An investigation on support vector clustering for big data in quantum paradigm

Abstract

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 $O\left( {M^{2} N} \right)$ runtime complexity, where M is the number of input objects and N is the dimension of the feature space. Our proposed quantum version converges in $\sim O\left( {\log MN} \right)$ runtime complexity. The clustering identification phase with adjacency matrix exhibits $O\left( {\sqrt {M^{3} lgM} } \right)$ runtime complexity in the quantum version, whereas the runtime complexity in the classical implementation is $O\left( {M^{2} } \right)$. The proposed quantum version of the support vector clustering method demonstrates a significant speedup gain on the overall runtime complexity as compared to the classical counterpart.