Kernels Neural

Polynomial kernel, Radial basis kernel, Neural network kernel,... 

Keerthi, S. S. and Lin, C. J. (2003). Asymptotic Behaviors of Support vector Machines with Gaussian Kernel, Neural computation, 15, pp. 1667-1689. 

Comparison of the integration of this last conservation equation with the direct simulation of an uncoupled neural population with a given distribution of states (v, u) at the initial time provides a validation for the simplified version of the model. Then adding the imposed flux accounting for connectivity allows us to simulate a large population of Izhikevich neurons with a given pattern of connectivity (number of afferents per neuron and delays kernel). 

B. Scholkopf, A. J. Smola and K.-R. Muller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5) 1299-1319, (1998). 

G. Baudat and F. Anouar, Generalized discriminant analysis using a kernel approach. Neural... 

A. Ruiz and E. Lopez-de Teruel, kernel-based statistical pattern analysis, IEEE Trans, on Neural Networks, 12(l) 16-32, (2001). 

This section introduces artificial neural networks, kernel-based techniques and support vector machines to establish the basis of monitoring techniques to be discussed in the subsequent chapters. 

T Van Gestel, J Suykens, G Lanckriet, A Lambrechts, B De Moor, and J Vandewalle. Bayesian framework for least squares support vector machine classifiers, Gaussian processes, and kernel Fisher discriminant analysis. Neural Computation, 15 1115-1148, 2002. 

Leslie, G., Eskin, E., Weston, J., Noble, W.S. Mismatch string kernels for SVM protein classification. In Advances in Neural Information Processing Systems, vol. 15, Vancouver, BG, Ganada, 2002, pp. 1441-8. 

An introduction to kernel-based learning algorithms. IEEE Transactions on Neural Networks, 12 (2), 181-201. 

Kernel methods, which include support vector machines and Gaussian processes, transform the data into a higher dimensional space, where it is possible to construct one or more hyperplanes for separation of classes or regression. These methods are more mathematically rigorous than neural networks and have in recent years been widely used in QSAR modeling. ... 

Huang SY, Yeh YR, Eguchi S, 2009. Robust kernel principal component analysis. Neural Comput 21,3179-213. 

Niculescu et al. have reported the application of a related probabilistic neural net to bioactive prediction (136). These authors investigated the connection between the data preprocessing strategy and kernel choiee on the quality of the derived models. Ajay et al. also employed Bayesian methods to design a CNS-active library (97). A neural network trained using Bayesian methods was trained on CNS-aetive and CNS-inaetive data and correctly predicted up to 92% and 71% accuracy on the aetives and inactives. They used the method to generate a small library of potentially CNS-active moleeules amenable to combinatorial synthesis. 

Niculescu, S. P., Kaiser, K. L. E., and Schuurmann, G. (1998) Influence of data preprocessing and kernel selection on probabilistic neural network modeling of the acute toxicity of chemicals to the fathead minnow and Vibrio fischeri bacteria. Water Qual. Res. J. Can. 33, 153-165. 

Muller, K.-S., Mika, S., Ratsch, G., Tsuda, K., Scholkopf, B., 2001, An introduction to kernel-based learning algorithms , IEEE Transactions on Neural Networks, vol. 12, No. 2, pp. 181-201. 

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