Support vector machine for functional data classification

In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In fact most of the traditional data analysis tools for regression, classification and clustering have been adapted to functional inputs under the general name of functional Data Analysis (FDA). In this paper, we investigate the use of Support Vector Machines (SVMs) for functional data analysis and we focus on the problem of curves discrimination. SVMs are large margin classifier tools based on implicit non linear mappings of the considered data into high dimensional spaces thanks to kernels. We show how to define simple kernels that take into account the unctional nature of the data and lead to consistent classification. Experiments conducted on real world data emphasize the benefit of taking into account some functional aspects of the problems.Comment: 13 page

Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition

We extend Generalized Additive Models for Location, Scale, and Shape (GAMLSS) to regression with functional response. This allows us to simultaneously model point-wise mean curves, variances and other distributional parameters of the response in dependence of various scalar and functional covariate effects. In addition, the scope of distributions is extended beyond exponential families. The model is fitted via gradient boosting, which offers inherent model selection and is shown to be suitable for both complex model structures and highly auto-correlated response curves. This enables us to analyze bacterial growth in \textit{Escherichia coli} in a complex interaction scenario, fruitfully extending usual growth models.Comment: bootstrap confidence interval type uncertainty bounds added; minor changes in formulation

Adaptation and learning over networks for nonlinear system modeling

In this chapter, we analyze nonlinear filtering problems in distributed environments, e.g., sensor networks or peer-to-peer protocols. In these scenarios, the agents in the environment receive measurements in a streaming fashion, and they are required to estimate a common (nonlinear) model by alternating local computations and communications with their neighbors. We focus on the important distinction between single-task problems, where the underlying model is common to all agents, and multitask problems, where each agent might converge to a different model due to, e.g., spatial dependencies or other factors. Currently, most of the literature on distributed learning in the nonlinear case has focused on the single-task case, which may be a strong limitation in real-world scenarios. After introducing the problem and reviewing the existing approaches, we describe a simple kernel-based algorithm tailored for the multitask case. We evaluate the proposal on a simulated benchmark task, and we conclude by detailing currently open problems and lines of research.Comment: To be published as a chapter in `Adaptive Learning Methods for Nonlinear System Modeling', Elsevier Publishing, Eds. D. Comminiello and J.C. Principe (2018

Multiple 2D self organising map network for surface reconstruction of 3D unstructured data

Surface reconstruction is a challenging task in reverse engineering because it must represent the surface which is similar to the original object based on the data obtained. The data obtained are mostly in unstructured type whereby there is not enough information and incorrect surface will be obtained. Therefore, the data should be reorganised by finding the correct topology with minimum surface error. Previous studies showed that Self Organising Map (SOM) model, the conventional surface approximation approach with Non Uniform Rational B-Splines (NURBS) surfaces, and optimisation methods such as Genetic Algorithm (GA), Differential Evolution (DE) and Particle Swarm Optimisation (PSO) methods are widely implemented in solving the surface reconstruction. However, the model, approach and optimisation methods are still suffer from the unstructured data and accuracy problems. Therefore, the aims of this research are to propose Cube SOM (CSOM) model with multiple 2D SOM network in organising the unstructured surface data, and to propose optimised surface approximation approach in generating the NURBS surfaces. GA, DE and PSO methods are implemented to minimise the surface error by adjusting the NURBS control points. In order to test and validate the proposed model and approach, four primitive objects data and one medical image data are used. As to evaluate the performance of the proposed model and approach, three performance measurements have been used: Average Quantisation Error (AQE) and Number Of Vertices (NOV) for the CSOM model while surface error for the proposed optimised surface approximation approach. The accuracy of AQE for CSOM model has been improved to 64% and 66% when compared to 2D and 3D SOM respectively. The NOV for CSOM model has been reduced from 8000 to 2168 as compared to 3D SOM. The accuracy of surface error for the optimised surface approximation approach has been improved to 7% compared to the conventional approach. The proposed CSOM model and optimised surface approximation approach have successfully reconstructed surface of all five data with better performance based on three performance measurements used in the evaluation