Neural networks: a pattern recognition perspective

The majority of current applications of neural networks are concerned with problems in pattern recognition. In this article we show how neural networks can be placed on a principled, statistical foundation, and we discuss some of the practical benefits which this brings.

Neural networks: a pattern recognition perspective

The majority of current applications of neural networks are concerned with problems in pattern recognition. In this article we show how neural networks can be placed on a principled, statistical foundation, and we discuss some of the practical benefits which this brings.

Category learning induces position invariance of pattern recognition across the visual field

Human object recognition is considered to be largely invariant to translation across the visual field. However, the origin of this invariance to positional changes has remained elusive, since numerous studies found that the ability to discriminate between visual patterns develops in a largely location-specific manner, with only a limited transfer to novel visual field positions. In order to reconcile these contradicting observations, we traced the acquisition of categories of unfamiliar grey-level patterns within an interleaved learning and testing paradigm that involved either the same or different retinal locations. Our results show that position invariance is an emergent property of category learning. Pattern categories acquired over several hours at a fixed location in either the peripheral or central visual field gradually become accessible at new locations without any position-specific feedback. Furthermore, categories of novel patterns presented in the left hemifield are distinctly faster learnt and better generalized to other locations than those learnt in the right hemifield. Our results suggest that during learning initially position-specific representations of categories based on spatial pattern structure become encoded in a relational, position-invariant format. Such representational shifts may provide a generic mechanism to achieve perceptual invariance in object recognition.

Peripheral vision and pattern recognition : a review

We summarize the various strands of research on peripheral vision and relate them to theories of form perception. After a historical overview, we describe quantifications of the cortical magnification hypothesis, including an extension of Schwartz's cortical mapping function. The merits of this concept are considered across a wide range of psychophysical tasks, followed by a discussion of its limitations and the need for non-spatial scaling. We also review the eccentricity dependence of other low-level functions including reaction time, temporal resolution, and spatial summation, as well as perimetric methods. A central topic is then the recognition of characters in peripheral vision, both at low and high levels of contrast, and the impact of surrounding contours known as crowding. We demonstrate how Bouma's law, specifying the critical distance for the onset of crowding, can be stated in terms of the retinocortical mapping. The recognition of more complex stimuli, like textures, faces, and scenes, reveals a substantial impact of mid-level vision and cognitive factors. We further consider eccentricity-dependent limitations of learning, both at the level of perceptual learning and pattern category learning. Generic limitations of extrafoveal vision are observed for the latter in categorization tasks involving multiple stimulus classes. Finally, models of peripheral form vision are discussed. We report that peripheral vision is limited with regard to pattern categorization by a distinctly lower representational complexity and processing speed. Taken together, the limitations of cognitive processing in peripheral vision appear to be as significant as those imposed on low-level functions and by way of crowding.

Pattern recognition analyses of brain activation elicited by happy and neutral faces in unipolar and bipolar depression

Objectives: Recently, pattern recognition approaches have been used to classify patterns of brain activity elicited by sensory or cognitive processes. In the clinical context, these approaches have been mainly applied to classify groups of individuals based on structural magnetic resonance imaging (MRI) data. Only a few studies have applied similar methods to functional MRI (fMRI) data. Methods: We used a novel analytic framework to examine the extent to which unipolar and bipolar depressed individuals differed on discrimination between patterns of neural activity for happy and neutral faces. We used data from 18 currently depressed individuals with bipolar I disorder (BD) and 18 currently depressed individuals with recurrent unipolar depression (UD), matched on depression severity, age, and illness duration, and 18 age- and gender ratio-matched healthy comparison subjects (HC). fMRI data were analyzed using a general linear model and Gaussian process classifiers. Results: The accuracy for discriminating between patterns of neural activity for happy versus neutral faces overall was lower in both patient groups relative to HC. The predictive probabilities for intense and mild happy faces were higher in HC than in BD, and for mild happy faces were higher in HC than UD (all p < 0.001). Interestingly, the predictive probability for intense happy faces was significantly higher in UD than BD (p = 0.03). Conclusions: These results indicate that patterns of whole-brain neural activity to intense happy faces were significantly less distinct from those for neutral faces in BD than in either HC or UD. These findings indicate that pattern recognition approaches can be used to identify abnormal brain activity patterns in patient populations and have promising clinical utility as techniques that can help to discriminate between patients with different psychiatric illnesses.

Peripheral vision and pattern recognition:a review

We summarize the various strands of research on peripheral vision and relate them to theories of form perception. After a historical overview, we describe quantifications of the cortical magnification hypothesis, including an extension of Schwartz's cortical mapping function. The merits of this concept are considered across a wide range of psychophysical tasks, followed by a discussion of its limitations and the need for non-spatial scaling. We also review the eccentricity dependence of other low-level functions including reaction time, temporal resolution, and spatial summation, as well as perimetric methods. A central topic is then the recognition of characters in peripheral vision, both at low and high levels of contrast, and the impact of surrounding contours known as crowding. We demonstrate how Bouma's law, specifying the critical distance for the onset of crowding, can be stated in terms of the retinocortical mapping. The recognition of more complex stimuli, like textures, faces, and scenes, reveals a substantial impact of mid-level vision and cognitive factors. We further consider eccentricity-dependent limitations of learning, both at the level of perceptual learning and pattern category learning. Generic limitations of extrafoveal vision are observed for the latter in categorization tasks involving multiple stimulus classes. Finally, models of peripheral form vision are discussed. We report that peripheral vision is limited with regard to pattern categorization by a distinctly lower representational complexity and processing speed. Taken together, the limitations of cognitive processing in peripheral vision appear to be as significant as those imposed on low-level functions and by way of crowding.

Neural networks: A principled perspective

Introductory accounts of artificial neural networks often rely for motivation on analogies with models of information processing in biological networks. One limitation of such an approach is that it offers little guidance on how to find optimal algorithms, or how to verify the correct performance of neural network systems. A central goal of this paper is to draw attention to a quite different viewpoint in which neural networks are seen as algorithms for statistical pattern recognition based on a principled, i.e. theoretically well-founded, framework. We illustrate the concept of a principled viewpoint by considering a specific issue concerned with the interpretation of the outputs of a trained network. Finally, we discuss the relevance of such an approach to the issue of the validation and verification of neural network systems.

Theoretical foundations of neural networks

Neural networks have often been motivated by superficial analogy with biological nervous systems. Recently, however, it has become widely recognised that the effective application of neural networks requires instead a deeper understanding of the theoretical foundations of these models. Insight into neural networks comes from a number of fields including statistical pattern recognition, computational learning theory, statistics, information geometry and statistical mechanics. As an illustration of the importance of understanding the theoretical basis for neural network models, we consider their application to the solution of multi-valued inverse problems. We show how a naive application of the standard least-squares approach can lead to very poor results, and how an appreciation of the underlying statistical goals of the modelling process allows the development of a more general and more powerful formalism which can tackle the problem of multi-modality.

Bayesian methods for neural networks

Bayesian techniques have been developed over many years in a range of different fields, but have only recently been applied to the problem of learning in neural networks. As well as providing a consistent framework for statistical pattern recognition, the Bayesian approach offers a number of practical advantages including a potential solution to the problem of over-fitting. This chapter aims to provide an introductory overview of the application of Bayesian methods to neural networks. It assumes the reader is familiar with standard feed-forward network models and how to train them using conventional techniques.

Bayesian methods for neural networks

Bayesian techniques have been developed over many years in a range of different fields, but have only recently been applied to the problem of learning in neural networks. As well as providing a consistent framework for statistical pattern recognition, the Bayesian approach offers a number of practical advantages including a potential solution to the problem of over-fitting. This chapter aims to provide an introductory overview of the application of Bayesian methods to neural networks. It assumes the reader is familiar with standard feed-forward network models and how to train them using conventional techniques.

Practical assessment of neural network applications

This paper reports the initial results of a joint research project carried out by Aston University and Lloyd's Register to develop a practical method of assessing neural network applications. A set of assessment guidelines for neural network applications were developed and tested on two applications. These case studies showed that it is practical to assess neural networks in a statistical pattern recognition framework. However there is need for more standardisation in neural network technology and a wider takeup of good development practice amongst the neural network community.

Neural networks: A principled perspective

Introductory accounts of artificial neural networks often rely for motivation on analogies with models of information processing in biological networks. One limitation of such an approach is that it offers little guidance on how to find optimal algorithms, or how to verify the correct performance of neural network systems. A central goal of this paper is to draw attention to a quite different viewpoint in which neural networks are seen as algorithms for statistical pattern recognition based on a principled, i.e. theoretically well-founded, framework. We illustrate the concept of a principled viewpoint by considering a specific issue concerned with the interpretation of the outputs of a trained network. Finally, we discuss the relevance of such an approach to the issue of the validation and verification of neural network systems.

Node centrality for continuous-time quantum walks

The study of complex networks has recently attracted increasing interest because of the large variety of systems that can be modeled using graphs. A fundamental operation in the analysis of complex networks is that of measuring the centrality of a vertex. In this paper, we propose to measure vertex centrality using a continuous-time quantum walk. More specifically, we relate the importance of a vertex to the influence that its initial phase has on the interference patterns that emerge during the quantum walk evolution. To this end, we make use of the quantum Jensen-Shannon divergence between two suitably defined quantum states. We investigate how the importance varies as we change the initial state of the walk and the Hamiltonian of the system. We find that, for a suitable combination of the two, the importance of a vertex is almost linearly correlated with its degree. Finally, we evaluate the proposed measure on two commonly used networks. © 2014 Springer-Verlag Berlin Heidelberg.

Transitive state alignment for the quantum jensen-shannon kernel

Kernel methods provide a convenient way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. One problem with the most widely used kernels is that they neglect the locational information within the structures, resulting in less discrimination. Correspondence-based kernels, on the other hand, are in general more discriminating, at the cost of sacrificing positive-definiteness due to their inability to guarantee transitivity of the correspondences between multiple graphs. In this paper we generalize a recent structural kernel based on the Jensen-Shannon divergence between quantum walks over the structures by introducing a novel alignment step which rather than permuting the nodes of the structures, aligns the quantum states of their walks. This results in a novel kernel that maintains localization within the structures, but still guarantees positive definiteness. Experimental evaluation validates the effectiveness of the kernel for several structural classification tasks. © 2014 Springer-Verlag Berlin Heidelberg.

Approximate axial symmetries from continuous time quantum walks

The analysis of complex networks is usually based on key properties such as small-worldness and vertex degree distribution. The presence of symmetric motifs on the other hand has been related to redundancy and thus robustness of the networks. In this paper we propose a method for detecting approximate axial symmetries in networks. For each pair of nodes, we define a continuous-time quantum walk which is evolved through time. By measuring the probability that the quantum walker to visits each node of the network in this time frame, we are able to determine whether the two vertices are symmetrical with respect to any axis of the graph. Moreover, we show that we are able to successfully detect approximate axial symmetries too. We show the efficacy of our approach by analysing both synthetic and real-world data. © 2012 Springer-Verlag Berlin Heidelberg.