Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Feature selection is an important and active issue in clustering and classification problems. By choosing an adequate feature subset, a dataset dimensionality reduction is allowed, thus contributing to decreasing the classification computational complexity, and to improving the classifier performance by avoiding redundant or irrelevant features. Although feature selection can be formally defined as an optimisation problem with only one objective, that is, the classification accuracy obtained by using the selected feature subset, in recent years, some multi-objective approaches to this problem have been proposed. These either select features that not only improve the classification accuracy, but also the generalisation capability in case of supervised classifiers, or counterbalance the bias toward lower or higher numbers of features that present some methods used to validate the clustering/classification in case of unsupervised classifiers.

The main contribution of this paper is a multi-objective approach for feature selection and its application to an unsupervised clustering procedure based on Growing Hierarchical Self-Organising Maps (GHSOMs) that includes a new method for unit labelling and efficient determination of the winning unit. In the network anomaly detection problem here considered, this multi-objective approach makes it possible not only to differentiate between normal and anomalous traffic but also among different anomalies. The efficiency of our proposals has been evaluated by using the well-known DARPA/NSL-KDD datasets that contain extracted features and labelled attacks from around 2 million connections. The selected feature sets computed in our experiments provide detection rates up to 99.8% with normal traffic and up to 99.6% with anomalous traffic, as well as accuracy values up to 99.12%.

/pdf/feature-selection-by-multi-objective-optimisation-393du3c5t4.pdf

Feature selection by multi-objective optimisation: application to network anomaly detection by hierarchical self-organising maps

In this paper, a new learning algorithm, called the Modified Recursive Least Square (MRLS), is introduced for the Hybrid Multilayered Perceptron (HMLP) network. Adopting the Recursive Least Square (RLS) algorithm as its basis, the MRLS algorithm differs from RLS in the way that the weight of the linear connections for the HMLP network is estimated. The convergence rate of the MRLS algorithm is further improved by varying the forgetting factor, optimizing the way the momentum and learning rate are assigned. To investigate its applicability, the MRLS algorithm is demonstrated on the HMLP network using six benchmark data sets obtained from the UCI repository. The classification performance of the HMLP network trained with the MRLS algorithm is compared with those of the HMLP network trained with the Modified Recursive Prediction Error (MRPE) algorithm and the MLP trained with the standard RLS algorithm as well as with other commonly adopted machine learning classifiers. The comparison results indicated that the proposed MRLS trained HMLP network provides significant improvement over RLS trained MLP network, MRPE trained HMLP network, and other machine learning classifiers in terms of accuracy, convergence rate and mean square error (MSE).

Modified Recursive Least Squares algorithm to train the Hybrid Multilayered Perceptron (HMLP) network

On the versatility of radial basis function neural networks: A case study in the field of intrusion detection

In the system identification context, neural networks are black-box models, meaning that both their parameters and structure need to be determined from data. Their identification is often done iteratively in an ad-hoc fashion focusing the first aspect. Frequently the selection of inputs, model structure, and model order are underlooked subjects by practitioners, because the number of possibilities is commonly huge, thus leaving the designer at the hands of the curse of dimensionality. Moreover, the design criteria may include multiple conflicting objectives, which gives to the model identification problem a multiobjective combinatorial optimisation character. Evolutionary multiobjective optimisation algorithms are particularly well suited to address this problem because they can evolve optimised model structures that meet pre-specified design criteria in acceptable computing time. In this article the subject is reviewed, the authors present their approach to the problem in the context of identifying neural network models for time-series prediction and for classification purposes, and two application case studies are described, one in each of these fields.

Evolutionary Multiobjective Neural Network Models Identification: Evolving Task-Optimised Models

This article deals with two key problems of data mining, the automation of the data mining process and the integration of human domain experts. We show how an evolutionary algorithm (EA) can be used to optimize radial basis function (RBF) neural networks used for classification tasks. First, input features will be chosen from a set of possible input features (feature selection). Second, the number of hidden neurons is adapted (model selection). It is known that interpretable (fuzzy-type) rule sets may be extracted from RBF networks. We show how appropriate training algorithms for RBF networks and penalty terms in the fitness function of the EA may improve the understandability of the extracted rules. The properties of our approach are set out by means of two industrial application examples (process identification and quality control).

Technical data mining with evolutionary radial basis function classifiers

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Technical data mining with evolutionary radial basis function classifiers