24 research outputs found

    Non-Euclidean principal component analysis by Hebbian learning

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    Principal component analysis based on Hebbian learning is originally designed for data processing inEuclidean spaces. We present in this contribution an extension of Oja's Hebbian learning approach fornon-Euclidean spaces. We show that for Banach spaces the Hebbian learning can be carried out using theunderlying semi-inner product. Prominent examples for such Banach spaces are the lp-spaces for p≠2.For kernels spaces, as applied in support vector machines or kernelized vector quantization, thisapproach can be formulated as an online learning scheme based on the differentiable kernel. Hence,principal component analysis can be explicitly carried out in the respective data spaces but nowequipped with a non-Euclidean metric. In the article we provide the theoretical framework and giveillustrative examples

    Neural computation as a tool for galaxy classification : methods and examples

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    We apply and compare various Artificial Neural Network (ANN) and other algorithms for automatic morphological classification of galaxies. The ANNs are presented here mathematically, as non-linear extensions of conventional statistical methods in Astronomy. The methods are illustrated using different subsets Artificial Neural Network (ANN) and other algorithms for automatic morphological classification of galaxies. The ANNs are presented here mathematically, as non-linear extensions of conventional statistical methods in Astronomy. The methods are illustrated using different subsets from the ESO-LV catalogue, for which both machine parameters and human classification are available. The main methods we explore are: (i) Principal Component Analysis (PCA) which tells how independent and informative the input parameters are. (ii) Encoder Neural Network which allows us to find both linear (PCA-like) and non-linear combinations of the input, illustrating an example of unsupervised ANN. (iii) Supervised ANN (using the Backpropagation or Quasi-Newton algorithms) based on a training set for which the human classification is known. Here the output for previously unclassified galaxies can be interpreted as either a continuous (analog) output (e.g. TT-type) or a Bayesian {\it a posteriori} probability for each class. Although the ESO-LV parameters are sub-optimal, the success of the ANN in reproducing the human classification is 2 TT-type units, similar to the degree of agreement between two human experts who classify the same galaxy images on plate material. We also examine the aspects of ANN configurations, reproducibility, scaling of input parameters and redshift information.Comment: uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

    Strategies for neural networks in ballistocardiography with a view towards hardware implementation

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    A thesis submitted for the degree of Doctor of Philosophy at the University of LutonThe work described in this thesis is based on the results of a clinical trial conducted by the research team at the Medical Informatics Unit of the University of Cambridge, which show that the Ballistocardiogram (BCG) has prognostic value in detecting impaired left ventricular function before it becomes clinically overt as myocardial infarction leading to sudden death. The objective of this study is to develop and demonstrate a framework for realising an on-line BCG signal classification model in a portable device that would have the potential to find pathological signs as early as possible for home health care. Two new on-line automatic BeG classification models for time domain BeG classification are proposed. Both systems are based on a two stage process: input feature extraction followed by a neural classifier. One system uses a principal component analysis neural network, and the other a discrete wavelet transform, to reduce the input dimensionality. Results of the classification, dimensionality reduction, and comparison are presented. It is indicated that the combined wavelet transform and MLP system has a more reliable performance than the combined neural networks system, in situations where the data available to determine the network parameters is limited. Moreover, the wavelet transfonn requires no prior knowledge of the statistical distribution of data samples and the computation complexity and training time are reduced. Overall, a methodology for realising an automatic BeG classification system for a portable instrument is presented. A fully paralJel neural network design for a low cost platform using field programmable gate arrays (Xilinx's XC4000 series) is explored. This addresses the potential speed requirements in the biomedical signal processing field. It also demonstrates a flexible hardware design approach so that an instrument's parameters can be updated as data expands with time. To reduce the hardware design complexity and to increase the system performance, a hybrid learning algorithm using random optimisation and the backpropagation rule is developed to achieve an efficient weight update mechanism in low weight precision learning. The simulation results show that the hybrid learning algorithm is effective in solving the network paralysis problem and the convergence is much faster than by the standard backpropagation rule. The hidden and output layer nodes have been mapped on Xilinx FPGAs with automatic placement and routing tools. The static time analysis results suggests that the proposed network implementation could generate 2.7 billion connections per second performance

    Sensor encoding using lateral inhibited, self-organized cellular neural networks

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    The paper focuses on the division of the sensor field into subsets of sensor events and proposes the linear transformation with the smallest achievable error for reproduction: the transform coding approach using the principal component analysis (PCA). For the implementation of the PCA, this paper introduces a new symmetrical, lateral inhibited neural network model, proposes an objective function for it and deduces the corresponding learning rules. The necessary conditions for the learning rate and the inhibition parameter for balancing the crosscorrelations vs. the autocorrelations are computed. The simulation reveals that an increasing inhibition can speed up the convergence process in the beginning slightly. In the remaining paper, the application of the network in picture encoding is discussed. Here, the use of non-completely connected networks for the self-organized formation of templates in cellular neural networks is shown. It turns out that the self-organizing Kohonen map is just the non-linear, first order approximation of a general self-organizing scheme. Hereby, the classical transform picture coding is changed to a parallel, local model of linear transformation by locally changing sets of self-organized eigenvector projections with overlapping input receptive fields. This approach favors an effective, cheap implementation of sensor encoding directly on the sensor chip. Keywords: Transform coding, Principal component analysis, Lateral inhibited network, Cellular neural network, Kohonen map, Self-organized eigenvector jets

    A Generalized Neural Network Approach to Mobile Robot Navigation and Obstacle Avoidance

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    In this thesis, we tackle the problem of extending neural network navigation algorithms for various types of mobile robots and 2-dimensional range sensors. We propose a general method to interpret the data from various types of 2-dimensional range sensors and a neural network algorithm to perform the navigation task. Our approach can yield a global navigation algorithm which can be applied to various types of range sensors and mobile robot platforms. Moreover, this method allows the neural networks to be trained using only one type of 2-dimensional range sensor, which contributes positively to reducing the time required for training the networks. Experimental results carried out in simulation environments demonstrate the effectiveness of our approach in mobile robot navigation for different kinds of robots and sensors. Therefore, the successful implementation of our method provides a solution to apply mobile robot navigation algorithms to various robot platforms

    GANs schön kompliziert: Applications of Generative Adversarial Networks

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    Scientific research progresses via model-building. Researchers attempt to build realistic models of real-world phenomena, ranging from bacterial growth to galactic motion, and study these models as a means of understanding these phenomena. However, making these models as realistic as possible often involves fitting them to experimentally measured data. Recent advances in experimental methods have allowed for the collection of large-scale datasets. Simultaneously, advancements in computational capacity have allowed for more complex model-building. The confluence of these two factors accounts for the rise of machine learning methods as powerful tools, both for building models and fitting these models to large scale datasets. In this thesis, we use a particular machine learning technique: generative adversarial networks (GANs). GANs are a flexible and powerful tool, capable of fitting a wide variety of models. We explore the properties of GANs that underpin this flexibility, and show how we can capitalize on them in different scientific applications, beyond the image- and text-generating applications they are well-known for. Here we present three different applications of GANs. First, we show how GANs can be used as generative models of neural spike trains, and how they are capable of capturing more features of these spike trains compared to other approaches. We also show how this could enable insight into how information about stimuli are encoded in the spike trains. Second, we demonstrate how GANs can be used as density estimators for extending simulation-based Bayesian inference to high-dimensional parameter spaces. In this form, we also show how GANs bridge Bayesian inference methods and variational inference with autoencoders and use them to fit complex climate models to data. Finally, we use GANs to infer synaptic plasticity rules for biological rate networks directly from data. We then show how GANs be used to test the robustness of the inferred rules to differences in data and network initialisation. Overall, we repurpose GANs in new ways for a variety of scientific domains, and show that they confer specific advantages over the state-of-the-art methods in each of these domains
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