Image classification based on quantum K-Nearest-Neighbor algorithm

Image classification is an important task in the field of machine learning and image processing. However, common classification method, the K-Nearest-Neighbor algorithm, has high complexity, because its two main processes: similarity computing and searching, are time-consuming. Especially in the era of big data, the problem is prominent when the amount of images to be classified is large. In this paper, we try to use the powerful parallel computing ability of quantum computers to optimize the efficiency of image classification. The scheme is based on quantum K-Nearest-Neighbor algorithm. Firstly, the feature vectors of images are extracted on classical computers. Then, the feature vectors are inputted into a quantum superposition state, which is used to achieve parallel computing of similarity. Next, the quantum minimum search algorithm is used to speed up searching process for similarity. Finally, the image is classified by quantum measurement. The complexity of the quantum algorithm is only O(kM)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\sqrt{kM})$$\end{document}, which is superior to the classical algorithms. Moreover, the measurement step is executed only once to ensure the validity of the scheme. The experimental results show that the classification accuracy is 83.1%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$83.1\%$$\end{document} on Graz-01 dataset and 78%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$78\%$$\end{document} on Caltech-101 dataset, which is close to existing classical algorithms. Hence, our quantum scheme has a good classification performance while greatly improving the efficiency.