The nature of statistical learning theory
The nature of statistical learning theory
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Pulsed neural networks
Advances in kernel methods: support vector learning
Advances in kernel methods: support vector learning
Fractal-Based Point Processes
A Spike-Train Probability Model
Neural Computation
Neural Computation
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Kernel principal components are maximum entropy projections
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Reconstruction of sensory stimuli encoded with integrate-and-fire neurons with random thresholds
EURASIP Journal on Advances in Signal Processing - Special issue on statistical signal processing in neuroscience
An information-geometric framework for statistical inferences in the neural spike train space
Journal of Computational Neuroscience
Improved similarity measures for small sets of spike trains
Neural Computation
Strictly positive-definite spike train kernels for point-process divergences
Neural Computation
| Hi-index | 0.00 |
This letter presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical description as point processes. Moreover, because many inner products can be formulated, a particular definition can be crafted to best fit an application. These ideas are illustrated by the definition of a number of spike train inner products. To further elicit the advantages of the RKHS framework, a family of these inner products, the cross-intensity (CI) kernels, is analyzed in detail. This inner product family encapsulates the statistical description from the conditional intensity functions of spike trains. The problem of their estimation is also addressed. The simplest of the spike train kernels in this family provide an interesting perspective to others' work, as will be demonstrated in terms of spike train distance measures. Finally, as an application example, the RKHS framework is used to derive a clustering algorithm for spike trains from simple principles.