This paper proposes a novel classifier based on the theory of Learning Automata (LA), reckoned to as PolyLA. The essence of our scheme is to search for a separator in the feature space by imposing an LA-based random walk in a grid system. To each node in the grid, we attach an LA whose actions are the choices of the edges forming a separator. The walk is self-enclosing, and a new random walk is started whenever the walker returns to the starting node forming a closed classification path yielding a many-edged polygon. In our approach, the different LA attached to the different nodes search for a polygon that best encircles and separates each class. Based on the obtained polygons, we perform classification by labeling items encircled by a polygon as part of a class using a ray casting function. From a methodological perspective, PolyLA has appealing properties compared to SVM. In fact, unlike PolyLA, the SVM performance is dependent on the right choice of the kernel function (e.g., linear kernel, Gaussian kernel)—which is considered a “black art.” PolyLA, on the other hand, can find arbitrarily complex separator in the feature space. We provide sound theoretical results that prove the optimality of the scheme. Furthermore, experimental results show that our scheme is able to perfectly separate both simple and complex patterns outperforming existing classifiers, such as polynomial and linear SVM, without the need to map the problem to many dimensions or to introduce a “kernel trick.” We believe that the results are impressive, given the simplicity of PolyLA compared to other approaches such as SVM.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
It is easy to generalize the current model to multi-dimensional by considering pairs of dimensions. In this article, we limit ourselves to the two-dimensional case as a proof of concept. Experiments for the multi-dimensional case can be provided if the requested by the referee.
By some of the authors of this paper.
Note that s is one of the possible polygons with the shortest circumference that is able to perfectly separate the data. The reason for this is explained in Sect. 5.5.
Caruana R, Niculescu-Mizil A (2006) An empirical comparison of supervised learning algorithms. In: Proceedings of the 23rd international conference on machine learning. ACM, pp 161–168
Caruana R, Karampatziakis N, Yessenalina A (2008) An empirical evaluation of supervised learning in high dimensions. In: Proceedings of the 25th international conference on machine learning. ACM, pp 96–103
Madjarov G, Kocev D, Gjorgjevikj D, Džeroski S (2012) An extensive experimental comparison of methods for multi-label learning. Pattern Recognit 45(9):3084–3104
Goodwin M, Tufteland T, Ødesneltvedt G, Yazidi A (2017) Polyaco+: a multi-level polygon-based ant colony optimisation classifier. Swarm Intell 11(3–4):317–346
Agache M, Oommen BJ (2002) Generalized pursuit learning schemes: new families of continuous and discretized learning automata. IEEE Trans Syst Man Cybern Part B Cybern 32(6):738–749
Lakshmivarahan S (1981) Learning algorithms theory and applications. Springer, Berlin
Najim K, Poznyak AS (1994) Learning automata: theory and applications. Pergamon Press, Oxford
Narendra KS, Thathachar MAL (1989) Learning automata: an introduction. Prentice-Hall, Inc, Upper Saddle River
Obaidat MS, Papadimitriou GI, Pomportsis AS (2002) Learning automata: theory, paradigms, and applications. IEEE Trans Syst Man Cybern Part B Cybern 32(6):706–709
Poznyak AS, Najim K (1997) Learning automata and stochastic optimization. Springer, Berlin
Thathachar MAL, Sastry PS (2003) Networks of learning automata: techniques for online stochastic optimization. Kluwer Academic, Boston
Tsetlin ML (1973) Automaton theory and the modeling of biological systems. Academic Press, New York
Misra S, Oommen BJ (2004) GPSPA: a new adaptive algorithm for maintaining shortest path routing trees in stochastic networks. Int J Commun Syst 17:963–984
Obaidat MS, Papadimitriou GI, Pomportsis AS, Laskaridis HS (2002) Learning automata-based bus arbitration for shared-edium ATM switches. IEEE Trans Syst Man Cybern Part B 32:815–820
Oommen BJ, Roberts TD (2000) Continuous learning automata solutions to the capacity assignment problem. IEEE Trans Comput 49:608–620
Papadimitriou GI, Pomportsis AS (2000) Learning-automata-based TDMA protocols for broadcast communication systems with bursty traffic. IEEE Commun Lett 4:107–109
Atlassis AF, Loukas NH, Vasilakos AV (2000) The use of learning algorithms in ATM networks call admission control problem: a methodology. Comput Netw 34:341–353
Atlassis AF, Vasilakos AV (2002) The use of reinforcement learning algorithms in traffic control of high speed networks. In: Zimmermann H-J, Tselentis G, van Someren M, Dounias G (eds) Advances in computational intelligence and learning. International Series in Intelligent Technologies, vol 18. Springer, Dordrecht, pp 353–369
Vasilakos AV, Saltouros MP, Atlassis AF, Pedrycz W (2003) Optimizing QoS routing in hierarchical ATM networks using computational intelligence techniques. IEEE Trans Syst Man Cybern Part C 33:297–312
Seredynski F (1998) Distributed scheduling using simple learning machines. Eur J Oper Res 107:401–413
Kabudian J, Meybodi MR, Homayounpour MM (2004) Applying continuous action reinforcement learning automata (CARLA) to global training of hidden markov models. In: Proceedings of the international conference on information technology: coding and computing, ITCC’04. Nevada, Las Vegas, pp 638–642
Meybodi MR, Beigy H (2002) New learning automata based algorithms for adaptation of backpropagation algorithm pararmeters. Int J Neural Syst 12:45–67
Unsal C, Kachroo P, Bay JS (1997) Simulation study of multiple intelligent vehicle control using stochastic learning automata. Trans Soc Comput Simul 14:193–210
Oommen BJ, de St Croix EV (1995) Graph partitioning using learning automata. IEEE Trans Comput 45:195–208
Collins JJ, Chow CC, Imhoff TT (1995) Aperiodic stochastic resonance in excitable systems. Phys Rev E 52:R3321–R3324
Cook RL (1986) Stochastic sampling in computer graphics. ACM Trans Graph 5:51–72
Barzohar M, Cooper DB (1996) Automatic finding of main roads in aerial images by using geometric-stochastic models and estimation. IEEE Trans Pattern Anal Mach Intell 7:707–722
Brandeau ML, Chiu SS (1989) An overview of representative problems in location research. Manag Sci 35:645–674
Bettstetter C, Hartenstein H, Prez-Costa X (2004) Stochastic properties of the random waypoint mobility model. J Wirel Netw 10:555–567
Rowlingson BS, Diggle PJ (1991) SPLANCS: spatial point pattern analysis code in S-plus. University of Lancaster, North West Regional Research Laboratory
Paola M (1998) Digital simulation of wind field velocity. J Wind Eng Ind Aerodyn 74–76:91–109
Cusumano JP, Kimble BW (1995) A stochastic interrogation method for experimental measurements of global dynamics and basin evolution: application to a two-well oscillator. Nonlinear Dyn 8:213–235
Baddeley A, Turner R (2005) Spatstat: an R package for analyzing spatial point patterns. J Stat Softw 12:1–42
Oommen BJ, Agache M (2001) Continuous and discretized pursuit learning schemes: various algorithms and their comparison. IEEE Trans Syst Man Cybern Part B Cybern 31:277–287
Misra S, Oommen BJ (2005) Dynamic algorithms for the shortest path routing problem: learning automata-based solutions. IEEE Trans Syst Man Cybern Part B Cybern 35(6):1179–1192
Misra S, Oommen BJ (2006) An efficient dynamic algorithm for maintaining all-pairs shortest paths in stochastic networks. IEEE Trans Comput 55(6):686–702
Li H, Mason L, Rabbat M (2009) Distributed adaptive diverse routing for voice-over-ip in service overlay networks. IEEE Trans Netw Serv Manag 6(3):175–189
Mason L (1973) An optimal learning algorithm for s-model environments. IEEE Trans Autom Control 18(5):493–496
Beigy H, Meybodi MR (2006) Utilizing distributed learning automata to solve stochastic shortest path problems. Int J Uncertain Fuzziness Knowl Based Syst 14(05):591–615
Torkestani JA, Meybodi MR (2010) An intelligent backbone formation algorithm for wireless ad hoc networks based on distributed learning automata. Comput Netw 54(5):826–843
Torkestani JA, Meybodi MR (2012) Finding minimum weight connected dominating set in stochastic graph based on learning automata. Inf Sci 200:57–77
Torkestani JA, Meybodi MR (2012) A learning automata-based heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs. J Supercomput 59(2):1035–1054
Thathachar MAL, Sastry PS (2002) Varieties of learning automata: an overview. IEEE Trans Syst Man Cybern Part B Cybern 32(6):711–722
Sastry P, Thathachar M (1999) Learning automata algorithms for pattern classification. Sadhana 24(4):261–292
Shah S, Sastry PS (1999) New algorithms for learning and pruning oblique decision trees. IEEE Trans Syst Man Cybern Part C (Appl Rev) 29(4):494–505
Thathachar MAL, Sastry PS (1987) Learning optimal discriminant functions through a cooperative game of automata. IEEE Trans Syst Man Cybern 17(1):73–85
Santharam G, Sastry P, Thathachar M (1994) Continuous action set learning automata for stochastic optimization. J Frankl Inst 331(5):607–628
Zahiri S (2008) Learning automata based classifier. Pattern Recognit Lett 29(1):40–48
Zeng X, Liu Z (2005) A learning automata based algorithm for optimization of continuous complex functions. Inf Sci 174(3):165–175
Afshar S, Mosleh M, Kheyrandish M (2013) Presenting a new multiclass classifier based on learning automata. Neurocomputing 104:97–104
Howell M, Gordon T, Brandao F (2002) Genetic learning automata for function optimization. IEEE Trans Syst Man Cyber 32(6):804–815
Barto AG, Anandan P (1985) Pattern-recognizing stochastic learning automata. IEEE Trans Syst Man Cybern 3:360–375
Meybodi MR, Beigy H (2002) New learning automata based algorithms for adaptation of backpropagation algorithm parameters. Int J Neural Syst 12(01):45–67
Cochran JJ, Cox LA, Keskinocak P, Kharoufeh JP, Smith JC, Stützle T, López‐Ibáñez M, Dorigo M (2011) A concise overview of applications of ant colony optimization. In: Cochran JJ, Cox LA, Keskinocak P, Kharoufeh JP, Smith JC (eds) Wiley encyclopedia of operations research and management science. https://doi.org/10.1002/9780470400531.eorms0001
Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39
Goodwin M, Yazidi A (2016) Ant colony optimisation-based classification using two-dimensional polygons. In: International conference on swarm intelligence. Springer, pp 53–64
Tufteland T, Ødesneltvedt G, Goodwin M (2016) Optimizing polyaco training with GPU-based parallelization. In: International conference on swarm intelligence. Springer, pp 233–240
Goodwin M, Tufteland T, Ødesneltvedt G, Yazidi A (2016) Polyaco+: a many-dimensional polygon-based ant colony optimization classifier for multiple classes. Journal Article (under review)
Di Caro G, Dorigo M (1998) Antnet: distributed stigmergetic control for communications networks. J Artif. Intell. Res. 9:317–365
Kushner HJ, Clark DS (2012) Stochastic approximation methods for constrained and unconstrained systems, vol 26. Springer, Berlin
Vázquez-Abad FJ, Mason LG (1996) Adaptive decentralized control under non-uniqueness of the optimal control. Discrete Event Dyn Syst 6(4):323–359
Roth SD (1982) Ray casting for modeling solids. Comput Graph Image Process 18(2):109–144
The third author passed away on February 04, 2018, and the authors dedicate this manuscript to his memory.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Goodwin, M., Yazidi, A. & Jonassen, T.M. Distributed Learning Automata-based S-learning scheme for classification. Pattern Anal Applic 23, 1235–1250 (2020). https://doi.org/10.1007/s10044-019-00848-6
- Learning Automata
- Distributed learning