feed forward neural network with backpropagation learning algorithm is considered as a black box learning classifier since there is no certain interpretation or anticipation of the behavior of a neural network weights. The weights of a neural network are considered as the learning tool of the classifier, and the learning task is performed by the repetition modification of those weights. This modification is performed using the delta rule which is mainly used in the gradient descent technique. In this article a proof is provided that helps to understand and explain the behavior of the weights in a feed forward neural network with backpropagation learning algorithm. Also, it illustrates why a feed forward neural network is not always guaranteed to converge in a global minimum. Moreover, the proof shows that the weights in the neural network are upper bounded (i.e. they do not approach infinity).

ABSTRACT:In this article, a number of posterior probabilistic based equations were introduced to detect the effect of controlling the correlation between variables on the behavior of feed forward neural network weights. In this paper it was proofed that, under certain assumptions, in a feed forward neural network with backprobagation learning algorithm, the correlation between the input variables on one side and the target variable on the other, is directly proportional to the values of the connection weights from the input layer to the output layer through the hidden layer.

A set of tubes known as bile ducts connects the liver to an organ below it directly that is called Gallbladder. The dilation of a bile duct is an important indicator regarding any serious issue in the human body. Number of reasons may cause bile duct dilation, such as: stones, tumors which commonly occur due to pancreas or papilla of vater. In this paper, the main contributions are: 1) a novel framework that consists of three phases to be applied on a set of Magnetic Resonance Imaging (MRI) images 2) an extracted set of features with their accurate values that express the condition of the biliary trees from the MRI images. Such dataset can be used in several applications to determine whether a bile duct is dilated or not. The dataset is organized as the following: half of the MRI images are for normal bile ducts, while the other half is for dilated bile ducts. To extract the useful features to diagnose the medical condition of the bile ducts from the MRI images, we implemented and applied the proposed framework that is started by using the enhanced active contour technique without edges in combination with Denoising Convolutional Neural Networks (DnCNN) to perform the segmentation and features extraction process. After that, the output of the segmentation process is the segmented biliary tree that will be used later to extract the needful features to make a diagnostic decision whether there is a dilation or not by comparing the features values of the normal versus the dilated bile ducts. We applied the feed forward neural network with backpropagation training algorithm for classification purposes. According to the experiments, the overall accuracy of the proposed framework was 90.00%. Such approach improves and increases the accuracy of the physicians’ diagnostic decisions which is considered as of significant importance for treatment and cure.

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