimal number of clusters in a dataset is a difficult task due to insufficient knowledge. Therefore, the indispensability of sophisticated automatic clustering algorithms for this purpose has been contemplated by some researchers. Several automatic clustering algorithms assisted by quantum-inspired metaheuristics have been developed in recent years. However, the literature lacks definitive documentation of the state-of-the-art quantum-inspired metaheuristic algorithms for automatically clustering datasets. This article presents a brief overview of the automatic clustering process to establish the importance of making the clustering process automatic. The fundamental concepts of the quantum computing paradigm are also presented to highlight the utility of quantum-inspired algorithms. This article thoroughly analyses some algorithms employed to address the automatic clustering of various datasets. The reviewed algorithms were classified accord...

2021

The development of Noisy Intermediate Scale Quantum computers is expected to signify potential advantages of quantum computing over classical computing. This paper focuses on quantum paradigm usage to speed up unsupervised machine learning algorithms particularly the K-means clustering method. The main approach is to build a quantum circuit that performs the distance calculation required for the clustering process. This proposed technique is a collaboration of data mining techniques with quantum computation. Initially extracted heart disease dataset is preprocessed and classical K-means performance is evaluated. Later, the quantum concept is applied to the classical approach of the clustering algorithm. The comparative analysis is performed between quantum and classical processing to check performance metrics.

2008

In the field of information processing like data mining, information retrieval, natural language processing and machine learning, Quantum Computing play vital role for extracting the implicit, potentially useful and previously unknown information from huge sets of data. In [1] and [2], proposed two techniques of document ranking and document clustering with Quantum concept. The Quantum Clustering (QC) technique used for information processing which is basically depends on time independent Schrödinger equation for clustering the data and the Dynamic Quantum Clustering (DQC) came into existence when dynamic of the system is computed by means of the time dependent Schrödinger equation. The Dynamic Quantum Clustering (DQC),is a recent clustering technique based on physical perception from quantum mechanics where clusters are computed by means of the time dependent Schrödinger equation and clusters are identified as the minima of the potential function of the Schrödinger equation. In thi...

International Journal of Data Mining, Modelling and Management, 2010

The emerging field of quantum computing has recently created much interest in the computer science community due to the new concepts it suggests to store and process data. In this paper, we explore some of these concepts to cope with the data clustering problem. Data clustering is a key task for most fields like data mining and pattern recognition. It aims to discover cohesive groups in large datasets. In our work, we cast this problem as an optimisation process and we describe a novel framework, which relies on a quantum representation to encode the search space and a quantum evolutionary search strategy to optimise a quality measure in quest of a good partitioning of the dataset. Results on both synthetic and real data are very promising and show the ability of the method to identify valid clusters and also its effectiveness comparing to other evolutionary algorithms. . Her areas of interest include computational intelligence, quantum inspired computing, bioinformatics and image analysis.

Theoretical Computer Science, 2014

In this paper we investigate the use of quantum computing systems in the field of image processing. We consider histogram-based image processing operations and develop quantum algorithms for histogram computation and threshold-based segmentation. The underlying principle used for constructing the proposed quantum algorithms is to reformulate them in order to exploit the performance of the quantum Fourier transform and of quantum amplitude amplification. We show that, compared to the classical correspondents, a significant speedup can be achieved by expressing parts of the computational process in terms of problems that can be solved using these quantum techniques.

2021

Enormous activity in the Quantum Computing area has resulted in considering them to solve different difficult problems, including those of applied nature, together with classical computers. An attempt is made in this work to nail down a pipeline consisting of both quantum and classical processing blocks for the task of image classification and segmentation in a systematic fashion. Its efficacy and utility are brought out by applying it to Surface Crack segmentation. Being a sophisticated software engineering task, the functionalities are orchestrated through our in-house Cognitive Model Management framework.

2008

ArXiv, 2019

In this paper, we have proposed a deep quantum SVM formulation, and further demonstrated a quantum-clustering framework based on the quantum deep SVM formulation, deep convolutional neural networks, and quantum K-Means clustering. We have investigated the run time computational complexity of the proposed quantum deep clustering framework and compared with the possible classical implementation. Our investigation shows that the proposed quantum version of deep clustering formulation demonstrates a significant performance gain (exponential speed up gains in many sections) against the possible classical implementation. The proposed theoretical quantum deep clustering framework is also interesting & novel research towards the quantum-classical machine learning formulation to articulate the maximum performance.

Frontiers in Physics, 2018

We present an algorithm for quantum-assisted cluster analysis that makes use of the topological properties of a D-Wave 2000Q quantum processing unit. 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 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 [1], have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization, sampling, and clustering [2-17]. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical clustering algorithm.