Computational and Mathematical Methods in Medicine

Volume 2018, Article ID 1461470, 10 pages

https://doi.org/10.1155/2018/1461470

## Pulmonary Nodule Recognition Based on Multiple Kernel Learning Support Vector Machine-PSO

^{1}School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China^{2}School of Computer Science and Engineering, Changchun University of Technology, Jilin 130012, China^{3}Faculty of Statistics, Jilin University of Finance and Economics, Changchun, Jilin 130117, China

Correspondence should be addressed to Alin Hou; moc.361@uohnila

Received 28 December 2017; Accepted 12 March 2018; Published 29 April 2018

Academic Editor: Nadia A. Chuzhanova

Copyright © 2018 Yang Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Pulmonary nodule recognition is the core module of lung CAD. The Support Vector Machine (SVM) algorithm has been widely used in pulmonary nodule recognition, and the algorithm of Multiple Kernel Learning Support Vector Machine (MKL-SVM) has achieved good results therein. Based on grid search, however, the MKL-SVM algorithm needs long optimization time in course of parameter optimization; also its identification accuracy depends on the fineness of grid. In the paper, swarm intelligence is introduced and the Particle Swarm Optimization (PSO) is combined with MKL-SVM algorithm to be MKL-SVM-PSO algorithm so as to realize global optimization of parameters rapidly. In order to obtain the global optimal solution, different inertia weights such as constant inertia weight, linear inertia weight, and nonlinear inertia weight are applied to pulmonary nodules recognition. The experimental results show that the model training time of the proposed MKL-SVM-PSO algorithm is only 1/7 of the training time of the MKL-SVM grid search algorithm, achieving better recognition effect. Moreover, Euclidean norm of normalized error vector is proposed to measure the proximity between the average fitness curve and the optimal fitness curve after convergence. Through statistical analysis of the average of 20 times operation results with different inertial weights, it can be seen that the dynamic inertial weight is superior to the constant inertia weight in the MKL-SVM-PSO algorithm. In the dynamic inertial weight algorithm, the parameter optimization time of nonlinear inertia weight is shorter; the average fitness value after convergence is much closer to the optimal fitness value, which is better than the linear inertial weight. Besides, a better nonlinear inertial weight is verified.

#### 1. Introduction

The number of deaths from lung cancer is as high as 137 million annually around the world, accounting for 18% of cancer mortality ratio. Early surgical treatment is the most effective treatment for lung cancer, but most patients are diagnosed in the late stage of the disease. In 2015, the European Academy of Imaging and the European Respiratory Society published the latest white paper on lung cancer screening in European Respiratory Journal (ERJ) to guide clinical lung cancer screening for early detection and early treatment of lung cancer.

As early representation form of lung cancer in the lung CT image, a pulmonary nodule is defined as a nearly spherical opacity with a diameter smaller than 3 cm. Computed Tomography (CT) technology is an important means of early detection of pulmonary nodules disease. According to the CT characterization, pulmonary nodules can be divided into solid nodules (such as solitary pulmonary nodules, pulmonary wall adhesion nodules, and vascular adhesion nodules), ground glass nodules, and cavitary nodules.

Computer-Aided Detection (CAD) system of lung is one of the applications of machine vision; it can reduce overload visual fatigue of the radiologist and decrease the possibility of the resulting miscarriage or omission and also provide auxiliary diagnosis results for the doctor as “third party.” Usually, the lung CAD system includes the following modules: acquisition of the lung CT image data, preprocessing of CT image, lung parenchyma segmentation, detection of VOI (Volume of Interest) or ROI (Region of Interest) in candidate nodules images (mainly refers to the extraction or segmentation), calculation and selection of ROI or VOI features, and recognition of pulmonary nodules, where pulmonary nodules recognition is the core module of the CAD system. The algorithm of Support Vector Machine (SVM) has been widely used in the detection and recognition of pulmonary nodules (see, e.g., [1–15]). Among them, Li et al. [1] applied mixed kernel SVM algorithm to distinguish benign and malignant lung nodules, making the recognition accuracy (ACC) reach 92% and the sensitivity index reach 92.59%; Wang et al. [2] detected lung lesions by use of three-dimensional SVM with Latent Variable algorithm. Furthermore, Demir and Çamurcu [16] and Chang et al. [17] imported the algorithm of Particle Swarm Optimization (PSO) into SVM and selected the optimal parameter group by PSO and then used SVM for identification. In addition, Ma et al. [18] adopted the method of multiple classifiers fusion for lung disease identification.

The Multiple Kernel Learning Support Vector Machine (MKL-SVM) algorithm has achieved good recognition accuracy not just in recognition of lung nodules in [1] but also in other application fields (see [19, 20]). In [21], the Multiple Kernel Learning (MKL) method was elaborated and the latest research progresses were presented in this field. However, the MKL-SVM algorithm involves a large number of parameters, and the selection of parameters will have an important impact on the actual results. In [1], the selection of the optimal parameters is obtained by the grid search algorithm. The advantage of the grid search algorithm is the easiness to get the global optimal solution in the case of dense mesh division, but the disadvantage of the method is that it has a large amount of computation, a long time to search, and a poor real-time performance, which is not easy to form online identification algorithm. The selection of the relevant parameters is an urgent problem to be solved in the MKL-SVM, and the Particle Swarm Optimization (PSO) algorithm based on swarm intelligence algorithm provides an idea to solve the problem.

In this paper, the PSO algorithm and MKL-SVM algorithm are combined to realize the parameter optimization of the MKL-SVM. On this basis, the PSO algorithm with different inertia weights was compared and analyzed in order to obtain the parametric array similar or superior to that of the grid search algorithm aiming at quickly searching the optimal parametric array and the reasonable inertia weight and then precise identification of the pulmonary nodules.

#### 2. Multiple Kernel Learning Support Vector Machine (MKL-SVM)

##### 2.1. Support Vector Machine

SVM is a learning method using small amount of samples, which can be applied to predict or classify unknown samples by structural risk minimization. The training sample is represented as follows:where* l* is the number of training samples, denotes the input vector of SVM, corresponding to the feature of the above -dimension region of interest (ROI), ; indicates category label; here, corresponds to nodules and corresponds to nonnodules.

When SVM is used in the two classification problems, the original model can be written as the following nonlinear optimization problem: where is the weight vector and is the threshold, and the aim of SVM is to maximize the classification interval , that is, minimization of .* C* is the regularization coefficient or penalty parameter, which describes the degree of penalty for misclassification samples. The greater is, the more obvious the penalty for misclassification is. When the data cannot be completely separated, the maximum interval will be negative, thus introducing slack variables which can measure the distance between the actual output and the Support Vector Machine output.

In the feature space, SVM is used to map the input data into a high-dimensional feature space by nonlinear transformation , and then the optimal classification hyperplane is constructed in the high-dimensional feature space to realize the SVM. In the process of constructing the hyperplane in the feature space , the training algorithm uses the dot product and the kernel function to represent the inner products and ; that is, a function can be found to form the next formula:Thus, it is not necessary to construct and solve the convex quadratic programming problem for a given training sample, and the problem is transformed into the following optimization problem by using Lagrange multiplier:The offset in (2) can be solved by means of the following equation:The decision function is constructed as follows:where

##### 2.2. Multiple Kernel Learning SVM (MKL-SVM)

Various kernel functions have diverse advantages. One of the keys to improve the performance of SVM is to design an appropriate kernel function for a given problem. The common basic kernel functions are polynomial kernel function and radial basis function (RBF), which are presented, respectively, as follows:where the parameter represents the order of the polynomial kernel, the parameter denotes the width of the RBF kernel, and* d* and need to be given in advance.

Proposition 1. *The convex combination form of the kernel function is still a kernel function:whereand is the pth species of basic kernel function and corresponds to the weights of the pth species of basic kernel function in the total multiple kernel function. U species basic kernel functions are used in the multiple kernel function, and the weight sum of various basic kernel functions is one so as to limit the weight proportion of various basic kernel functions in the multiple kernel functions in proportion.*

*Proof. *Let be a set of points in any given ; we just need to prove that the Gram matrix in (9) is positive semidefinite matrix.

Let be the Gram matrix of for ; for any , we obtainSo is positive semidefinite matrix; that is, is a kernel function, and the evidence is proven.

It is proven that the kernel function expressed by (9) satisfies the Mercer condition and can be used for the training and classification of SVM. By using the above MKL-SVM, we can use nonlinear transformation of the sample points to get the corresponding kernel matrix so as to obtain the classification results during the training of SVM classifier.

RBF kernel has a strong ability to learn, and polynomial kernel has strong generalization ability; thus the combination of the two can take into account the ability of both learning and generalization. If we use only two kinds of basic kernel functions of both RBF kernel and polynomial kernel, that is, , = , and = , the multiple kernel function of (12) is able to be formed. Compared with the single kernel function, we need to estimate a set of kernel parameters and a weight coefficient . The weight coefficient can regulate freely the proportion of different kernel functions mixed in multiple kernels, adjust flexibly the ability of learning and generalization, and make the results unbiased towards the promotion of a particular target.In [1], the grid search algorithm in the sense of CV is used to find the optimal regularization coefficient* C*, the order of the polynomial kernel, the kernel width of the RBF kernel, and the weight coefficient of the multiple kernels. The optimal parameter group can be obtained by the grid search algorithm during the CV process corresponding to the highest classification accuracy. Lots of parameters and short step length of mesh induce large amount of calculation and long running time. The global optimal solution could be found by the heuristic algorithm, not needing to traverse all the parameter points in the grid.

##### 2.3. MKL-SVM Based on Modified Particle Swarm Optimization Algorithm

Particle Swarm Optimization (PSO) is a typical heuristic algorithm on the basis of swarm intelligence optimization theory. In 1955, PSO was first proposed by Kennedy and Eberhart in [22], whose basic principle was originated from the research on the predation behavior of artificial life and birds. When birds prey upon food, the simplest and most effective method of finding food is to search the current area around the food nearest to birds. Compared with Generic Algorithm (GA), PSO searches the optimal particles by tracking the particles in the solution space without selection, crossover, and mutation.

It is assumed that the population consists of particles in a -dimensional search space, where represents the position of the th particle in -dimensional search space and also is a candidate solution of problem denoted by a vector of dimensions as . According to the objective function, we can calculate the fitness value of each particle position . The speed of the th particle is , and its individual extreme value and group extreme value are and , respectively. During each iteration, the particle updates its velocity and position by the individual extrema and the group extrema, which are given, respectively, as follows:where is an inertia weight; = ; represents the number of parameters to be searched; is the number of the present iterations; is the velocity of particles, and are acceleration factors, which are nonnegative constants, and and are random numbers distributed within the interval . In order to prevent the blind search of particles, the position and velocity are usually limited to the range of and .

The PSO algorithm is applied into MKL-SVM algorithm of (12). Because the corresponding order of polynomial kernel is defined as positive integer for and with the increase of , generalization ability of polynomial kernel decreases gradually, so only the two values and were calculated, and there is no need to search other parameters. Here the dimension of the search space of the particle is set to ; represents the solution of the th particles, where , , and of each dimension are corresponding to the regularization coefficient* C*, the kernel width of RBF, and the multiple kernel weight to be searched, respectively.

#### 3. Application of MKL-SVM-PSO Algorithm in Pulmonary Nodule Recognition

After introducing the classic PSO algorithm, the recognition accuracy rate (ACC) of pulmonary nodules in the sense of CV is regarded as the final target and determined as the fitness function value of PSO, and then ACC is defined as follows:where TP denotes the detected true positive nodule; FP is the detected false positive nodule; FN indicates the undetected false negative nodule; TN is the detected true negative nodule, that is, nonnodule. ACC measures total recognition accuracy to measure the actual detection rate of pulmonary nodules; the SEN is defined as follows:The parameter optimization algorithm of MKL-SVM-PSO algorithm is described in Figure 1.