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An investigation on support vector clustering for big data in quantum paradigm
Quantum Information Processing
The support vector clustering algorithm is a well-known clustering algorithm based on support vector machines using Gaussian or polynomial kernels. The classical support vector clustering algorithm works well in general, but its performance degrades when applied on big data. In this paper, we have investigated the performance of support vector clustering algorithm implemented in a quantum paradigm for possible runtime improvements. We have developed and analyzed a quantum version of the support vector clustering algorithm. The proposed approach is based on the quantum support vector machine [1] and quantum kernels (i.e., Gaussian and polynomial). The classical support vector clustering algorithm converges in (2) runtime complexity, where is the number of input objects and is the dimension of the feature space. Our proposed quantum version converges in ~() runtime complexity. The clustering identification phase with adjacency matrix exhibits (√ 3) runtime complexity in the quantum version, whereas the runtime complexity in the classical implementation is (2). The proposed quantum version of the SVM clustering method demonstrates a significant speed-up gain on the overall runtime complexity as compared to the classical counterpart.
Quantum support vector machine for big data classification
Physical review letters, 2014
Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.
Quantum algorithms for supervised and unsupervised machine learning
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].
Quantum Clustering with k-Means: a Hybrid Approach
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.
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.
Classical Equivalent Quantum Unsupervised Learning Algorithms
Procedia Computer Science, 2020
The paper presents necessity of data pre-processing to process the data set through machine learning raw data to make the data as in compatible format for analysis purpose. The and dimensionality reduction are used for data smoothing to predict best possible outcome as per the analysis. Machine learning became famous for such p unsupervised learning we are capable of processing over various data formats. Such algorithms but as per the availability of inherent parallel processing through designing classical equivalent quantum machine learning algorithms. In this paper, we discussed some of the classical unsupervised learning algorithms, and then we propose the equivalent quantum version of algorithms along with th mathematical justification over the complexity analysis and achieved computational speedup and show processing such problems over quantum machines.
ILF: A Quantum Semi-Supervised Learning Approach for Binary Classification
International Journal of Advanced Research in Computer and Communication Engineering., 2023
The lack of enough labeled data is a great issue when designing a real-life scheme. Data labeling is timeconsuming as well as costly. Semi-supervised learning (SSL) is a way to solve the issues of data labeling. SSL uses a tiny quantity of labeled data to find labels of massive quantities of unlabeled data. This paper presents a quantum-classical SSL mechanism named "Iterative Labels Finding (ILF)" by combining the Quantum Support Vector Machine algorithm (QSVM) and Ising Models Based Binary Clustering algorithm. The proposed method performs a matching and iteration process to discover the labels of unlabeled data. ILF is designed for binary classification purposes. We have illustrated the experimental result of ILF with a real-time dataset and with a practical example. From experimental results, we have found ILF as a highly efficient approach for quantum SSL.
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.
Performance Analysis of Quantum Classifier on Benchmarking Datasets
IJEER, 2022
Quantum machine learning (QML) is an evolving field which is capable of surpassing the classical machine learning in solving classification and clustering problems. The enormous growth in data size started creating barrier for classical machine learning techniques. QML stand out as a best solution to handle big and complex data. In this paper quantum support vector machine (QSVM) based models for the classification of three benchmarking datasets namely, Iris species, Pumpkin seed and Raisin has been constructed. These QSVM based classification models are implemented on real-time superconducting quantum computers/simulators. The performance of these classification models is evaluated in the context of execution time and accuracy and compared with the classical support vector machine (SVM) based models. The kernel based QSVM models for the classification of datasets when run on IBMQ_QASM_simulator appeared to be 232, 207 and 186 times faster than the SVM based classification model. The results indicate that quantum computers/algorithms deliver quantum speed-up.
Measurement-Based Quantum Clustering Algorithms
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.