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International Conference on Contemporary Computing and Informatics (IC3I)

Big data classification with quantum multiclass SVM and quantum one-against-all approach

Arit Kumar Bishwas, Ashish Mani, Vasile Palade

Published Dec 1, 2016• 20 citations
Publisher

Abstract

In this paper, we have proposed a quantum approach for multiclass support vector machines to handle big data classification. To achieve this goal, we have also developed and implemented a quantum version of the one-against-all algorithm. The proposed approach demonstrates that the big data multiclass classification can be implemented with quantum multiclass support vector machine in logarithmic time complexity on a quantum computer, compared to the classical multiclass support vector machines that can be implemented with polynomial time complexity. Hence, our proposed approach exhibits an exponential speed up in time complexity for big data multiclass classification.

DOI
10.1109/ic3i.2016.7918805

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In this paper, we have proposed a quantum approach for multiclass support vector machines to handle big data classification. To achieve this goal, we have also developed and implemented a quantum version of the one-against-all algorithm. The proposed approach demonstrates that the big data multiclass classification can be implemented with quantum multiclass support vector machine in logarithmic time complexity on a quantum computer, compared to the classical multiclass support vector machines that can be implemented with polynomial time complexity. Hence, our proposed approach exhibits an exponential speed up in time complexity for big data multiclass classification.
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.
Abstract Classical machine learning algorithms seem to be totally incapable of processing tremendous data, while quantum machine learning algorithms could deal with big data unhurriedly and provide exponential acceleration over classical counterparts. In this paper, we propose two quantum support vector machine algorithms for multi classification. One is the quantum version of the directed acyclic graph support vector machine. The other one is to use the Grover search algorithm before measurement, which amplifies the amplitude of the phase storing of the classification result. For k classification, the former provides quadratic reduction in computational complexity when classifying. The latter accelerates the training speed significantly and more importantly, the classification result can be read out with a probability of at least 50% using only one measurement. We conduct numerical simulations on two algorithms, and their classification success rates are 96% and 88.7%, respectively.
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 linear and non-linear binary classifier, can be implemented on a quantum computer, with exponential speedups in the size of the vectors and the number of training data examples. At the core of the algorithm is a non-sparse matrix simulation technique to efficiently perform a principal component analysis and matrix inversion of the training data kernel matrix. We thus provide an example of a quantum big feature and big data algorithm and pave the way for future developments at the intersection of quantum computing and machine learning.
Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space and the number of data points. To tackle the big data challenge, a quantum SVM algorithm was proposed, which is claimed to achieve exponential speedup for least squares SVM (LS-SVM). Here, inspired by the quantum SVM algorithm, we present a quantum-inspired classical algorithm for LS-SVM. In our approach, an improved fast sampling technique, namely indirect sampling, is proposed for sampling the kernel matrix and classifying. We first consider the LS-SVM with a linear kernel, and then discuss the generalization of our method to nonlinear kernels. Theoretical analysis shows our algorithm can make classification with arbitrary success probability in logarithmic runtime of both the dimension of data space and the number of data points for low rank, low condition number, and high dimensional data matrix, matching the runtime of the quantum SVM.
The evolution of quantum computers and quantum machine learning (QML) algorithms have started demonstrating exponential speed-ups. In machine learning problems, the efficient handling and manipulation of linear algebra subroutines defines the complexity of the task to be performed. Quantum computers handle big datasets in the form of vectors and matrix operations very efficiently. In this paper, quantum support vector machine (QSVM) algorithm is used to solve a classification problem using a benchmarking MNIST dataset of handwritten images of digits. Quantum SVM variational and kernel matrix algorithms are implemented to analyze quantum speedup on quantum simulator and physical quantum processor back-ends. The study compared classical and quantum SVM algorithms in terms of execution time and accuracy. The results explicitly prove quantum speed-up achieved by quantum classifiers on quantum back-ends for machine learning applications.
The exponential growth of data and the increasing complexity of high-dimensional classification problems have pushed classical computing methods to their limits. Quantum computing emerges as a promising paradigm to address these challenges. This research article explores advanced quantum algorithms for big data clustering and high-dimensional classification. We investigate quantum versions of K-means, spectral clustering, and support vector machines, comparing their performance with classical counterparts. Our results demonstrate significant speedups in processing time and improvements in clustering quality for high-dimensional datasets. Additionally, we propose a novel quantum-inspired classical algorithm that bridges the gap between quantum and classical approaches. This comprehensive study provides insights into the potential of quantum computing in revolutionizing data analysis and machine learning, paving the way for future advancements in the field.