#ifndef _NEURAL_NETWORK_H_ #define _NEURAL_NETWORK_H_ #include #define SLOPE 1.0 #define S(x) (1.0 / (1.0 + exp (0.0 - SLOPE*(x)))) #define WRONG 0 #define GOOD 1 #define CORRECT 2 //**************************************************************************** // // Neural_network class: // // This class performs all the necessary functions needed to train // a Neural Network. The network has an input layer, two hidden // layers, and an output layer. The size of each layer is specified // a run time so there is no restriction on size except memory. // This is a feed-forward network with full connctions from one // layer to the next. // // The network can perform straight back-propagation with no // modifications (Rumelhart, Hinton, and Williams, 1985) which // will find a solution but not very quickly. The network can also // perform back-propagation with the delta-bar-delta rule developed // by Robert A. Jacobs, University of Massachusetts // (Neural Networks, Vol 1. pp.295-307, 1988). The basic idea of this // rule is that every weight has its own learning rate and each // learning rate should be continously changed according to the // following rules - // - If the weight changes in the same direction as the previous update, // then the learning rate for that weight should increase by a constant. // - If the weight changes in the opposite direction as the previous // update, then the learning rate for that weight should decrease // exponentially. // // learning rate = e(t) for each individual weight // The exact formula for the change in learning rate (DELTA e(t)) is // // // | K if DELTA_BAR(t-1)*DELTA(t) > 0 // DELTA e(t) = | -PHI*e(t) if DELTA_BAR(t-1)*DELTA(t) < 0 // | 0 otherwise // // where DELTA(t) = dJ(t) / dw(t) ---> Partial derivative // // and DELTA_BAR(t) = (1 - THETA)*DELTA(t) + THETA*DELTA_BAR(t-1). // // For full details of the algorithm, read the article in // Neural Networks. // // // To perform straight back-propagation, just construct a Neural_network // with no learning parameters specified (they default to straight // back-propagation) or set them to // K = 0, PHI = 0, THETA = 1.0 // // However, using the delta-bar-delta rule should increase your rate of // convergence by a factor of 10 to 100 generally. The parameters for // the delta-bar-delta rule I use are // K = 0.025, PHI = 0.2, THETA = 0.8 // // One more heuristic method has been employed in this Neural net class- // the skip heuristic. This is something I thought of and I am sure // other people have also. If the output activation is within // skip_epsilon of its desired for each output, then the calc_forward // routine returns the skip_flag = 1. This allows you to not waste // time trying to push already very close examples to the exact value. // If the skip_flag comes back '1', then don't bother calculating forward // or back-propagating the example for X number of epochs. You must // write the routine to skip the example yourself, but the Neural_network // will tell you when to skip the example. This heuristic also has the // advantage of reducing memorization and increases generalization. // Typical values I use for this heuristic - // skip_epsilon = 0.01 - 0.05 // number skipped = 2-10. // // Experiment with all the values to see which work best for your // application. // // // Comments and suggestions are welcome and can be emailed to me // anstey@sun.soe.clarkson.edu // //**************************************************************************** class Neural_network { private: // We need // // Matrix for hidden layer 1 activation [num_hidden1] // Matrix for hidden layer 2 activation [num_hidden2] // Matrix for output layer activation [num_outputs] // // Matrix for input to first hidden layer weights [num_inputs] [num_hidden1] // Matrix for hidden layer 1 to hidden layer 2 weights [hidden1] [hidden2] // Matrix for hidden layer 2 to output layer weights [hidden2] [outputs] // 3 Matrices for sum of all the deltas in an epoch - Back propagation // 2 Matrices for sum of deltas * weight for each neuron in hidden layers // 1 and 2 for backpropagation - Back propagation // // 3 Matrices for each weight's learning rate - delta-bar-delta rule // 3 Matrices for each weight's learning delta - delta-bar-delta rule // 3 Matrices for each weight's learning delta_bar - delta-bar-delta rule int num_inputs; int num_hidden1; int num_hidden2; int num_outputs; double epsilon; double skip_epsilon; double learning_rate; double theta; double phi; double K; long training_examples; long examples_since_update; double *hidden1_act; double *hidden2_act; double *output_act; double *input_weights; double *hidden1_weights; double *hidden2_weights; double *input_learning_rate; double *hidden1_learning_rate; double *hidden2_learning_rate; double *input_learning_delta; double *hidden1_learning_delta; double *hidden2_learning_delta; double *input_learning_delta_bar; double *hidden1_learning_delta_bar; double *hidden2_learning_delta_bar; double *input_weights_sum_delta; double *hidden1_weights_sum_delta; double *hidden2_weights_sum_delta; double *hidden1_sum_delta_weight; double *hidden2_sum_delta_weight; void allocate_matrices (); void initialize_matrices (double range); void deallocate_matrices (); public: //*********************************************************************** // Constructors : * // Full size specifications and learning parameters. * // Learning parameters are provided defaults which are set to * // just use the BP algorithm with no modifications. * // * // Read constructor which reads in the size and all the weights from * // a file. The network is resized to match the size specified * // by the file. Learning parameters must be specified * // separately. * //*********************************************************************** Neural_network (int number_inputs = 1, int number_hidden1 = 1, int number_hidden2 = 1, int number_outputs = 1, double t_epsilon = 0.1, double t_skip_epsilon = 0.0, double t_learning_rate = 0.1, double t_theta = 1.0, double t_phi = 0.0, double t_K = 0.0, double range = 3.0); Neural_network (String& filename, int& file_error, double t_epsilon = 0.1, double t_skip_epsilon = 0.0, double t_learning_rate = 0.1, double t_theta = 1.0, double t_phi = 0.0, double t_K = 0.0); ~Neural_network () { deallocate_matrices ();}; //************************************************************************** // Weight parameter routines: * // save_weights : This routine saves the weights of the network * // to the file . * // * // read_weights : This routine reads the weight values from the file * // . The network is automatically resized to the * // size specified by the file. * // * // Activation routines return the node activation after a calc_forward * // has been performed. * // * // get_weight routines return the weight between node1 and node2. * // * //************************************************************************** int save_weights (String& filename); int read_weights (String& filename); double get_hidden1_activation (int node) { return (hidden1_act [node]); }; double get_hidden2_activation (int node) { return (hidden2_act [node]); }; double get_output_activation (int node) { return (output_act [node]); }; double get_input_weight (int input_node, int hidden1_node) { return (input_weights [hidden1_node * num_inputs + input_node]);}; double get_hidden1_weight (int hidden1_node, int hidden2_node) { return (hidden1_weights [hidden2_node * num_hidden1 + hidden1_node]);}; double get_hidden2_weight (int hidden2_node, int output_node) { return (hidden2_weights [output_node * num_hidden2 + hidden2_node]);}; //******************************************************************* // Size parameters of network. * // The size of the network may be changed at any time. The weights * // will be copied from the old size to the new size. If the new * // size is larger, then the extra weights will be randomly set * // between +-range. The matrices used to hold learning updates * // and activations will be re-initialized (cleared). * //******************************************************************* int get_number_of_inputs () { return (num_inputs); }; int get_number_of_hidden1 () { return (num_hidden1); }; int get_number_of_hidden2 () { return (num_hidden2); }; int get_number_of_outputs () { return (num_outputs); }; void set_size_parameters (int number_inputs, int number_hidden1, int number_hidden2, int number_outputs, double range = 3.0); //******************************************************************* // Learning parameters functions. These parameters may be changed * // on the fly. The learning rate and K may have to be reduced as * // more and more training is done to prevent oscillations. * //******************************************************************* void set_epsilon (double eps) { epsilon = eps; }; void set_skip_epsilon (double eps) { skip_epsilon = eps; }; void set_learning_rate (double l_rate) { learning_rate = l_rate; }; void set_theta (double t_theta) { theta = t_theta; }; void set_phi (double t_phi) { phi = t_phi; }; void set_K (double t_K) { K = t_K; }; double get_epsilon () { return (epsilon); }; double get_skip_epsilon () { return (skip_epsilon); }; double get_learning_rate () { return (learning_rate); }; double get_theta () { return (theta); }; double get_phi () { return (phi); }; double get_K () { return (K); }; long get_iterations () { return (training_examples); }; //************************************************************************** // The main neural network routines: * // * // The network input is an array of doubles which has a size of * // number_inputs. * // The network desired output is an array of doubles which has a size * // of number_outputs. * // * // back_propagation : Calculates how each weight should be changed. * // Assumes that calc_forward has been called just prior to * // this routine to calculate all of the node activations. * // * // calc_forward : Calculates the output for a given input. Finds * // all node activations which are needed for back_propagation * // to calculate weight adjustment. Returns abs (error). * // The parameter skip is for use with the skip_epsilon * // parameter. What it means is if the output is within * // skip_epsilon of the desired, then it is so close that it * // should be skipped from being calculated the next X times. * // Careful use of this parameter can significantly increase * // the rate of convergence and also help prevent over-learning. * // * // calc_forward_test : Calculates the output for a given input. This * // routine is used for testing rather than training. It returns * // whether the test was CORRECT, GOOD or WRONG which is * // determined by the parameters correct_epsilon and * // good_epsilon. CORRECT > GOOD > WRONG. * // * // update_weights : Actually adjusts all the weights according to * // the calculations of back_propagation. This routine should * // be called at the end of every training epoch. The weights * // can be updated by the straight BP algorithm, or by the * // delta-bar-delta algorithm developed by Robert A. Jacobs * // which increases the rate of convergence generally by at * // least a factor of 10. The parameters THETA, PHI, and K * // determine which algorithm is used. The default settings * // for these parameters cause update_weights to use the straight * // BP algorithm. * // * // kick_weights : This routine changes all weights by a random amount * // within +-range. It is useful in case the network gets * // 'stuck' and is having trouble converging to a solution. I * // use it when the number wrong has not changed for the last 200 * // epochs. Getting the range right will take some trial and * // error as it depends on the application and the weights' * // actual values. * // * //************************************************************************** void back_propagation (double input [], double desired_output [], int& done); double calc_forward (double input [], double desired_output [], int& num_wrong, int& skip, int print_it, int& actual_printed); int calc_forward_test (double input [], double desired_output [], int print_it, double correct_eps, double good_eps); void update_weights (); void kick_weights (double range); }; #endif