Neural Networks for Complex Data

Artificial neural networks are simple and efficient machine learning tools. Defined originally in the traditional setting of simple vector data, neural network models have evolved to address more and more difficulties of complex real world problems, ranging from time evolving data to sophisticated data structures such as graphs and functions. This paper summarizes advances on those themes from the last decade, with a focus on results obtained by members of the SAMM team of Universit\'e Paris

Feed-forward neural networks and topographic mappings for exploratory data analysis

A recent novel approach to the visualisation and analysis of datasets, and one which is particularly applicable to those of a high dimension, is discussed in the context of real applications. A feed-forward neural network is utilised to effect a topographic, structure-preserving, dimension-reducing transformation of the data, with an additional facility to incorporate different degrees of associated subjective information. The properties of this transformation are illustrated on synthetic and real datasets, including the 1992 UK Research Assessment Exercise for funding in higher education. The method is compared and contrasted to established techniques for feature extraction, and related to topographic mappings, the Sammon projection and the statistical field of multidimensional scaling

Topographic mappings and feed-forward neural networks

This thesis is a study of the generation of topographic mappings - dimension reducing transformations of data that preserve some element of geometric structure - with feed-forward neural networks. As an alternative to established methods, a transformational variant of Sammon's method is proposed, where the projection is effected by a radial basis function neural network. This approach is related to the statistical field of multidimensional scaling, and from that the concept of a 'subjective metric' is defined, which permits the exploitation of additional prior knowledge concerning the data in the mapping process. This then enables the generation of more appropriate feature spaces for the purposes of enhanced visualisation or subsequent classification. A comparison with established methods for feature extraction is given for data taken from the 1992 Research Assessment Exercise for higher educational institutions in the United Kingdom. This is a difficult high-dimensional dataset, and illustrates well the benefit of the new topographic technique. A generalisation of the proposed model is considered for implementation of the classical multidimensional scaling (¸mds}) routine. This is related to Oja's principal subspace neural network, whose learning rule is shown to descend the error surface of the proposed ¸mds model. Some of the technical issues concerning the design and training of topographic neural networks are investigated. It is shown that neural network models can be less sensitive to entrapment in the sub-optimal global minima that badly affect the standard Sammon algorithm, and tend to exhibit good generalisation as a result of implicit weight decay in the training process. It is further argued that for ideal structure retention, the network transformation should be perfectly smooth for all inter-data directions in input space. Finally, there is a critique of optimisation techniques for topographic mappings, and a new training algorithm is proposed. A convergence proof is given, and the method is shown to produce lower-error mappings more rapidly than previous algorithms

A Spiking Self-Organising Map Combining STDP, Oscillations and Continuous Learning

Open Access article EPSRC EP/C010841/1, EP/J004561/

Spatial Clustering Using Hierarchical SOM

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Approximation contexts in addressing graph data structures

While the application of machine learning algorithms to practical problems has been expanded from fixed sized input data to sequences, trees or graphs input data, the composition of learning system has developed from a single model to integrated ones. Recent advances in graph based learning algorithms include: the SOMSD (Self Organizing Map for Structured Data), PMGraphSOM (Probability Measure Graph Self Organizing Map,GNN (Graph Neural Network) and GLSVM (Graph Laplacian Support Vector Machine). A main motivation of this thesis is to investigate if such algorithms, whether by themselves individually or modified, or in various combinations, would provide better performance over the more traditional artificial neural networks or kernel machine methods on some practical challenging problems. More succinctly, this thesis seeks to answer the main research question: when or under what conditions/contexts could graph based models be adjusted and tailored to be most efficacious in terms of predictive or classification performance on some challenging practical problems? There emerges a range of sub-questions including: how do we craft an effective neural learning system which can be an integration of several graph and non-graph based models? Integration of various graph based and non graph based kernel machine algorithms; enhancing the capability of the integrated model in working with challenging problems; tackling the problem of long term dependency issues which aggravate the performance of layer-wise graph based neural systems. This thesis will answer these questions. Recent research on multiple staged learning models has demonstrated the efficacy of multiple layers of alternating unsupervised and supervised learning approaches. This underlies the very successful front-end feature extraction techniques in deep neural networks. However much exploration is still possible with the investigation of the number of layers required, and the types of unsupervised or supervised learning models which should be used. Such issues have not been considered so far, when the underlying input data structure is in the form of a graph. We will explore empirically the capabilities of models of increasing complexities, the combination of the unsupervised learning algorithms, SOM, or PMGraphSOM, with or without a cascade connection with a multilayer perceptron, and with or without being followed by multiple layers of GNN. Such studies explore the effects of including or ignoring context. A parallel study involving kernel machines with or without graph inputs has also been conducted empirically