Abstract
The Naive Bayes classifier is a popular classification technique for data mining and machine learning. It has been shown to be very effective on a variety of data classification problems. However, the strong assumption that all attributes are conditionally independent given the class is often violated in real-world applications. Numerous methods have been proposed in order to improve the performance of the Naive Bayes classifier by alleviating the attribute independence assumption. However, violation of the independence assumption can increase the expected error. Another alternative is assigning the weights for attributes. In this paper, we propose a novel attribute weighted Naive Bayes classifier by considering weights to the conditional probabilities. An objective function is modeled and taken into account, which is based on the structure of the Naive Bayes classifier and the attribute weights. The optimal weights are determined by a local optimization method using the quasisecant method. In the proposed approach, the Naive Bayes classifier is taken as a starting point. We report the results of numerical experiments on several real-world data sets in binary classification, which show the efficiency of the proposed method.
Similar content being viewed by others
References
Asuncion A, Newman D (2007) UCI machine learning repository. School of Information and Computer Science, University of California http://www.ics.uci.edu/mlearn/MLRepository.html
Bagirov AM, Nazari Ganjehlou A (2010) A quasisecant method for minimizing nonsmooth functions. Optim Methods Soft 25(1):3–18
Chang C, Lin C (2001) LIBSVM: A library for support vector machines Software available at http://www.csie.ntu.edu.tw/cjlin/libsvm
Chickering DM (1996) Learning Bayesian networks is NP-complete. In: Fisher D, Lenz H (eds) Learning from data: artificial intelligence and statistics V. Springer, Berlin, pp 121–130
Domingos P, Pazzani M (1997) On the optimality of the simple Bayesian classifier under zero-one loss. Mach Learn 29:103–130
Dougherty J, Kohavi R, Sahami M (1995) Supervised and unsupervised discretization of continuous features. In: Proceedings of the 12th international conference on machine learning, pp 194–202
Fayyad UM, Irani KB (1993) On the handling of continuous-valued attributes in decision tree generation. Mach Learn 8:87–102
Friedman N, Geiger D, Goldszmidt M (1997) Bayesian network classifierss. Mach Learn 29:131–163
Hall M (2007) A decision tree-based attribute weighting filter for Naive Bayes. Knowl Based Syst 20:120–126
Heckerman D, Chickering DM, Meek C (2004) Large-sample learning of Bayesian networks is NP-Hard. J Mach Learn Res 5:1287–1330
Jiang L, Zhang H (2006) Weightily averaged one-dependence estimators. In: Proceedings of the 9th biennial pacific rim international conference on artificial intelligence, Guilin, China, pp 970–974
Jiang L, Wang D, Cai Z, Yan X (2007) Survey of improving Naive Bayes for classification. In: Proceedings of the 3rd international conference on advanced data mining and applications, 4632, Springer, Berlin, pp 134–145
Keogh EJ, Pazzani MJ (1999) Learning augmented Bayesian classifiers: A comparison of distribution-based and classification-based approaches. In: Proceedings of international workshop on artificial intelligence and statistics, pp 225–230
Kohavi R (1996) Scaling up the accuracy of naive-Bayes classifiers: a decision-tree hybrid. In: Proceedings of 2nd ACM SIGKDD International, conference on knowledge discovery and data mining, pp 202–207
Langley P, Iba W, Thompson K (1992) An analysis of Bayesian classifiers. In: 10th international conference artificial intelligence, AAAI Press, pp 223–228
Langley P, Saga S (1994) Induction of selective Bayesian classifiers. In: Proceedings of tenth conference, uncertainty in artificial intelligence, Morgan Kaufmann, pp 399–406
Lu J, Yang Y, Webb GI (2006) Incremental discretization for naive-Bayes classifier. Springer, Heidelberg, 4093, pp 223–238
Ozsen S, Gunecs S (2009) Attribute weighting via genetic algorithms for attribute weighted artificial immune system (AWAIS) and its application to heart disease and liver disorders problems. Expert Syst Appl 36:386–392
Pazzani MJ (1996) Constructive induction of cartesian product attributes, ISIS: In-formation, Stat Induction Sci 66–77
Pearl J (1988) Probabilistic reasoning in Intelligent systems: networks of plausible inference. Morgan Kaufmann
Sun W, Yuan YX (2006) Optimization theory and methods: nonlinear programming. Springer, Berlin
Taheri S, Mammadov M, Bagirov AM (2011) Improving Naive Bayes classifier using conditional probabilities, In the proceedings of ninth Australasian data mining conference (AusDM 2011), vol 125. Ballarat, Australia
Taheri S, Mammadov M (2011) Tree augmented Naive Bayes based on optimization. In: Proceedings of 42nd annual Iranian mathematics conference, Vali-e-Asr University of Rafsanjan, Iran
Wang S, Min F, Wang Z, Cao T (2009) OFFD: Optimal Flexible Frequency Discretization for Naive Bayes Classification. Springer, Heidelberg, pp 704–712
Webb GI, Boughton J, Wang Z (2005) Not so Naive Bayes: aggregating one dependence estimators. Mach Learn 58:5–24
Wu J, Cai Z (2011) Attribute weighting via differential evolution algorithm for attribute weighted Naive Bayes (WNB). J Comput Inf Syst 7(5):1672–1679
Xindong W et al (2008) Top 10 algorithms in data mining. Knowl Inf Syst 14:1–37
Yatsko A, Bagirov AM, Stranieri A (2010) On the discretization of continuous features for classification, School of Information Technology and Mathematical Sciences, University of Ballarat Conference. (http://researchonline.ballarat.edu.au:8080/vital/access/manager/Repository)
Ying Y, Geoffrey I (2009) Discretization for naive-Bayes learning: managing discretization bias and variance. Mach Learn 74(1):39–74
Ying Y (2003) Discretization for naive-Bayes learning, PhD thesis, School of Computer Science and Software Engineering of Monash University
Zhang H, Sheng S (2005) Learning weighted Naive Bayes with accurate ranking. In: Proceedings of the 4th IEEE international conference on data mining 567–570
Zhou Y, Huang TS (2006) Weighted Bayesian network for visual tracking. In: Proceedings of the 18th international conference on pattern recognition (ICPR’O6), 0-7695-2521-0106
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Taheri, S., Yearwood, J., Mammadov, M. et al. Attribute weighted Naive Bayes classifier using a local optimization. Neural Comput & Applic 24, 995–1002 (2014). https://doi.org/10.1007/s00521-012-1329-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-012-1329-z