Analysis of Artificial Neural Network Backpropagation Using Conjugate Gradient Fletcher Reeves In The Predicting Process

Backpropagation is a good artificial neural network algorithm used to predict, one of which is to predict the rate of Consumer Price Index (CPI) based on the foodstuff sector. While conjugate gradient fletcher reeves is a suitable optimization method when juxtaposed with backpropagation method, because this method can shorten iteration without reducing the quality of training and testing result. Consumer Price Index (CPI) data that will be predicted to come from the Central Statistics Agency (BPS) Pematangsiantar. The results of this study will be expected to contribute to the government in making policies to improve economic growth. In this study, the data obtained will be processed by conducting training and testing with artificial neural network backpropagation by using parameter learning rate 0,01 and target error minimum that is 0.001-0,09. The training network is built with binary and bipolar sigmoid activation functions. After the results with backpropagation are obtained, it will then be optimized using the conjugate gradient fletcher reeves method by conducting the same training and testing based on 5 predefined network architectures. The result, the method used can increase the speed and accuracy result.


Introduction
Artificial Intelligence is one area that is quite reliable in solving problems such as prediction (forecasting) . Artificial Neural Network (ANN) is one of the artificial representations of the human brain that always tries to simulate the learning process in the human brain [1] [2]. ANN approach can imitate any complex and non-linear relationship through non-linear units (neurons) and has been widely used in the forecasting area [3]. Prediction (forecasting) is basically a presumption about the occurrence of an event or event in the future. Prediction (forecasting) is very helpful in planning and decisionmaking activities of a policy [4]. One of the sub areas of Artificial Intelligence that can be relied upon in doing a prediction is the artificial neural network backpropagation. To produce a good Backpropagation, the selected parameters must be precise. Therefore, an algorithm that can help accelerate Backpropagation training, one of the reliable algorithms is Conjugate Gradient Fletcher Reeves. This algorithm is expected to improve the performance of the system, because the algorithm is  able to optimize so that it can minimize a function, where the search is based on the direction of conjugation orthogonal value [5]. Due to its orthogonal searching nature, so this algorithm can quickly reach convergence on the solution sought. These methods will be used to predict. The data to be predicted is the data of Consumer Price Index of Pematangsiantar that come from the Central Bureau of Statistics. The Consumer Price Index is one of the common economic indicators used to measure the rate of price change (inflation / deflation) at the consumer level, especially in urban areas. In Indonesia, the inflation rate is measured from the percentage change of the Consumer Price Index and announced to the public at the beginning of each month (first business day) [6]. The expenditure group from the Consumer Price Index can be seen in Table 1 below:

Stage Data Processing
At this writing, it was Created a pattern recognition system and predicted the Consumer Price Index (CPI). This process has two stages where the first stage is to do pattern recognition by finding the best architecture of the Artificial Neural Network model created. The process of training and testing the data to get the best model is obtained from the Consumer Price Index (CPI) data at the Central Bureau of Statistics Pematangsiantar as much as 24 Patterns counted from 2014 to 2016, with the criteria Pattern 1 to Pattern 12 is training data (training) , While Pattern 13 through Pattern 24 is the Test data. The second stage is to make predictions with the best architectural patterns obtained in the first stage.

Data Normalization
Normalization of the data is done so that the output of the network appropriateto the activation function used. The activation function that the author uses in this writing is the sigmoid activation function. Sigmoid function is asymptotic function (never reach 0 or 1), then data transformation is done at smaller interval [0,1; 0.9], shown by the equation (following) [9].
Based on table 4, Then we will get the result of transformation as follows: By using the normalization formula as follows : Then will get result Normalization data 1 for January 0,22885. So on for all data, normalized by using the same formula in equation (1).

Analysis
Previously, the data to be tested should be divided into two (2) sections, where the first part is for training data and the second part is for the test data. Standard Backpropagation method uses gradient decrease algorithm (descent gradient). Variations on the standard model are done by replacing the algorithm with another algorithm. The parameters used in this training and testing : Architecture = 1 hidden layer, Input neurons = 12, Activation Function = Sigmoid, Initialization weights = Random, Target Error Minimum= 0,001 -0,09, Maximum Epoch = 10000, Learning Rate = 0,01.

Results
This research uses 5 architecture. Among others are 12-6-1, 12-15-1, 12-24-1, 12-33-1, and 12-34-1. From the 5 architectures, this is the best architecture is 12-15-1. Whether it is using standard backpropagation or merging between backpropagation with conjugate gradient fletcher reeves. The architecture is better because of the high accuracy and stable results, the lesser Epoch and the smaller MSE (Mean Square Error).   The results of standard backpropagation methods have been optimized using Conjugate Gradient Fletcher Reeves. Optimization is done by using the Traincgf function. Traincgf is a network function that updates the weights and biases according to the backpropagation gradient convergence with the Fletcher-Reeves update. Based on the results of tests conducted with 5 experiments on backpropagation with different architectures, there was an average of 2716 iterations. While with the same architecture using Backpropagation with Conjugate Gradient Fletcher Reeves there was an increase of iteration with an average of 38. For accuracy of training conducted with the same 5 experiments, there was increased accuracy of training in the first (1 st ) experiment with the network architecture 12-6-1, the fourth (4 th ) experiment with 12-33-1 network architecture and fifth (5 th ) experiment with 12-34-1 network architecture. The decline in the level of accuracy of training in second (2 nd ) experiment with network architecture 12-15-1 and third (3 th ) experiment with the network architecture 12-24-1. For accuracy testing conducted with the same 5 experiments, increased accuracy testing in first (1 st ) experiment with network architecture 12-6-1, fourth (4 th ) experiment with network architecture 12-33-1 and fourth (5 th ) experiment with network architecture 12-34-1. The decline in the level of accuracy testing in second (2 nd ) experiment with the network architecture 12-15-1 and third (3 th ) experiment with the network architecture 12-24-1.