When running data-mining algorithms on big data platforms, a parallel, distributed framework, such asMAPREDUCE, may be used. However, in a parallel framework, each individual model fits the data allocated to its own computing node without necessarily fitting the entire dataset. In order to induce a single consistent model, ensemble algorithms such as majority voting, aggregate the local models, rather than analyzing the entire dataset directly. Our goal is to develop an efficient algorithm for choosing one representative model from multiple, locally induced decision-tree models. The proposed SySM (syntactic similarity method) algorithm computes the similarity between the models produced by parallel nodes and chooses the model which is most similar to others as the best representative of the entire dataset. In 18.75% of 48 experiments on four big datasets, SySM accuracy is significantly higher than that of the ensemble; in about 43.75% of the experiments, SySM accuracy is significantly lower; in one case, the results are identical; and in the remaining 35.41% of cases the difference is not statistically significant. Compared with ensemble methods, the representative tree models selected by the proposed methodology are more compact and interpretable, their induction consumes less memory, and, as confirmed by the empirical results, they allow faster classification of new records.
AlSabti, K., Ranka, S. and Singh, V. (1998). Clouds: Classification for large or out-of-core datasets, Conference on Knowledge Discovery and Data Mining, New York, NY, USA, pp. 2-8.
Amado, N., Gama, J. and Silva, F. (2001). Parallel implementation of decision tree learning algorithms, in P.
Brazdil and A. Jorge (Eds.), Progress in Artificial Intelligence, Springer, Berlin/Heidelberg, pp. 6-13.
Amado, N., Gama, J. and Silva, F. (2003). Exploiting parallelism in decision tree induction, ECML/PKDDWorkshop on Parallel and Distributed Computing for Machine Learning, Cavtat/Dubrovnik, Croatia, pp. 13-22.
Andrzejak, A., Langner, F. and Zabala, S. (2013). Interpretable models from distributed data via merging of decision trees, IEEE Symposium on Computational Intelligence and Data Mining (CIDM), Savannah, GA, USA, pp. 1-9.
Bekkerman, R., Bilenko, M. and Langford, J. (2011). Scaling up Machine Learning: Parallel and Distributed Approaches, Cambridge University Press, Cambridge.
Ben-Haim, Y. and Tom-Tov, E. (2010). A streaming parallel decision tree algorithm, The Journal of Machine Learning Research 11: 849-872.
Breiman, L. (1999). Pasting small votes for classification in large databases and on-line, Machine Learning 36(1-2): 85-103.
Dai, W. and Ji, W. (2014). A MAPREDUCE implementation of c4.5 decision tree algorithm, International Journal of Database Theory and Application 7(1): 49-60.
DeWitt, D.J., Naughton, J.F. and Schneider, D. (1991). Parallel sorting on a shared-nothing architecture using probabilistic splitting, Proceedings of the 1st International Conference on Parallel and Distributed Information Systems, Miami Beach, FL, USA, pp. 280-291.
Domingos, P. and Hulten, G. (2000). Mining high-speed data streams, Proceedings of the 6th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Boston, MA, USA, pp. 71-80.
Fan, W. and Bifet, A. (2013). Mining big data: Current status, and forecast to the future, ACM sIGKDD Explorations Newsletter 14(2): 1-5.
Gehrke, J., Ganti, V., Ramakrishnan, R. and Loh, W.-Y. (1999). Boat-optimistic decision tree construction, in S. Davidson and C. Faloutsos (Eds.), ACM SIGMOD Record, Vol. 28, ACM, New York, NY, pp. 169-180.
Goil, S. and Choudhary, A. (2001). Parsimony: An infrastructure for parallel multidimensional analysis and data mining, Journal of Parallel and Distributed Computing 61(3): 285-321.
Hansen, L.K. and Salamon, P. (1990). Neural network ensembles, IEEE Transactions on Pattern Analysis & Machine Intelligence 12(10): 993-1001.
Jin, R. and Agrawal, G. (2003). Communication and memory efficient parallel decision tree construction, Proceedings of the 3rd SIAM International Conference on Data Mining, San Francisco, CA, USA, pp. 119-129.
Joshi, M.V., Karypis, G. and Kumar, V. (1998). SCALPARC: A new scalable and efficient parallel classification algorithm for mining large datasets, Parallel Processing Symposium, Los Alamitos, CA, USA, pp. 573-579.
Kargupta, H. and Park, B.-H. (2004). A Fourier spectrum-based approach to represent decision trees for mining data streams in mobile environments, IEEE Transactions on Knowledge and Data Engineering 16(2): 216-229.
Kourtellis, N., Morales, G.D.F., Bifet, A. and Murdopo, A. (2016). VHT: Vertical Hoeffding tree, arXiv preprint, 1607.08325.
Louppe, G. and Geurts, P. (2012). Ensembles on random patches, in P.A. Flach et al. (Eds.), Machine Learning and Knowledge Discovery in Databases, Springer, Berlin/Heidelberg, pp. 346-361.
Mehta, M., Agrawal, R. and Rissanen, J. (1996). SLIQ: A fast scalable classifier for data mining, in P. Aspers et al. (Eds.), Advances in Database Technology, Springer, Berlin/Heidelberg, pp. 18-32.
Miglio, R. and Soffritti, G. (2004). The comparison between classification trees through proximity measures, Computational Statistics & Data Analysis 45(3): 577-593.
Narlikar, G.J. (1998). A parallel, multithreaded decision tree builder, Technical report, DTIC Document, http://www.dtic.mil/docs/citations/ADA363531
Ntoutsi, I., Kalousis, A. and Theodoridis, Y. (2008). A general framework for estimating similarity of datasets and decision trees: Exploring semantic similarity of decision trees, in C. Apte et al. (Eds.), SIAM Conference on Data Mining, SIAM, Philadelphia, PA, pp. 810-821.
Panda, B., Herbach, J.S., Basu, S. and Bayardo, R.J. (2009). Planet: Massively parallel learning of tree ensembles with MapReduce, Proceedings of the VLDB Endowment 2(2): 1426-1437.
Pawlik, M. and Augsten, N. (2011). RTED: A robust algorithm for the tree edit distance, Proceedings of the VLDB Endowment 5(4): 334-345.
Shafer, J., Agrawal, R. and Mehta, M. (1996). Sprint: A scalable parallel classifier for data mining, International Conference on Very Large Data Bases, Mumbai (Bombay), India, pp. 544-555.
Shannon, W.D. and Banks, D. (1999). Combining classification trees using MLE, Statistics in Medicine 18(6): 727-740.
Sollich, P. and Krogh, A. (1996). Learning with ensembles: How overfitting can be useful, in D.S. Touretzky et al. (Eds.)Advances in Neural Information Processing Systems 8, MIT Press, Cambridge, MA, pp. 190-196.
Sreenivas, M.K., AlSabti, K. and Ranka, S. (2000). Parallel out-of-core decision tree classifiers, in H. Kargupta and P. Chan (Eds.), Advances in Distributed and Parallel Knowledge Discovery, Cambridge, MA, pp. 317-336.
Srivastava, A., Han, E.-H., Kumar, V. and Singh, V. (1995). Parallel formulations of decision-tree classification algorithms, Data Mining and Knowledge Discovery 3(3): 237-261.
Triguero, I., Peralta, D., Bacardit, J., Garc´ıa, S. and Herrera, F. (2015). MRPR: A MAPREDUCE solution for prototype reduction in big data classification, Neurocomputing 150(A): 331-345.
Zhang, K. and Shasha, D. (1989). Simple fast algorithms for the editing distance between trees and related problems, SIAM Journal on Computing 18(6): 1245-1262.
Zhang, X. and Jiang, S. (2012). A splitting criteria based on similarity in decision tree learning, Journal of Software 7(8): 1775-1782.
Zhang, Y., Gao, Q., Gao, L. and Wang, C. (2012). IMAPREDUCE: A distributed computing framework for iterative computation, Journal of Grid Computing 10(1): 47-68.