An All-Pair Approach for Big Data Multiclass Classification with Quantum SVM Arit Kumar Bishwas 1 , Ashish Mani 2 , Vasile Palade 3 1 Department of Information Technology, Amity Uttar Pradesh University , Noida, India 2 Department of EEE, Amity Uttar Pradesh University, Noida, India 3 Faculty of Engineering and Computing, Coventry University, Coventry, UK Abstract In this paper we have discussed a quantum approach for the all-pair multiclass classification problem. We have shown that the multiclass support vector machine for big data classification with a quantum all-pair approach can be implemented in logarithm time complexity on a quantum computer. In an all-pair approach, there is one binary classification problem for each pair of classes, and so there are  ( − 1)/2 classifiers for a -class problem. As compared to the classical multiclass support vector machine that can be implemented with polynomial time complexity, our approach exhibits exponential speed up in the quantum version. The quantum all-pair algorithm can be used with other classification algorithms, and a speed up gain can be achieved as compared to their classical counterparts. Keywords: All-Pair Approach, Quantum Algorithm, Multiclass Classification, SVM The recent technological advancements led us to depend on huge volume of data and on the mining of useful information out of it. Many challenging problems nowadays require effective machine learning techniques. Performing any machine-learning task with huge volumes of data has high computational burden. Machine learning (ML) deals with the development of algorithms that can learn from and make predictions on data. At present, one of the most important challenges in machine learning is how to deal with very large data sets (the so called Big Data). ML tasks can be spanned between supervised and unsupervised learning [1-4]. Clustering is an unsupervised learning process where the task is to find patterns with unlabeled data. Whereas classification is a supervised learning process in which labelled (classified) data are used for training purpose and then inferences are made to classify new data examples. Support vector machines (SVM) are widely used as a binary classifier, but in recent years, multiclass support vector machines (MSVM) are one of the widely discussed supervised learning algorithms, which classifies vectors into multiple sets with the help of trained oracles [5]. Many approaches have been proposed for constructing multiclass support vector machines with the help of a binary SVM, one of the most popular being the all-pair approach [6]. In this approach, there is one binary classification problem for each pair of classes, and ( ( − 1)/2 ) classifiers will be constructed. Generally in multiclass classification, the training activity can be implemented by constructing an optimal hyperplane, which divides the input data sets into two sets, either in the original feature space or in a higher- dimensional kernel space and then repeat the activity for k number of times, k being the number of classes. The multiclass SVM problem can be generally formulated as a quadratic programming problem. The multiclass support vector machine quadratic programming problem can then be solved in polynomial run time. In [7], Rebentrost et. al. demonstrated a quantum version of a binary support vector machine classification approach which shows logarithm time complexities for both training and classification stages, so an exponential speed up was achieved as compared to the classical counterpart. The quantum binary SVM algorithm accomplishes an exponential speed up (polynomial to logarithm time complexity) for binary classification. However, this approach does not support multiclass classification. In [8], we have developed a quantum version of one-against- all technique to handle he quantum multiclass classification problem. Now further extending our work, in this paper we have proposed a quantum algorithm for multiclass classification by using a quantum version of an all-pair approach. We have demonstrated that the quantum multiclass approach can be implemented with logarithm time complexity as compared to polynomial time complexity in a classical multiclass approach. We have used the technique mentioned in [7] to construct the binary quantum SVM as a base and then transform it for a multiclass quantum SVM by using the quantum all-pair technique. In this approach, the strategy is to first formulate  ( − 1)/2 quantum binary least square support vector machines. We construct the classifiers by considering all pair of classes, hence there will be  ( − 1)/2 classifiers,  being the cardinality of the class set. Then, all the( ( − 1)/2) classifiers quantum mechanically