Inversion of Complex Valued Neural Networks Using Complex Back-propagation Algorithm
Anita S. Gangal, P.K. Kalra, Devendra Singh Chauhan · 2009
This paper presents the inversion of complex valued neural networks. Inversion means predicting the inputs for given output. We have tried inversion of complex valued neural network using complex back-propagation algorithm. We have used split sigmoid activation function both for training and inversion of neural network to overcome the problem of singularities. Since inversion is a one to many mapping, means for a given output there are number of possible combinations of inputs. So in order to get the inputs in the desired range conditional constraints are applied to inputs. Simulation on benchmark complex valued problems support the investigation. numerous solutions. This method results in population of initial points in the search space at a time and new points are generated in the input space to replace existing points so as to explore all the solutions. Single element search method for inversion of real valued neural network was first introduced by Williams (2) and then Kinderman and Linden (3). They used this to extract codebook vectors for digits. This method of inversion involves two main steps: first training the network and the second step is inversion. During the training neural network is trained to learn a mapping from input to output with the help of training data. The weights are the free parameters and by finding the proper set by minimizing some error criterion, neural network learns a functional relationship between the inputs and the outputs. All the weights are fixed after training of neural network. After training, the network is initialized with a random input vector. Output is calculated, compared with the given output. Error is calculated. This error is back propagated to minimize the error function and the input vector is updated. This iterative process continues till the error is less than the minimum set value. Eberhart and Dobbins (4) applied it to invert the trained real valued neural network for the diagnosis of appendicitis. Jordan and Rumelhart (5) have proposed a method to invert the feed forward real valued neural network. They tried to solve the inverse kinematics problems for redundant manipulators. There approach is a two-stage procedure. In the first stage, a network is trained to approximate the forward mapping. In the second stage, a particular inverse solution is obtained by connecting another network with the previously trained network in series and learning an identity mapping across the composite network. Behera, Gopal, Chaudhary (6) used real valued neural network inversion in the control of multilink robot manipulators. They have developed an inversion algorithm for inverting radial basis function (RBS) neural networks which is based on an extended Kalman filter. Bio- Liang Lu, Hajime, and Nishikawa (7) have formulated the inversion problem as a nonlinear programming problem and a separable programming problem or a linear programming problem according to the architectures of the real valued network to be inverted.