Retinal Diseases Classification Using Levenberg-Marquath (LM) Learning Algorithm for Pi Sigma Network (PSN) and Principal Component Analysis (PCA) Methods

Eye is one of the most important part of the body that has many parts or layers, one of which is the retina of the eye. Retina is a slight layer coating the back of the eye and serves to receive light, converting light into nerve signals which then sent to the brain. As well as the other body parts, retina is also able of experiencing disorders or abnormalities that can inhibit the vision process. Several of the retinal eye diseases are Retinal Ablatio, Age-related Macular Degeneration, and Diabetic Retinopathy. Eye fundus examination can be used to classify eye retinal diseases. Pi Sigma Network with Lavenberg Marquath Learning Algorithm is a method applied for classification of eye retinal diseases. Before executing classification process, image processing resulting grayscale image and data reduction using Principal Components Analysis are carried out for reducing the size of the fundus image. The accuracy obtained from the classification process using the applied methods is 100%.


Introduction
Eye is one of the most crucial body parts that detects light and changes it into impulses at nerve cell. Part of the eye that is sensitive to light stimulation is retina, which is located at the back of the eye. This means that the role of retina is very crucial in vision system. Any kind of abnormality should be responded quickly in order to avoid any more damage that can disrupt vision system, whether partly or whole. There are several retinal abnormalities, for instance, Age-related Macular Degeneration (AMD), Retinal Detachment (RD), and Diabetic Retinopathy (DR).
One of the ways to differentiate or classify these retinal disruptions is by using neural network, in this case, we use Pi Sigma Network (PSN). PSN was first introduced by Shin and Ghosh in 1991. The architecture of PSN shows that the weights adapting during the learning process of training algorithm occurs only to the weights that connecting the input neurons of input layer to the hidden neurons of hidden layer, while the weights that connecting the hidden neurons to output layer are fixed to one. Due to this such of topology, it helps on reducing the time for training algorithm [1]. In addition, PSN provides higher order capabilities in increasing its computational power, provides better capability in classifying [2], and requires less memory [3].
The general structure of PSN uses Gradient Decent Algorithm (GDA) for the weights adapting in training algorithm [3]. But in this study, the training algorithm uses the Levenberg-Marquardt (LM) Learning Algorithm instead since it can simplify the optimization of Newton algorithm resulting faster convergence if it is compared to basic GDA method. It is also not as complex as Newton's optimization algorithm [4].
As we use fundus image of retina as the data of the whole process, we will need a method to reduce the value of the image without losing much of its information, so we use Principal Components Analysis (PCA). PCA is a mathematical equation that is used in data dimensions reducing and allows standards identification of data and its expression so that its similarities and differences are emphasized. When the patterns are found, compressing can be done. PCA can also be used as compression algorithm of image with a low level of information loss [5].
In this study, we will use various learning rate value for each trial on classifying the fundus images, resulting in various percentage of training and validation process. In the previous research [6] which classifying Diabetic Retinopathy (DR) using fundus images has a result that the classification accuracy using Artificial Neural Network (ANN) and Local Binary Pattern (LBP) is 96.73%. Another research [7], which classifying Diabetic Retinopathy (DR) and Age-related Macular Degeneration (AMD) using Support Vector Machine (SVM) can achieve 96.67% of classification accuracy. This study is expected to have a better result than the previous studies in classifying retinal diseases using the Pi Sigma Network (PSN) and Principal Component Analysis (PCA) methods.

Methodology
The stages in this study are pre-processing, feature reduction, and retinal diseases classification.

Pre-processing
Pre-processing is the beginning of data input processing before getting into the main stage, PSN process. In this study, the stage of pre-processing is done by turning the original image into grayscale image. The purpose of this stage is to improve the quality of the image in order to give clearer and more detail information about the image's characteristic, numerically [8].

Grayscale Image
Grayscale image is an image which has one channel value for each of the pixel. Grayscale can be represented in two-dimension array which each of its element shows the intensity of the image. Grayscale can be calculated using the following equation: Grayscale value is in the range of 0 to 255 which 0 represents the most obscure intensity and 255 represents the brightest intensity [8].

Principal Components Analysis (PCA)
PCA reduces data dimensions by using linear combinations for its principal components. If there are variables, then there will be principal components. The result of PCA can be obtained by analyzing in the process of finding the eigenvalues of a sample covariance matrix. The steps normally followed in a PCA of a digital image can be established by following the steps below [5]: Step 1: Correcting the image so that its columns have zero means and unitary variances.
Step 2: Calculating the C matrix covariance using this following equation: Step 3: Calculating the eigenvalues and the corresponding eigenvectors.
Step 4: The value of the characteristic vector ( ) is obtained in shape of a matrix containing the list of eigenvectors (matrix columns) of the covariance matrix.
Step 5: Calculating the final data Step 6: The matrix of original image is obtained from the final data without compression using Step 7: Any components explaining only a small compression are discarded.
Because the output is the product of all the hidden nodes, there is no need in updating all the weights. We can randomly choose a hidden node and update its adjustable weights using Gradient Decent Algorithm (GDA).
Where is learning rate value, is the -th training pattern, and are the target and actual output, is the first derivative of activation function ( ). Below is the formulation to calculate the MSE.

Levenberg-Marquardt Learning Algorithm
Levenberg-Marquardt (LM) Learning Algorithm is developed from backpropagation algorithm using hessian matrix approach to determine the changes of its weight and bias (Damayanti, 2016) and is designed to minimize the function of sum-of-square error (Aldrich, 2002). Weight and bias changes can be calculated using these formulations below. There are several stages done in this study, that are pre-processing, feature reduction with PCA, and retinal diseases classification using PSN and LM Learning Algorithm. In image preprocessing, the original fundus images will be turned into grayscale image. Figure 2 shows the result of changing original image into grayscale image.  After going through image pre-processing, the next stage is feature reduction using PCA. The input for PCA reduction uses the numerical result of pre-processing containing a matrix with the size is 34225 × 60. This size will get into PCA until the size is reduced to 60 × 60, called the principal component matrix ( ). Then, it will be normalized in order to reduce the value of in between -1 and 1.
The classification step using PSN and LM Learning Algorithm begins with inputting and initializing the parameters needed, such as learning rate ( ), maximum iteration, and MSE target. It is then followed by feedforwarding process to hidden layer and output layer. After the output is done, then calculating the output value. The process of weights updating using LM Learning Algorithm is the next step of this process. When all the output of all the matrix's column has been determined, the MSE will be calculated. If the MSE is still bigger than MSE target or the maximum iteration hasn't been achieved yet, then the process should be continued. Else, the process is stopped, and the classification process is achieved.
In this study, the number of input nodes of the input layer and the hidden nodes of the hidden layer are 40 nodes and 4 nodes. Due to this reason, there are 164 adapted weight connecting the input layer to the hidden layer. Several trials have been done to this study using various learning rates. The best accuracy percentage on classifying the images based on its category is achieved by using = 0.6049 at the 235 th iteration and = 0.4719 at the 134 th iteration, resulting 100% of training and validation process on classifying the images.

Conclusions
The focus of this study is to classify the retinal diseases, in this case, Age-related Macular Degeneration (AMD), Retinal Detachment (RD), and Diabetic Retinopathy (DR). The stages that have to be done to classify them are, image processing and reduction, and classification process. The results show 100% of training and validation success, using = . and = .
, in classifying retinal diseases using Levenberg-Marquardt Learning Algorithm for Pi Sigma Network (PSN) and Principal Components Analysis (PCA) methods.