International Journal of Machine Learning and Computing, Vol. 9, No. 4, August 2019 Diagnosis of Brain Cancer Using Radial Basis Function Neural Network with Singular Value Decomposition Method Agus Maman Abadi, Dhoriva Urwatul Wustqa, and Nurhayadi observation and analysis them. Then, they consult the results Abstract—Brain cancer is one of the most dangerous cancers of the analysis to the doctor. The diagnosis using MRI image that can attack anyone, so early detection needs to be done so can only categorize the brain as normal or abnormal. that brain cancer can be treated quickly. The purpose of this Regarding the important of the early diagnosis of brain study is to develop a new procedure of modeling radial basis cancer, many researchers are tempted doing research in this function neural network (RBFNN) using singular value field. Several methods have been applied to classify brain decomposition (SVD) method and to apply the procedure to diagnose brain cancer. This study uses 114 brain Magnetic cancer, such as artificial neural networks based on brain MRI Resonance Images (MRI). The RBFNN model is constructed by data [3], [4], and backpropagation network techniques using steps as follows; image preprocessing, image extracting (BPNN) and principal component analysis (PCA) [5], using Gray Level Co-Occurrence Matrix (GLCM), determining probabilistic neural network method [6], [7]. Several of parameters of radial basis function and determining of researches have proposed the combining several intelligent weights of neural network. The input variables are 14 features system methods, those are adaptive neuro-fuzzy inference of image extractions and the output variable is a classification of system (ANFIS), neural Elman network (Elman NN), brain cancer. Before learning process, the input data is nonlinier autoregressive with exogenous neural network normalized. The modeling is done by using K-means clustering (NARXNN), and feedforward NN [8] and artificial neural method where the activation function in the hidden layer is network based on MRI image segmentation data using fuzzy Gaussian function and by determining the optimum weights of the model using SVD method. The best RBFNN model is 14 c-means and bounding Box method [9]. Studies to diagnose input neurons, 10 hidden layer neurons, and 1 output neuron. brain cancers have also been done using support vector The results show that the sensitivity, specificity, and accuracy of machine (SVM) and multi-SVM [10], adaptive neuro-fuzzy RBFNN diagnoses with backpropagation equal to those of inference system [11]. RBFNN with SVD. However, the RBFNN-SVD delivers an Recently, research on brain cancer diagnosis still become advantage in the running speed of the program. interesting area to develop the method in order to improve accuracy of the diagnosis. One of the methods that can be Index Terms—Radial basis function neural network, used as diagnosis tool is the radial basis function neural diagnosis brain cancer, singular value decomposition. network (RBFNN). The RBFNN is suitable for large training data, provide a good generalization. The RBFNN has simple network structure, since it has only one hidden layer. This I. INTRODUCTION property leads to speed up the learning process. Study related Brain cancer is a dangerous disease and can be fatal to to the diagnosis of brain cancer by applying RBFNN has been someone. In 2012, brain cancer cases in Indonesia are 1.9 per performed using CT scan data of normal and abnormal brain 100,000 population, while the brain mortality rate is 1.3 per [12]. The other study uses principle component analysis 100,000 inhabitants [1]. This fact shows the level of brain based on electroencephalograph (EEG) digital signals [13] cancer patients in Indonesia is high. Therefore, early and set those values as the inputs of RBFNN model. diagnosis is needed to prevent the death caused by brain The RBFNN model has been applied to diagnose various cancer. According to the Ministry of Health of the Republic types of diseases. The classification of breast cancer using of Indonesia [2], there are several steps in diagnosing brain improved F-score with support vector machine and RBF cancer (1) physical examination; (2) laboratory examination; network has been done [14]. The result shows that the and (3) radiological examination. Standard radiological improved F-score and support vector machines method gives examinations are CT Scan and MRI which produce the the better accuracy than improved F-score and RBF network digital images. The radiologists interpret the MRI images by method. The study of cancer prediction based on gene expression data using deep learning has been done [15]. The modified neural network has been applied to diagnosis of epilepsy based on EEG signals and the result shows that the ensemble TPunit neural networks method gives the better accuracy than neural network method for diagnosis of Manuscript received October 20, 2018; revised April 26, 2019. This work was supported in part by the Directorate of Research and Community epilepsy [16]. The RBFNN model has been applied for Service, Ministry of Research, Technology, and Higher Education of the detection of lung cancer based on radiograph images [17]. Republic of Indonesia under grant No. 01/Penelitian/ PDUPT/ In the RBFNN modeling, the weights of output target can UN.34.21/2018. Agus Maman Abadi and Dhoriva Urwatul Wutsqa are with Mathematics be determined by back propagation or global ridge regression Departnment, Yogyakarta State University, Karangmalang Yogyakarta methods. However, these methods require a long iteration to Indonesia, 55281 (e-mail: [email protected], [email protected]). get the solution, while singular value decomposition method Nurhayadi is with Mathematics Education Department, Tadulako University, Sulawesi Tengah, Indonesia (e-mail: [email protected]). does not require iteration and is more efficient for doi: 10.18178/ijmlc.2019.9.4.836 527 International Journal of Machine Learning and Computing, Vol. 9, No. 4, August 2019 determining the weights of output target. This study aims to The learning process in RBFNN includes unsupervised diagnose brain cancer based on MRI image data using the learning to ascertain the number of hidden neurons as well as combination of radial basis function neural network (RBFNN) to obtain the parameter values of the radial basis function, and singular value decomposition method. and supervised learning to obtain the weights between the hidden layer and output layer. The number of neurons in the hidden layer equals to the number of basis functions. The II. RADIAL BASIS FUNCTION NEURAL NETWORK unsupervised learning is performed using the K-means The RBFNN is one of the neural network model with a clustering method. It is commonly used in RBFNN modeling, three-layer, namely an input layer, a single hidden layer, and whose placement of the objects in each cluster based on the an output layer. The performance of RBFNN depends on the Euclidian distance. The Euclidian distance between two choice of exactly three important parameters (cluster center, points P(푥1, 푥2, . , 푥푝) and Q(푦1, 푦2, . , 푦푝) is expressed as distance and weight). Each input variable is assigned to the 2 neuron in the input layer and enters directly to the hidden 2 푑(푃, 푄) = √(푥1 − 푦1) +. +(푥푝 − 푦푝) layer without weight. In the hidden layer, the RBFNN performs a nonlinear transformation of the data from the The following steps are the K-means clustering algorithm input layer using the basic radial function before it is linearly [19]. processed at the output layer. The architecture of the RBFNN 1) Partition the data into K cluster is shown in Fig. 1. 2) Place any objects to the nearest cluster. 3) Recalculate the center of the clusters that receive 휑1 new data and the clusters that lose data. 푥1 4) Repeat step (1) to (3) until the new centers equal to the old ones. 푤1 휑 2 Futhermore, it will be determined the weight 휔푗 in (2) 푤2 푥2 minimized the equation (3). 푤푗 휑 푓(푥) 푗 푛 2 ⁝ 푆푆퐸 = ∑푘=1(푦푘 − 푦̂푘) (3) ⁝ 푤푘 Output Layer where n is the number of training data,⁡푦̂푘 is the output of the 푥푝 휑 푤 푡ℎ 푞 0 model for 푘 ⁡ observation, ⁡푦푘 is the target for 푡ℎ Input 푘 ⁡observation. layer Then, we apply (2) and (3) for all training data to get (4). 1 Bias Hidden layer 푦1 푦 Fig. 1. The architecture of RBFNN. 풚 = [ 2] = 흋풘̂ (4) ⋮ 푦 In Fig. 1, (푥푖, 푖 = 1, 2, . 푝) are input neurons, (휑푗, 푗 = 푛 where 1, 2, . , 푞) are hidden neurons, and 푓(푥) is output neuron. The weights between the hidden layer and the output layer 휑 [휇(푥)] 휑 [휇(푥)] … 휑푞[휇(푥)]1 1 1 1 2 1 are denoted as 푤푗 and the bias 푤0 is added to the hidden … 휑1[휇(푥)]2 휑2[휇(푥)]2 휑푞[휇(푥)]2 1 layer. The activation function 휑 (푥) is determined by the 흋 = ⋱⁡ (5) 푗 ⋮ ⋮ ⁡⁡ ⁡⁡⁡⁡⁡⁡⁡⋮ ⁡⁡⁡⁡⁡⁡⁡⁡1 … mean cluster and width cluster. The RBFNN model is [휑1[휇(푥)]푛 휑2[휇(푥)]푛 휑푞[휇(푥)]푛 1] characterized by the activation function, which are included in the class of radial basis function. There are several and 풘̂ is a vector of weights 푤̂푗. activation functions in RBFNN namely Gaussian function, multi quadratic inverse and Cauchy functions [18]. In this research, we use Gaussian activation function III. SINGULAR VALUE DECOMPOSITION In this section, we will introduce singular value 2 (푥−푐) decomposition of matrix and its properties referred from 휑(푥) = exp (⁡− 2 ) (1) 푟 Scheick [20]. Any m x n matrix A can be expressed as where c is the mean of cluster, r is maximum distance of each A= USV T (6) object to the mean of cluster. The output y of the RBFNN model is the linear combination of the weights 푤푗 included where U and V are orthogonal matrices of dimensions m x m, w0 and the activation function 휑푗(푥) n x n respectively and S is m x n matrix whose entries are 0 푞 except sii = i ir= 1,2,..., with 12 ..