Semi-supervised time series classification method for quantum computing
Tóm tắt
In this paper we develop methods to solve two problems related to time series (TS) analysis using quantum computing: reconstruction and classification. We formulate the task of reconstructing a given TS from a training set of data as an unconstrained binary optimization (QUBO) problem, which can be solved by both quantum annealers and gate-model quantum processors. We accomplish this by discretizing the TS and converting the reconstruction to a set cover problem, allowing us to perform a one-versus-all method of reconstruction. Using the solution to the reconstruction problem, we show how to extend this method to perform semi-supervised classification of TS data. We present results indicating our method is competitive with current semi- and unsupervised classification techniques, but using less data than classical techniques.
Tài liệu tham khảo
Acharya J, Das H, Milenkovic O, Orlitsky A, Pan S (2010) On reconstructing a string from its substring compositions. 1238–1242 07
Aghabozorgi S, Shirkhorshidi AS, Wah TY (2015) Time-series clustering – a decade review. Inf Syst 53:16–38
Aharonov D, Van Dam W, Kempe J, Landau Z, Lloyd S, Regev O (2008) Adiabatic quantum computation is equivalent to standard quantum computation. SIAM Rev 50(4):755–787
Aimeur E, Brassard G, Gambs S (2013) Quantum speed-up for unsupervised learning. Mach Learn 90(02):261–287
AL G, LAN A, L G, JM I, Hausdorff amd PC, RG M, JE M, Moody G, C-K P, Stanley H (2003) Mit-bih long-term ecg database. physionet.org/content/ltdb/1.0.0/. PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulation 101(23):e215-e220
Alexander C, Shi L, Akhmametyeva S (2018) Using quantum mechanics to cluster time series. arXiv
Arute F, Arya K, Babbush R, Bacon D, Bardin JC, Barends R, Biswas R, Boixo S, Brandao FG, Buell DA et al (2019) Quantum supremacy using a programmable superconducting processor. Nature 574(7779):505–510
Bagnall A, Lines J, Bostrom A, Large J, Keogh E (2017) The great time series classification bake off: a review and experimental evaluation of recent algorithmic advances. Data Mining Knowl Disc 31 (3):606–660
Bagnall A, Lines J, Vickers W, Keogh E The uea & ucr time series classification repository. www.timeseriesclassification.com. Accessed: 2020-02-01
Barahona F (1982) On the computational complexity of ising spin glass models. J Phys A Math Gen 15(10):3241
Chinatown DHA (2020). . http://www.pedestrian.melbourne.vic.gov.au. Accessed: 2020-02-01
Christ M, Braun N, Neuffer J, Kempa-Liehr AW (2018) Time series feature extraction on basis of scalable hypothesis tests (tsfresh – a python package). Neurocomputing 307:72–77
Chu S, Keogh EJ, Hart DM, Pazzani MJ (2002) Iterative deepening dynamic time warping for time series. In: SDM
D-Wave Systems (2021) D-Wave Dimod Package. https://docs.ocean.dwavesys.com/projects/dimod/
Farhi E, Goldstone J, Gutmann S (2014) A quantum approximate optimization algorithm. arXiv:1411.4028
Frieze AM, Preparata FP, Upfal E (1999) Optimal reconstruction of a sequence from its probes. J Comput Biol 6(3-4):361–368
Fu T (2011) A review on time series data mining. Eng Appl Artif Intell 24(1):164–181
Gomaa WH, Fahmy AA, et al. (2013) A survey of text similarity approaches. Int J Comput Appl 68(13):13–18
Gonzalez JA, Zolhavarieh S, Aghabozorgi S, Teh YW (2014) A review of subsequence time series clustering. The Scientific World Journal 312521
Grimsley HR, Economou SE, Barnes E, Mayhall NJ (2019) An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nat Commun 10(1):3007
Guo C, Li H, Pan D (2010) An improved piecewise aggregate approximation based on statistical features for time series mining. In: Bi Y, Williams M-A (eds) Knowledge Science, Engineering and Management. Springer, Berlin, pp 234–244
Hautamaki V, Nykanen P, Franti P (2008) Time-series clustering by approximate prototypes. In: 2008 19th International conference on pattern recognition, pp 1–4
Hills J, Lines J, Baranauskas E, Mapp J, Bagnall A (2014) Classification of time series by shapelet transformation. Data Min Knowl Disc 28(4):851–881
Horn D, Gottlieb A (2001) The method of quantum clustering. In: Proceedings of the 14th international conference on neural information processing systems: natural and synthetic, NIPS’01, pp769–776, Cambridge, MA, USA, MIT Press
Iwama K, Teruyama J, Tsuyama S (2018) Reconstructing strings from substrings: Optimal randomized and average-case algorithms. arXiv:1808.00674
Johnson MW, Amin MHS, Gildert S, Lanting T, Hamze F, Dickson N, Harris R, Berkley AJ, Johansson J, Bunyk P, Chapple EM, Enderud C, Hilton JP, Karimi K, Ladizinsky E, Ladizinsky N, Oh T, Perminov I, Rich C, Thom MC, Tolkacheva E, Truncik CJS, Uchaikin S, Wang J, Wilson B, Rose G (2011) Quantum annealing with manufactured spins. Nature 473(7346):194–198
Kadowaki T, Nishimori H (1998) Quantum annealing in the transverse ising model. Phys Rev E 58:5355–5363
Karp R (1972) Reducibility among combinatorial problems, volume 85. Complexity of Computer Computations
Keogh E, Lin J, Fu A (2005) Hot sax: Efficiently finding the most unusual time series subsequence. In: Proceedings of the Fifth IEEE international conference on data mining, ICDM ’05, pp 226–233, USA, IEEE Computer Society
Kumar V, Bass G, Tomlin C, Dulny J (2018) Quantum annealing for combinatorial clustering. Quantum Inf Process 17(2):39
Liao TW (2005) Clustering of time series data—a survey. Pattern Recogn 38(11):1857–1874
Lin J, Keogh E, Lonardi S, Chiu B (2003) A symbolic representation of time series, with implications for streaming algorithms. In: Proceedings of the 8th ACM SIGMOD workshop on research issues in data mining and knowledge Discovery, DMKD ’03, page 2–11, New York, NY, USA. Association for Computing Machinery
Lin J, Keogh E, Lonardi S, Patel P (2002) Finding motifs in time series. Proceedings of the Second Workshop on Temporal Data Mining 10
Lloyd S, Mohseni M, Rebentrost P (2013) Quantum algorithms for supervised and unsupervised machine learning
Lucas A (2014) Ising formulations of many np problems. Front Phys 2:5
McCaskey AJ, Parks ZP, Jakowski J, Moore SV, Morris TD, Humble TS, Pooser RC (2019) Quantum chemistry as a benchmark for near-term quantum computers. npj Quantum Inform 5(1):99
Mueen A, Keogh E, Young N (2011) Logical-shapelets: an expressive primitive for time series classification. In: Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 1154–1162. ACM
Neukart F, Compostella G, Seidel C, von Dollen D, Yarkoni S, Parney B (2017) Traffic flow optimization using a quantum annealer. Frontiers in ICT 4:29
Neukart F, Dollen DV, Seidel C (2018) Quantum-assisted cluster analysis on a quantum annealing device. Front Phys 6:55
Nishimura N, Tanahashi K, Suganuma K, Miyama MJ, Ohzeki M (2019) Item listing optimization for e-commerce websites based on diversity. Front Comput Sci 1:2
Patel P, Keogh EJ, Lin J, Lonardi S (2002) Mining motifs in massive time series databases. . In: 2002 IEEE International conference on data mining, 2002. Proceedings, pp 370–377
Preskill J (2018) Quantum Computing in the NISQ era and beyond. Quantum 2:79
Ratanamahatana CA, Keogh EJ (2005) Three myths about dynamic time warping data mining. In: Kargupta H, Srivastava J, Kamath C, Goodman A (eds) SDM, pp 506–510. SIAM
Raymond J, Yarkoni S, Andriyash E (2016) Global warming: Temperature estimation in annealers. Front ICT 3:23
Sakoe H, Chiba S (1978) Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans Acoust Speech Signal Process 26(1):43–49
Schäfer P, Högqvist M (2012) Sfa: a symbolic fourier approximation and index for similarity search in high dimensional datasets. In: Proceedings of the 15th International conference on extending database technology, pp 516–527. ACM
Senin P, Lin J, Wang X, Oates T, Gandhi S, Boedihardjo AP, Chen C, Frankenstein S. (2018) Grammarviz 3.0: Interactive discovery of variable-length time series patterns. ACM Trans Knowl Discov Data 12(1):10:1–10:28
Skiena SS, Sundaram G (1995) Reconstructing strings from substrings. J Comput Biol 2 (2):333–353
Stollenwerk T, O’Gorman B, Venturelli D, Mandrà S, Rodionova O, Ng H, Sridhar B, Rieffel EG, Biswas R (2020) Quantum annealing applied to de-conflicting optimal trajectories for air traffic management. IEEE Trans Intell Transp Syst 21(1):285–297
Streif M, Neukart F, Leib M (2019) Solving quantum chemistry problems with a d-wave quantum annealer. In: Feld S, Linnhoff-Popien C (eds) Quantum technology and optimization problems. Springer International Publishing, Cham, pp 111–122
Van Dam W, Mosca M, Vazirani U (2001) How powerful is adiabatic quantum computation?. In: Proceedings 42nd IEEE symposium on foundations of computer science. pp 279–287 IEEE
Venturelli D, Kondratyev A (2019) Reverse quantum annealing approach to portfolio optimization problems. Quantum Mach Intell 1(1):17–30
Venturelli D, Marchand DJ, Rojo G (2015) Quantum annealing implementation of job-shop scheduling. arXiv:1506.08479
Verdon G, Broughton M, Biamonte J (2017) A quantum algorithm to train neural networks using low-depth circuits
Vlachos M, Gunopulos D, Kollios G (2002) Discovering similar multidimensional trajectories. In: Proceedings 18th international conference on data engineering. pp 673–684
Wagner P, Strodthoff N, Bousseljot R-D, Kreiseler D, Lunze FI, Samek W, Schaeffter T (2020) Ptb-xl, a large publicly available electrocardiography dataset. Scient Data 7(1):154
Wiebe N, Kapoor A, Svore K (2015) Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning. Quantum Inform Comput 15:318–358 03
Xiaodong F, Changling C, Changling L, Shao H (2002) An improved process data compression algorithm. In: Proceedings of the 4th world congress on intelligent control and automation (Cat. no.02EX527) volume 3, vol 3, pp 2190–2193