A new loss function for robust classification
- Authors: Zhao, Lei , Mammadov, Musa , Yearwood, John
- Date: 2014
- Type: Text , Journal article
- Relation: Intelligent Data Analysis Vol. 18, no. 4 (2014), p. 697-715
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- Description: Loss function plays an important role in data classification. Manyloss functions have been proposed and applied to differentclassification problems. This paper proposes a new so called thesmoothed 0-1 loss function, that could be considered as anapproximation of the classical 0-1 loss function. Due to thenon-convexity property of the proposed loss function, globaloptimization methods are required to solve the correspondingoptimization problems. Together with the proposed loss function, wecompare the performance of several existing loss functions in theclassification of noisy data sets. In this comparison, differentoptimization problems are considered in regards to the convexity andsmoothness of different loss functions. The experimental resultsshow that the proposed smoothed 0-1 loss function works better ondata sets with noisy labels, noisy features, and outliers. © 2014 - IOS Press and the authors. All rights reserved.
Learning the naive bayes classifier with optimization models
- Authors: Taheri, Sona , Mammadov, Musa
- Date: 2013
- Type: Text , Journal article
- Relation: International Journal of Applied Mathematics and Computer Science Vol. 23, no. 4 (2013), p. 787-795
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- Description: Naive Bayes is among the simplest probabilistic classifiers. It often performs surprisingly well in many real world applications, despite the strong assumption that all features are conditionally independent given the class. In the learning process of this classifier with the known structure, class probabilities and conditional probabilities are calculated using training data, and then values of these probabilities are used to classify new observations. In this paper, we introduce three novel optimization models for the naive Bayes classifier where both class probabilities and conditional probabilities are considered as variables. The values of these variables are found by solving the corresponding optimization problems. Numerical experiments are conducted on several real world binary classification data sets, where continuous features are discretized by applying three different methods. The performances of these models are compared with the naive Bayes classifier, tree augmented naive Bayes, the SVM, C4.5 and the nearest neighbor classifier. The obtained results demonstrate that the proposed models can significantly improve the performance of the naive Bayes classifier, yet at the same time maintain its simple structure.
The effect of regularization on drug-reaction relationships
- Authors: Mammadov, Musa , Zhao, L. , Zhang, Jianjun
- Date: 2012
- Type: Text , Journal article
- Relation: Optimization Vol. 61, no. 4 (2012), p. 405-422
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- Description: The least-squares method is a standard approach used in data fitting that has important applications in many areas in science and engineering including many finance problems. In the case when the problem under consideration involves large-scale sparse matrices regularization methods are used to obtain more stable solutions by relaxing the data fitting. In this article, a new regularization algorithm is introduced based on the Karush-Kuhn-Tucker conditions and the Fisher-Burmeister function. The Newton method is used for solving corresponding systems of equations. The advantages of the proposed method has been demonstrated in the establishment of drug-reaction relationships based on the Australian Adverse Drug Reaction Advisory Committee database. © 2012 Copyright Taylor and Francis Group, LLC.
Optimality conditions in nonconvex optimization via weak subdifferentials
- Authors: Kasimbeyli, Refail , Mammadov, Musa
- Date: 2011
- Type: Text , Journal article
- Relation: Nonlinear Analysis, Theory, Methods and Applications Vol. 74, no. 7 (2011), p. 2534-2547
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- Description: In this paper we study optimality conditions for optimization problems described by a special class of directionally differentiable functions. The well-known necessary and sufficient optimality condition of nonsmooth convex optimization, given in the form of variational inequality, is generalized to the nonconvex case by using the notion of weak subdifferentials. The equivalent formulation of this condition in terms of weak subdifferentials and augmented normal cones is also presented. © 2011 Elsevier Ltd. All rights reserved.
From convex to nonconvex: A loss function analysis for binary classification
- Authors: Zhao, Lei , Mammadov, Musa , Yearwood, John
- Date: 2010
- Type: Text , Conference paper
- Relation: Paper presented at10th IEEE International Conference on Data Mining Workshops, ICDMW 2010 p. 1281-1288
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- Description: Problems of data classification can be studied in the framework of regularization theory as ill-posed problems. In this framework, loss functions play an important role in the application of regularization theory to classification. In this paper, we review some important convex loss functions, including hinge loss, square loss, modified square loss, exponential loss, logistic regression loss, as well as some non-convex loss functions, such as sigmoid loss, ø-loss, ramp loss, normalized sigmoid loss, and the loss function of 2 layer neural network. Based on the analysis of these loss functions, we propose a new differentiable non-convex loss function, called smoothed 0-1 loss function, which is a natural approximation of the 0-1 loss function. To compare the performance of different loss functions, we propose two binary classification algorithms for binary classification, one for convex loss functions, the other for non-convex loss functions. A set of experiments are launched on several binary data sets from the UCI repository. The results show that the proposed smoothed 0-1 loss function is robust, especially for those noisy data sets with many outliers. © 2010 IEEE.
Optimization of multiple classifiers in data mining based on string rewriting systems
- Authors: Dazeley, Richard , Kelarev, Andrei , Yearwood, John , Mammadov, Musa
- Date: 2009
- Type: Text , Journal article
- Relation: Asian-European Journal of Mathematics Vol. 2, no. 1 (2009), p. 41-56
- Relation: https://purl.org/au-research/grants/arc/DP0211866
- Relation: https://purl.org/au-research/grants/arc/LP0669752
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- Description: Optimization of multiple classifiers is an important problem in data mining. We introduce additional structure on the class sets of the classifiers using string rewriting systems with a convenient matrix representation. The aim of the present paper is to develop an efficient algorithm for the optimization of the number of errors of individual classifiers, which can be corrected by these multiple classifiers.
Optimization of parameters of the Kelvin element in vibration analysis
- Authors: Kuznetsov, Alexey , Mammadov, Musa , Hajilarov, Eldar
- Date: 2009
- Type: Text , Conference paper
- Relation: Paper presented at 2009 IEEE International Conference on Industrial Technology, ICIT 2009, Churchill, VIC January 2009
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- Description: In this paper we consider the problem of finding optimal parameters of the Kelvin element in vibration analysis. This problem is based on finding analytical solution of the initial ODE for development of the optimization model. Such technique allows us to compute optimal parameters of Kelvin element.