Artificial Neural Networks and Sensitivity Analysis

A multilayer perceptron (MLP) neural networks is feed-forward neural network typically used for predict response of one or more variables by one or many explanatory variables trained by backpropagation algorithm. In this study, we select appropriate monthly period of climate variables based on highest coefficient correlation between SOS/EOS and climate variables. As a pre-processing approach, all of the data normalized to 0-1, this is require to dodge saturating in the activation function. In total 110 data observation we randomized separate data into training set (2/3 of the records) and independent test set (1/3 of the records). A multilayer perceptron (MLP) neural network architecture we adopt for predicting SOS/EOS based on explanatory variables (climate variables). Traditional MLP neural network categorized with three layers, the first is input layer (i); the second is hidden layer (h) that receive and process information from input layers; and the third is output neurons (o) as well as response of the network architecture. A trial-and-error approach used for determining the optimal neural network. To purpose generate the optimal models, we comparing combination of several parameters such as; number of hidden layers, activation function, output function, and starting weight. We evaluate model by different number of nodes in the hidden layer range from 1 to 20, combining with two activation function including ‘logistic’ and ‘tangent hyperbolic’ used for transfer information from input nodes to hidden layers and from hidden layers to output. In addition, we also implement linear activation function for calculate output layer. Two different set starting weights including -0. 3 and 0. 3 implement for each model. We also Applying 5-fold cross calibration, which is recomended for small data-set. Test set data used to judge the quality of training model using linear relationships indicate by coefficient determination (R2) between observed and predicted values from neural network models. Various studies were concern to “illuminate the black box” of ANNs, they are believed to offer little explanation of relationships among variables described by model. Sensitivity analysis (SA) have been widely used for investigate contribute of input variables in the neural network. We applying sensitivity analysis to interpret the importance input variable and analysis of neural network response to input variables by following methods: Garson’s Algorithm, Olden’s Method, Lek’s Profile Method. We examined sensitivity analysis using R package NeuralNetTools developed by Beck. Garson algorithm established by Garson, later modified by. This method essentially partitioning all of the connection weight in the neural network architecture from the input layer to hidden neuron and hidden neuron to output. The detail and implementation of the Garson algorithm available in the appendix of Goh. This method summarize all of connection weight for all input nodes then scaled into absolute magnitude for describing the relative importance of the input variables. Similar from the previous one, Olden algorithm use connection weight approach for obtaining the relative importance variable from the input layers. This method quantifies the raw values of connection weight from input-hidden and hidden-output, whereas Garson algorithm using absolute value. The summed of the connection weight potentially provide positive or negative sigh of importance variables. Another alternative method to determine sensitivity of input variables in the neural network is the Lek Profile approach. The principle of the Lek Profile technique is evaluate behavior of output variable as a response of the input variable using plot profile wherein the input variable kept in the percentile class (e. g, 0th, 25th, 50th, 75th, 100th). Every single input variable processes above-mentioned, and as the results generate response curves depend on the change of input variable.