This paper presents us with an automatic prediction and analysis of basketball referees movement which is useful for educational software. Such software would be very beneficial in training the young basketball referees. The paper proposes that the movement prediction of basketball referees can be achieved with a multilayered perceptron neural network. Network will reason on the basis of a ball movement during a play action. Proposed neural network will be trained with a modified Back Propagation algorithm which essentially presents a special algorithm for a multiple dependent Time Series prediction. In this paper, we will also describe initial designs of a neural network structure that, we believe, would better suit the nature of a multiple dependent Time Series prediction problems. The aforementioned educational software is capable of determining whether a referee was moving properly in a certain situation or not. Determination is possible on the basis of numerical values that are calculated by simulating the human visual field. The referee's horizontal field of view simulation is based on the standard set by the American Optometric Association. It is implemented through a modified Sweep and Prune algorithm which is also discussed in this paper.Keywords Multiple dependent time series · MLP neural networks · LTR -MDTS model · Field of vision simulation · Basketball referee movement Predrag Pecev

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The subject of research presented in this paper is to model a neural network structure and appropriate training algorithm that is most suited for multiple dependent time series prediction / deduction. The basic idea is to take advantage of neural networks in solving the problem of prediction of synchronized basketball referees' movement during a basketball action. Presentation of time series stemming from the aforementioned problem, by using traditional Multilayered Perceptron neural networks (MLP), leads to a sort of paradox of backward time lapse effect that certain input and hidden layers nodes have on output nodes that correspond to previous moments in time. This paper describes conducted research and analysis of different methods of overcoming the presented problem. Presented paper is essentially split into two parts. First part gives insight on efforts that are put into training set configuration on standard Multi Layered Perceptron back propagation neural networks, in order to decrease backwards time lapse effects that certain input and hidden layers nodes have on output nodes. Second part of paper focuses on the results that a new neural network structure called LTR-MDTS provides. Foundation of LTR-MDTS design relies on a foundation on standard MLP neural networks with certain, left-to-right synapse removal to eliminate aforementioned backwards time lapse effect on the output nodes.

What is presented in this paper is a solution that bears large applicable values depending on implementation and realization. The paper describes the methods and the developed software which, based on the action and the movement of the ball, using the neural network, determines the movement of a basketball referee on the court, in order to gain the best view of the action. The solution is developed in Microsoft Visual Studio 2010, written in the programming language C#, reffering to AForge .NET Framework for the support in the aspects of configuring, training and usage of neural networks. AForge .NET Framework is published with LGPL v3 licence. The developed solution is named BBFBR, which stands for Basketball Board for Basketball Referees. Current implementation of the solution is based on drawing the ball's movement on the court, which is the input vector of the neural network, whilst the output vector of the neural network consists of movement coordinates of the referees.The current solution enables calculating optimal ways of the referees movement in the case that the movement of the ball in an action consists of not more than 15 key points, e.g. guiding the ball from one point to another, passing the ball to another player, shooting etc. Applicable value of the current solution bears only the educative purpose because it is possible to apply it for training young basketball referees in the terms of their movement to enable them to be aware of an action and to be able to analyze it.