Quantum speed-up for unsupervised learning

• Published in: Machine learning Vol. 90; no. 2; pp. 261 - 287
• Main Authors: Aïmeur, Esma, Brassard, Gilles, Gambs, Sébastien
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.02.2013; Springer; Springer Nature B.V; Springer Verlag
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Artificial Intelligence; Classical and quantum physics: mechanics and fields; Cluster analysis; Clustering; Clusters; Computer Science; Computer science; control theory; systems; Construction costs; Control; Cost engineering; Counting; Cryptography and Security; Exact sciences and technology; Graph theory; Information retrieval. Graph; Learning; Mechatronics; Natural Language Processing (NLP); Physics; Quantum computation; Quantum information; Quantum theory; Robotics; Simulation and Modeling; Theoretical computing; France; Quantum learning; Quantum information processing; Clustering; Unsupervised learning; Grover’s algorithm; Cluster analysis; Data analysis; Costs; Quantum algorithm; Transmission protocol; Cluster; Minimal spanning tree; Unsupervised classification; Grover algorithm; Outlier; Quantum computation; Signal quantization; K median problem; Quantum information; Grover's algorithm
• ISSN: 0885-6125; 1573-0565
• DOI: 10.1007/s10994-012-5316-5

We show how the quantum paradigm can be used to speed up unsupervised learning algorithms. More precisely, we explain how it is possible to accelerate learning algorithms by quantizing some of their subroutines. Quantization refers to the process that partially or totally converts a classical algorithm to its quantum counterpart in order to improve performance. In particular, we give quantized versions of clustering via minimum spanning tree, divisive clustering and k -medians that are faster than their classical analogues. We also describe a distributed version of k -medians that allows the participants to save on the global communication cost of the protocol compared to the classical version. Finally, we design quantum algorithms for the construction of a neighbourhood graph, outlier detection as well as smart initialization of the cluster centres.