br i f xi and T is a
i+1) f ( xi) and T is a controlling parameter. As the solution procedure proceeds, tem-acceptance probability. The temperature decreasing rule has the form as below:
where T0 is the initial temperature and ξ is the temperature decay factor, which usually taken in the interval of 0–1.
4.4. SVM for classification
The SVM was originally developed by Vapnik (1995), and it is based on the Vapnik–Chervonenkis (VC) LLY507 and structural risk minimization (SRM) principle (Vapnik, 1995, 1999). It can automatically determine the classification of data samples with a superior ability to distinguish the support vector, and the resulting classifier can maximize the interval between the class, leading to a better generalization ability and a higher classification accuracy. In addition, one major advantage of the SVM is the utilization of convex quadratic programming, which provides only global minimal and hence avoids trapping in local minimum (Vapnik, 1995; Cristianini
& Shawe-Taylor, 2000). In our work, we take into consideration the unequal misclassification costs and introduce CSSVM method performing classification task. The more details about CSSVM can refer to Section 4.2. Herein, our proposed hybrid model has been implemented on the LIBSVM package (Chang & Lin, 2011) and employed Radial Basis Function (RBF) kernel.
5. The framework of our proposed approach
This section proposed the framework of our proposed approach. In our work, we firstly employs IGSAGAW for feature selection, which rely on IG ranking the importance of feature and help to reduce the computing complexity of SAGA wrapper approach, then we filtering some of the redundancy and unrelated features, and thereby extracting the top m optimal feature utilize the CSSVM learning algorithm. However, to apply this model to breast cancer diagnosis, there has an urgent problem need to be solved that is how to construct the fitness function. The selection of the fitness function is very important, which directly determine whether or not an optimal solution can be found. In this paper, we take fully account of the misclassification cost and the classification error rate, and construct the fitness function as follows:
false negative and false positive respectively. N. Liu et al. Information Processing and Management 56 (2019) 609–623
The cost matrix used by the classifiers.
Benign/majority class Malignant/minority class
Benign/majority class cos tbm Malignant/minority class cos tmb
In formula (6), fmb and costmb are the number of samples and the misclassification cost of the malignant tumors diagnosed as benign ones; fbm and costbm are the number of samples and the value of the benign tumors diagnosed as malignant ones and n represents the number of samples. The cost matrix is shown in Table 2. where the costbm is the misclassification cost associated with the benign tumor assigned to the category of malignant tumor, and costmb is the misclassification cost associated with the malignant tumor assigned to the category of benign tumor.
5.1. The approach of CSSVM for classification
In cost-sensitive decision system. We define D as a decision variable, which including z th category label of d(1), d(2), …, d(z) .
As for each input and output variable, a sample pair can be formed as follows:
This study integrated different misclassification costs information into the CSSVM classifier, and design the objective function based on the empirical cost and structural cost minimization. According to Xu, Zhou, and Chen (2018), the standard cost-insensitive SVM has shown in formula (8). where in formula (8), (C1 i : yi =+1 i + C2 i : yi = 1 i) can fully represent the misclassification cost of