Representation of Functional Data in Neural Networks

Functional Data Analysis (FDA) is an extension of traditional data analysis to functional data, for example spectra, temporal series, spatio-temporal images, gesture recognition data, etc. Functional data are rarely known in practice; usually a regular or irregular sampling is known. For this reason, some processing is needed in order to benefit from the smooth character of functional data in the analysis methods. This paper shows how to extend the Radial-Basis Function Networks (RBFN) and Multi-Layer Perceptron (MLP) models to functional data inputs, in particular when the latter are known through lists of input-output pairs. Various possibilities for functional processing are discussed, including the projection on smooth bases, Functional Principal Component Analysis, functional centering and reduction, and the use of differential operators. It is shown how to incorporate these functional processing into the RBFN and MLP models. The functional approach is illustrated on a benchmark of spectrometric data analysis.Comment: Also available online from: http://www.sciencedirect.com/science/journal/0925231

Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs

Many real world data are sampled functions. As shown by Functional Data Analysis (FDA) methods, spectra, time series, images, gesture recognition data, etc. can be processed more efficiently if their functional nature is taken into account during the data analysis process. This is done by extending standard data analysis methods so that they can apply to functional inputs. A general way to achieve this goal is to compute projections of the functional data onto a finite dimensional sub-space of the functional space. The coordinates of the data on a basis of this sub-space provide standard vector representations of the functions. The obtained vectors can be processed by any standard method. In our previous work, this general approach has been used to define projection based Multilayer Perceptrons (MLPs) with functional inputs. We study in this paper important theoretical properties of the proposed model. We show in particular that MLPs with functional inputs are universal approximators: they can approximate to arbitrary accuracy any continuous mapping from a compact sub-space of a functional space to R. Moreover, we provide a consistency result that shows that any mapping from a functional space to R can be learned thanks to examples by a projection based MLP: the generalization mean square error of the MLP decreases to the smallest possible mean square error on the data when the number of examples goes to infinity

Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis

In this paper, we study a natural extension of Multi-Layer Perceptrons (MLP) to functional inputs. We show that fundamental results for classical MLP can be extended to functional MLP. We obtain universal approximation results that show the expressive power of functional MLP is comparable to that of numerical MLP. We obtain consistency results which imply that the estimation of optimal parameters for functional MLP is statistically well defined. We finally show on simulated and real world data that the proposed model performs in a very satisfactory way.Comment: http://www.sciencedirect.com/science/journal/0893608

Face Recognition Using Fixed Spread Radial Basis Function Neural Network

This paper presents face recognition using spread fixed spread radial basis function neural network. Acquired image will be going through image processing process. General preprocessing approach is use for normalizing the image. Radial Basis Function Neural Network is use for face recognition and Support Vector Machine is used as the face detector. RBF Neural Networks offer several advantages compared to other neural network architecture such as they can be trained using fast two stages training algorithm and the network possesses the property of best approximation. The output of the network can be optimized by setting suitable values of the center and spread of the RBF but in this paper fixed spread is used as there is only one train image for every user and to limit the output value

Experiments in Aggregating Air Ordnance Effectiveness Data for the TACWAR Model

An interactive MS Access&trademark; based application that aggregates the output of the SABSEL model for input into the TACWAR model is developed. The application was developed following efforts to create a functional approximation of the SABSEL data using neural networks, statistical networks, and traditional statistical techniques. These approximations were compared to a look-up table methodology on the basis of accuracy, (RMS

Redistribution of Synaptic Efficacy Supports Stable Pattern Learning in Neural Networks

Markram and Tsodyks, by showing that the elevated synaptic efficacy observed with single-pulse LTP measurements disappears with higher-frequency test pulses, have critically challenged the conventional assumption that LTP reflects a general gain increase. Redistribution of synaptic efficacy (RSE) is here seen as the local realization of a global design principle in a neural network for pattern coding. As is typical of many coding systems, the network learns by dynamically balancing a pattern-independent increase in strength against a pattern-specific increase in selectivity. This computation is implemented by a monotonic long-term memory process which has a bidirectional effect on the postsynaptic potential via functionally complementary signal components. These frequency-dependent and frequency-independent components realize the balance between specific and nonspecific functions at each synapse. This synaptic balance suggests a functional purpose for RSE which, by dynamically bounding total memory change, implements a distributed coding scheme which is stable with fast as well as slow learning. Although RSE would seem to make it impossible to code high-frequency input features, a network preprocessing step called complement coding symmetrizes the input representation, which allows the system to encode high-frequency as well as low-frequency features in an input pattern. A possible physical model interprets the two synaptic signal components in terms of ligand-gated and voltage-gated receptors, where learning converts channels from one type to another.Office of Naval Research and the Defense Advanced Research Projects Agency (N00014-95-1-0409, N00014-1-95-0657

Corporation robots

Nowadays, various robots are built to perform multiple tasks. Multiple robots working together to perform a single task becomes important. One of the key elements for multiple robots to work together is the robot need to able to follow another robot. This project is mainly concerned on the design and construction of the robots that can follow line. In this project, focuses on building line following robots leader and slave. Both of these robots will follow the line and carry load. A Single robot has a limitation on handle load capacity such as cannot handle heavy load and cannot handle long size load. To overcome this limitation an easier way is to have a groups of mobile robots working together to accomplish an aim that no single robot can do alon