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

Flood. An open source neural networks C++ library

The multilayer perceptron is an important model of neural network, and much of the literature in the eld is referred to that model. The multilayer perceptron has found a wide range of applications, which include function re- gression, pattern recognition, time series prediction, optimal control, optimal shape design or inverse problems. All these problems can be formulated as variational problems. That neural network can learn either from databases or from mathematical models. Flood is a comprehensive class library which implements the multilayer perceptron in the C++ programming language. It has been developed follow- ing the functional analysis and calculus of variations theories. In this regard, this software tool can be used for the whole range of applications mentioned above. Flood also provides a workaround for the solution of function opti- mization problems

An Artificial Neural Network technique for on-line hotel booking

In this paper the use of Artificial Neural Networks (ANNs) in on-line booking for hotel industry is investigated. The paper details the description, the modeling and the resolution technique of on-line booking. The latter problem is modeled using the paradigms of machine learning, in place of standard `If-Then-Else' chains of conditional rules. In particular, a supervised three layers MLP neural network is adopted, which is trained using information from previous customers' reservations. Performance of our ANN is analyzed: it behaves in a quite satisfactory way in managing the (simulated) booking service in a hotel. The customer requires single or double rooms, while the system gives as a reply the confirmation of the required services, if available. Moreover, we highlight that using our approach the system proposes alternative accommodations (from two days in advance to two days later with respect to the requested day), in case rooms or services are not available. Numerical results are given, where the effectiveness of the proposed approach is critically analyzed. Finally, we outline guidelines for future research.On-line booking; hotel reservation; machine learning; supervised multilayer perceptron networks

Medical imaging analysis with artificial neural networks

Given that neural networks have been widely reported in the research community of medical imaging, we provide a focused literature survey on recent neural network developments in computer-aided diagnosis, medical image segmentation and edge detection towards visual content analysis, and medical image registration for its pre-processing and post-processing, with the aims of increasing awareness of how neural networks can be applied to these areas and to provide a foundation for further research and practical development. Representative techniques and algorithms are explained in detail to provide inspiring examples illustrating: (i) how a known neural network with fixed structure and training procedure could be applied to resolve a medical imaging problem; (ii) how medical images could be analysed, processed, and characterised by neural networks; and (iii) how neural networks could be expanded further to resolve problems relevant to medical imaging. In the concluding section, a highlight of comparisons among many neural network applications is included to provide a global view on computational intelligence with neural networks in medical imaging

A Connection Between GRBF and MLP

Both multilayer perceptrons (MLP) and Generalized Radial Basis Functions (GRBF) have good approximation properties, theoretically and experimentally. Are they related? The main point of this paper is to show that for normalized inputs, multilayer perceptron networks are radial function networks (albeit with a non-standard radial function). This provides an interpretation of the weights w as centers t of the radial function network, and therefore as equivalent to templates. This insight may be useful for practical applications, including better initialization procedures for MLP. In the remainder of the paper, we discuss the relation between the radial functions that correspond to the sigmoid for normalized inputs and well-behaved radial basis functions, such as the Gaussian. In particular, we observe that the radial function associated with the sigmoid is an activation function that is good approximation to Gaussian basis functions for a range of values of the bias parameter. The implication is that a MLP network can always simulate a Gaussian GRBF network (with the same number of units but less parameters); the converse is true only for certain values of the bias parameter. Numerical experiments indicate that this constraint is not always satisfied in practice by MLP networks trained with backpropagation. Multiscale GRBF networks, on the other hand, can approximate MLP networks with a similar number of parameters