Tarek M. Hamdani

Multi-objective Feature Selection with NSGA II

This paper deals with the multi-objective definition of the feature selection problem for different pattern recognition domains. We use NSGA II the latest multi-objective algorithm developed for resolving problems of multi-objective aspects with more accuracy and a high convergence speed. We define the feature selection as a problem including two competing objectives and we try to find a set of optimal solutions so called Pareto-optimal solutions instead of a single optimal solution. The two competing objectives are the minimization of both the number of used features and the classification error using 1-NN classifier. We apply our method to five databases selected from the UCI repository and we report the results on these databases. We present the convergence of the NSGA II on different problems and discuss the behavior of NSGA II on these different contexts.

Distributed Genetic Algorithm with Bi-Coded Chromosomes and a New Evaluation Function for Features Selection

We propose a new feature selection method based on distributed genetic algorithms and bi-coded genes. This solution uses homogeneous and heterogeneous population strategies to minimize the complexity and to accelerate the algorithm convergence. The importance rate is computed for each feature measure to estimate the contribution of each feature in the finale selected vector. A new fitness function was proposed to take into consideration the recognition rate relatively to the size of the selected features subset. Two genetic codes are used to represent each member; a binary code to represent when the corresponding feature was selected or not; the second real code was used to estimate the importance rate of the selected feature or the selection probability for the non selected feature.

Distributed MOPSO with a new population subdivision technique for the feature selection

In this paper, a new Multi-Objective Particle Swarm Optimization (MOPSO) is applied to solve a problem of feature selection defined as a multiobjective problem. This algorithm (pMOPSO), known for its fast convergence with negligible computation time is based on a distributed architecture. Sub-swarms are obtained from dynamic subdivision of the population using Pareto Fronts. The algorithm addresses a problem defined by two goals, characterized by their contradictory aspect, namely, minimizing the error rate and minimizing the number of features. The two objectives are treated simultaneously constituting the objective function. Performance of our approach is compared with other evolutionary techniques using databases choosing from the UCI repository [1].

Hierarchical genetic algorithm with new evaluation function and bi-coded representation for the selection of features considering their confidence rate

In this paper, we propose a new feature selection method based on a hierarchical genetic algorithm (GA) with a new evaluation function and a bi-coded representation. The hierarchical GA with homogeneous and heterogeneous population is used to minimize the computational load and to accelerate convergence speed. The fitness function is designed to find the solution that both maximizes the recognition rate and minimizes the feature set size. Each solution candidate is represented by two chromosomes which lengths are identical to the number of available features. The first binary chromosome represents the presence of features in the solution candidate; the second represents the confidence rates of features, which are used to assign different weights to features during the classification procedure and to achieve more accurate classifier. The proposed method is tested using five databases and is shown to outperform many commonly used feature selection algorithms.

Enhancing the structure and parameters of the centers for BBF Fuzzy Neural Network classifier construction based on data structure

This paper aims at presenting different strategies for the construction of beta basis function (BBF) fuzzy neural network. These strategies lead to the determination of the network architecture by determining the structure of the hidden layer and parameters of its centers based on data structure. For that, we use self organizing maps (SOM) clustering to construct a mapped structure of the real training data. By analyzing this structure, we proceed to neuron selection. Data sets were also analyzed with the fuzzy c-means (FCM) clustering technique to generate fuzzy membership values presenting fuzzy outputs for our fuzzy neural model. We propose to estimate the parameters of beta basis function in order to obtain better data coverage. Experimental results show that the use of the proposed technique produces better results.

2IBGSOM: interior and irregular boundaries growing self-organizing maps

In this paper, we introduce a new variant of growing self-organizing maps (GSOM) based on Alahakoons algorithm for SOM training; so called 2IBGSOM (interior and irregular boundaries growing self-organizing maps). Its dynamically evolving structure for SOM, which allocates map size and shape during the unsupervised training process. 2IBGSOM starts with a small number of initial nodes and generates new nodes from the boundary and the interior of the network. 2IBGSOM represents the structure of the training data as accurately as possible. Our proposed method was tested on real world databases and showed better performance than the classical SOM and the growing grid (GG) algorithms. Three criteria were used to compare the above algorithms with our proposed method; the quantization error; the topological error and the labeling error to have more accuracy on the produced structure. Results report that 2IBGSOM shows a very good capacity of estimation for the training data based on the three tested factors.

A multi objective particles swarm optimization algorithm for solving the routing pico-satellites problem

This paper belongs to the field of communication and computer networks. Networks of low earth orbiting satellites are able to provide wireless connectivity to any part of the world while ensuring timely and better performance lower bit error rate. This type of technology has been growing interest towards the development of small satellites. Especially, when we talk about the execution of the service quality system, we must use some optimization techniques. However, these systems have the drawback of energy management which is the biggest problem to worry about. Therefore, optimization of the processing time and the effective implementation of information flow and storage on board must be discussed with respect to topology changes fast. In this paper we will discuss various routing algorithms of data used in small satellites and terrestrial networks. As a multiobjective problem, we try to solve the problem of routing data with multiobjective particle swarm optimization (MOPSO).

An Iterative Method for Deciding SVM and Single Layer Neural Network Structures

We present two new classifiers for two-class classification problems using a new Beta-SVM kernel transformation and an iterative algorithm to concurrently select the support vectors for a support vector machine (SVM) and the hidden units for a single hidden layer neural network to achieve a better generalization performance. To construct the classifiers, the contributing data points are chosen on the basis of a thresholding scheme of the outputs of a single perceptron trained using all training data samples. The chosen support vectors are used to construct a new SVM classifier that we call Beta-SVN. The number of chosen support vectors is used to determine the structure of the hidden layer in a single hidden layer neural network that we call Beta-NN. The Beta-SVN and Beta-NN structures produced by our method outperformed other commonly used classifiers when tested on a 2-dimensional non-linearly separable data set.

A new data topology matching technique with Multilevel Interior Growing Self-Organizing Maps

Self-Organizing Maps (SOM) are widely used for their ability to preserve the topology in the projection. However, this topology is not perfectly preserved due to the static structure of SOM. Therefore, we show in this paper a novel architecture of SOM which organizes itself over time. The proposed method called MIGSOM (Multilevel Interior Growing Self-Organizing Maps) is generated by a growth process which allows to adds nodes where it is necessary. The network start with a minimum number of nodes, then nodes will be added from the boundary as well as the interior of the network. The MIGSOM algorithm adds the interior nodes in a superior level of the map. As a result, the map can have three-Dimensional structure with multi-levels oriented maps. To improve the performance of the proposed algorithm, comparison of MIGSOM to the Kohonen feature Map (SOM) and the Growing Grid (GG) is made. Our experiment results demonstrate that the MIGSOM constructs better mappings than the classic SOM and GG, especially, in terms of data quantification and topology preservation.

MIGSOM: Multilevel Interior Growing Self-Organizing Maps for High Dimensional Data Clustering

Understanding the inherent structure of high-dimensional datasets is a very challenging task. This can be tackled from visualization, summarizing or simply clustering points of view. The Self-Organizing Map (SOM) is a powerful and unsupervised neural network to resolve these kinds of problems. By preserving the data topology mapped onto a grid, SOM can facilitate visualization of data structure. However, classical SOM still suffers from the limits of its predefined structure. Growing variants of SOM can overcome this problem, since they have tried to define a network structure with no need an advance a fixed number of output units by dynamic growing architecture. In this paper we propose a new dynamic SOMs called MIGSOM: Multilevel Interior Growing SOMs for high-dimensional data clustering. MIGSOM present a different architecture than dynamic variants presented in the literature. Using an unsupervised training process MIGSOM has the capability of growing map size from the boundaries as well as the interior of the network in order to represent more faithfully the structure present in a data collection. As a result, MIGSOM can have three-dimensional (3-D) structure with different levels of oriented maps developed according to data direction. We demonstrate the potential of the MIGSOM with real-world datasets of high-dimensional properties in terms of topology preserving visualization, vectors summarizing by efficient quantization and data clustering. In addition, MIGSOM achieves better performance compared to growing grid and the classical SOM.