Complex Support Vector Machines for Regression and Quaternary Classification

The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for complex-valued data and considers two cases: a) the complex data are split into their real and imaginary parts and a typical real kernel is employed to map the complex data to a complexified feature space and b) a pure complex kernel is used to directly map the data to the induced complex feature space. The recently developed Wirtinger's calculus on complex reproducing kernel Hilbert spaces (RKHS) is employed in order to compute the Lagrangian and derive the dual optimization problem. As one of our major results, we prove that any complex SVM/SVR task is equivalent with solving two real SVM/SVR tasks exploiting a specific real kernel which is generated by the chosen complex kernel. In particular, the case of pure complex kernels leads to the generation of new kernels, which have not been considered before. In the classification case, the proposed framework inherently splits the complex space into four parts. This leads naturally in solving the four class-task (quaternary classification), instead of the typical two classes of the real SVM. In turn, this rationale can be used in a multiclass problem as a split-class scenario based on four classes, as opposed to the one-versus-all method; this can lead to significant computational savings. Experiments demonstrate the effectiveness of the proposed framework for regression and classification tasks that involve complex data.Comment: Manuscript accepted in IEEE Transactions on Neural Networks and Learning System

Machine Learning For In-Region Location Verification In Wireless Networks

In-region location verification (IRLV) aims at verifying whether a user is inside a region of interest (ROI). In wireless networks, IRLV can exploit the features of the channel between the user and a set of trusted access points. In practice, the channel feature statistics is not available and we resort to machine learning (ML) solutions for IRLV. We first show that solutions based on either neural networks (NNs) or support vector machines (SVMs) and typical loss functions are Neyman-Pearson (N-P)-optimal at learning convergence for sufficiently complex learning machines and large training datasets . Indeed, for finite training, ML solutions are more accurate than the N-P test based on estimated channel statistics. Then, as estimating channel features outside the ROI may be difficult, we consider one-class classifiers, namely auto-encoders NNs and one-class SVMs, which however are not equivalent to the generalized likelihood ratio test (GLRT), typically replacing the N-P test in the one-class problem. Numerical results support the results in realistic wireless networks, with channel models including path-loss, shadowing, and fading

Effective classifiers for detecting objects

Several state-of-the-art machine learning classifiers are compared for the purposes of object detection in complex images, using global image features derived from the Ohta color space and Local Binary Patterns. Image complexity in this sense refers to the degree to which the target objects are occluded and/or non-dominant (i.e. not in the foreground) in the image, and also the degree to which the images are cluttered with non-target objects. The results indicate that a voting ensemble of Support Vector Machines, Random Forests, and Boosted Decision Trees provide the best performance with AUC values of up to 0.92 and Equal Error Rate accuracies of up to 85.7% in stratified 10-fold cross validation experiments on the GRAZ02 complex image dataset

A support vector-based interval type-2 fuzzy system

In this paper, a new fuzzy regression model that is supported by support vector regression is presented. Type-2 fuzzy systems are able to tackle applications that have significant uncertainty. However general type-2 fuzzy systems are more complex than type-1 fuzzy systems. Support vector machines are similar to fuzzy systems in that they can also model systems that are non-linear in nature. In the proposed model the consequent parameters of type-2 fuzzy rules are learnt using support vector regression and an efficient closed-form type reduction strategy is used to simplify the computations. Support vector regression improved the generalisation performance of the fuzzy rule-based system in which the fuzzy rules were a set of interpretable IF-THEN rules. The performance of the proposed model was demonstrated by conducting case studies for the non-linear system approximation and prediction of chaotic time series. The model yielded promising results and the simulation results are compared to the results published in the area

A support vector-based interval type-2 fuzzy system

In this paper, a new fuzzy regression model that is supported by support vector regression is presented. Type-2 fuzzy systems are able to tackle applications that have significant uncertainty. However general type-2 fuzzy systems are more complex than type-1 fuzzy systems. Support vector machines are similar to fuzzy systems in that they can also model systems that are non-linear in nature. In the proposed model the consequent parameters of type-2 fuzzy rules are learnt using support vector regression and an efficient closed-form type reduction strategy is used to simplify the computations. Support vector regression improved the generalisation performance of the fuzzy rule-based system in which the fuzzy rules were a set of interpretable IF-THEN rules. The performance of the proposed model was demonstrated by conducting case studies for the non-linear system approximation and prediction of chaotic time series. The model yielded promising results and the simulation results are compared to the results published in the area

Nonlinear Channel Estimation for OFDM System by Complex LS-SVM under High Mobility Conditions

A nonlinear channel estimator using complex Least Square Support Vector Machines (LS-SVM) is proposed for pilot-aided OFDM system and applied to Long Term Evolution (LTE) downlink under high mobility conditions. The estimation algorithm makes use of the reference signals to estimate the total frequency response of the highly selective multipath channel in the presence of non-Gaussian impulse noise interfering with pilot signals. Thus, the algorithm maps trained data into a high dimensional feature space and uses the structural risk minimization (SRM) principle to carry out the regression estimation for the frequency response function of the highly selective channel. The simulations show the effectiveness of the proposed method which has good performance and high precision to track the variations of the fading channels compared to the conventional LS method and it is robust at high speed mobility.Comment: 11 page

ANTIDS: Self-Organized Ant-based Clustering Model for Intrusion Detection System

Security of computers and the networks that connect them is increasingly becoming of great significance. Computer security is defined as the protection of computing systems against threats to confidentiality, integrity, and availability. There are two types of intruders: the external intruders who are unauthorized users of the machines they attack, and internal intruders, who have permission to access the system with some restrictions. Due to the fact that it is more and more improbable to a system administrator to recognize and manually intervene to stop an attack, there is an increasing recognition that ID systems should have a lot to earn on following its basic principles on the behavior of complex natural systems, namely in what refers to self-organization, allowing for a real distributed and collective perception of this phenomena. With that aim in mind, the present work presents a self-organized ant colony based intrusion detection system (ANTIDS) to detect intrusions in a network infrastructure. The performance is compared among conventional soft computing paradigms like Decision Trees, Support Vector Machines and Linear Genetic Programming to model fast, online and efficient intrusion detection systems.Comment: 13 pages, 3 figures, Swarm Intelligence and Patterns (SIP)- special track at WSTST 2005, Muroran, JAPA