A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

Pattern Recognition Approach for Road Collision Hotspots Analysis: Case Study of Northern Ireland

In order to address road safety effectively, it is essential to understand all the factors, which
attribute to the occurrence of a road collision. This is achieved through road safety
assessment measures, which are primarily based on historical crash data. Recent advances
in uncertain reasoning technology have led to the development of robust machine learning
techniques, which are suitable for investigating road traffic collision data. These techniques
include supervised learning (e.g. SVM) and unsupervised learning (e.g. Cluster Analysis).
This study extends upon previous research work, carried out in Coll et al. [3], which
proposed a non-linear aggregation framework for identifying temporal and spatial hotspots.
The results from Coll et al. [3] identified Lisburn area as the hotspot, in terms of road safety,
in Northern Ireland. This study aims to use Cluster Analysis, to investigate and highlight any
hidden patterns associated with collisions that occurred in Lisburn area, which in turn, will
provide more clarity in the causation factors so that appropriate countermeasures can be put
in place.

Clustering-Based Ensemble Method as an Alternative to Stacking

One of the most popular techniques of generating classifier ensembles is known as stacking which is based on a meta-learning approach. In this paper, we introduce an alternative method to stacking which is based on cluster analysis. Similar to stacking, instances from a validation set are initially classified by all base classifiers. The output of each classifier is subsequently considered as a new attribute of the instance. Following this, a validation set is divided into clusters according to the new attributes and a small subset of the original attributes of the instances. For each cluster, we find its centroid and calculate its class label. The collection of centroids is considered as a meta-classifier. Experimental results show that the new method outperformed all benchmark methods, namely Majority Voting, Stacking J48, Stacking LR, AdaBoost J48, and Random Forest, in 12 out of 22 data sets. The proposed method has two advantageous properties: it is very robust to relatively small training sets and it can be applied in semi-supervised learning problems. We provide a theoretical investigation regarding the proposed method. This demonstrates that for the method to be successful, the base classifiers applied in the ensemble should have greater than 50% accuracy levels.

Learning from time series:Supervised Aggregative Feature Extraction

Many modeling problems require to estimate a scalar output from one or more time series. Such problems are usually tackled by extracting a fixed number of features from the time series (like their statistical moments), with a consequent loss in information that leads to suboptimal predictive models. Moreover, feature extraction techniques usually make assumptions that are not met by real world settings (e.g. uniformly sampled time series of constant length), and fail to deliver a thorough methodology to deal with noisy data. In this paper a methodology based on functional learning is proposed to overcome the aforementioned problems; the proposed Supervised Aggregative Feature Extraction (SAFE) approach allows to derive continuous, smooth estimates of time series data (yielding aggregate local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The SAFE paradigm enjoys several properties like closed form solution, incorporation of first and second order derivative information into the regressor matrix, interpretability of the generated functional predictor and the possibility to exploit Reproducing Kernel Hilbert Spaces setting to yield nonlinear predictive models. Simulation studies are provided to highlight the strengths of the new methodology w.r.t. standard unsupervised feature selection approaches. © 2012 IEEE.

A heterosynaptic learning rule for neural networks

In this article we intoduce a novel stochastic Hebb-like learning rule for neural networks that is neurobiologically motivated. This learning rule combines features of unsupervised (Hebbian) and supervised (reinforcement) learning and is stochastic with respect to the selection of the time points when a synapse is modified. Moreover, the learning rule does not only affect the synapse between pre- and postsynaptic neuron, which is called homosynaptic plasticity, but effects also further remote synapses of the pre-and postsynaptic neuron. This more complex form of synaptic plasticity has recently come under investigations in neurobiology and is called heterosynaptic plasticity. We demonstrate that this learning rule is useful in training neural networks by learning parity functions including the exclusive-or (XOR) mapping in a multilayer feed-forward network. We find, that our stochastic learning rule works well, even in the presence of noise. Importantly, the mean leaxning time increases with the number of patterns to be learned polynomially, indicating efficient learning.

Supervised Aggregative Feature Extraction for Big Data Time Series Regression

In many applications, and especially those where batch processes are involved, a target scalar output of interest is often dependent on one or more time series of data. With the exponential growth in data logging in modern industries such time series are increasingly available for statistical modeling in soft sensing applications. In order to exploit time series data for predictive modelling, it is necessary to summarise the information they contain as a set of features to use as model regressors. Typically this is done in an unsupervised fashion using simple techniques such as computing statistical moments, principal components or wavelet decompositions, often leading to significant information loss and hence suboptimal predictive models. In this paper, a functional learning paradigm is exploited in a supervised fashion to derive continuous, smooth estimates of time series data (yielding aggregated local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The proposed Supervised Aggregative Feature Extraction (SAFE) methodology can be extended to support nonlinear predictive models by embedding the functional learning framework in a Reproducing Kernel Hilbert Spaces setting. SAFE has a number of attractive features including closed form solution and the ability to explicitly incorporate first and second order derivative information. Using simulation studies and a practical semiconductor manufacturing case study we highlight the strengths of the new methodology with respect to standard unsupervised feature extraction approaches.