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Reproducing kernel Hilbert spaces for spike train analysis

Antonio R. C. Paiva, Il Park, Jose C. Principe
2008 Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing  
This paper introduces a generalized cross-correlation (GCC) measure for spike train analysis derived from reproducing kernel Hilbert spaces (RKHS) theory.  ...  An estimator for GCC is derived that does not depend on binning or a specific kernel and it operates directly and efficiently on spike times.  ...  Finally, the analysis is only valid for pairs of neurons. This paper discusses these issues and proposes an approach based on reproducing kernel Hilbert spaces (RKHS) to tackle them.  ... 
doi:10.1109/icassp.2008.4518834 dblp:conf/icassp/PaivaPP08 fatcat:mh5c5aei3fe45dmgikmc5qf4yq

Optimization in Reproducing Kernel Hilbert Spaces of Spike Trains [chapter]

António R.C. Paiva, Il Park, José C. Príncipe
2010 Computational Neuroscience  
This paper presents a framework based on reproducing kernel Hilbert spaces (RKHS) for optimization with spike trains.  ...  To establish the RKHS for optimization we start by introducing kernels for spike trains.  ...  Conclusion A reproducing kernel Hilbert space (RKHS) framework for optimization with spike trains is introduced.  ... 
doi:10.1007/978-0-387-88630-5_1 fatcat:4np3flf4lzgghlktdrryfvsrqy

A Reproducing Kernel Hilbert Space Framework for Spike Train Signal Processing

António R. C. Paiva, Il Park, José C. Príncipe
2009 Neural Computation  
This paper presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains.  ...  The simplest of the spike train kernels in this family provides an interesting perspective to other works presented in the literature, as will be illustrated in terms of spike train distance measures.  ...  A Proofs In this section the proofs for properties 2 and 5 given in section 4.1 are presented.  ... 
doi:10.1162/neco.2008.09-07-614 pmid:19431265 fatcat:kwrghzkc7rcjlmeakckimgrqjq

Instantaneous Cross-Correlation Analysis of Neural Ensembles with High Temporal Resolution [chapter]

António R.C. Paiva, Il Park, José C. Príncipe, Justin C. Sanchez
2013 Introduction to Neural Engineering for Motor Rehabilitation  
Over the last decade several positive definite kernels have been proposed to treat spike trains as objects in Hilbert space.  ...  This tutorial illustrates why kernel methods can, and have already started to, change the way spike trains are analyzed and processed.  ...  The theory of reproducing kernel Hilbert spaces provides a foundation for the existence of a (possibly) infinite dimensional Hilbert space-a feature space-associated with any positive definite function  ... 
doi:10.1002/9781118628522.ch10 fatcat:qwnlvtl45rgsnpuag6c6tanksy

Kernel Methods on Spike Train Space for Neuroscience: A Tutorial

Il Memming Park, Sohan Seth, Antonio R.C. Paiva, Lin Li, Jose C. Principe
2013 IEEE Signal Processing Magazine  
Over the last decade several positive definite kernels have been proposed to treat spike trains as objects in Hilbert space.  ...  This tutorial illustrates why kernel methods can, and have already started to, change the way spike trains are analyzed and processed.  ...  The theory of reproducing kernel Hilbert spaces provides a foundation for the existence of a (possibly) infinite dimensional Hilbert space-a feature space-associated with any positive definite function  ... 
doi:10.1109/msp.2013.2251072 fatcat:lxwgwxt7nzhazg5hroo254bdve

Biologically-Inspired Spike-Based Automatic Speech Recognition of Isolated Digits Over a Reproducing Kernel Hilbert Space

Kan Li, José C. Príncipe
2018 Frontiers in Neuroscience  
These spike trains are mapped into a function space of infinite dimension, i.e., a Reproducing Kernel Hilbert Space (RKHS) using point-process kernels, where a state-space model learns the dynamics of  ...  For spike-train front-end, spike-KAARMA also outperformed state-of-the-art SNN solutions.  ...  Harris for his helpful discussions during the research. We are also thankful to the editor and reviewers for their valuable comments and suggestions that improved the manuscript.  ... 
doi:10.3389/fnins.2018.00194 pmid:29666568 pmcid:PMC5891646 fatcat:weji6gclmzbrjl5frmbipfmjwy

Inner Products for Representation and Learning in the Spike Train Domain [chapter]

António R.C. Paiva, Il Park, José C. Príncipe
2010 Statistical Signal Processing for Neuroscience and Neurotechnology  
They build on the mathematical theory of reproducing kernel Hilbert spaces (RKHS) and kernel methods, allowing a multitude of analysis and learning algorithms to be easily developed.  ...  This chapter presents a general framework to develop spike train machine learning methods by defining inner product operators for spike trains.  ...  There exists an Hilbert space for which the defined spike trains inner products is a reproducing kernel.  ... 
doi:10.1016/b978-0-12-375027-3.00008-9 fatcat:uswwzvl5wfhxzdyf7g3jqiyeiy

Strictly Positive-Definite Spike Train Kernels for Point-Process Divergences

Il Memming Park, Sohan Seth, Murali Rao, José C. Príncipe
2012 Neural Computation  
We explore strictly positive definite kernels on the space of spike trains to offer both a structural representation of this space and a platform for developing statistical measures that explore features  ...  and real data through kernel principal component analysis and hypothesis testing.  ...  Acknowledgements We are grateful to the referees for their very helpful comments, which improved the paper significantly.  ... 
doi:10.1162/neco_a_00309 pmid:22509968 fatcat:h2vr2fqqgjbkbltheykkahkep4

A Tensor-Product-Kernel Framework for Multiscale Neural Activity Decoding and Control

Lin Li, Austin J. Brockmeier, John S. Choi, Joseph T. Francis, Justin C. Sanchez, José C. Príncipe
2014 Computational Intelligence and Neuroscience  
The availability of multiscale neural recordings including spike trains and local field potentials (LFPs) brings potential opportunities to enhance computational modeling by enriching the characterization  ...  For neural decoding, the framework is able to identify the nonlinear functional relationship between the multiscale neural responses and the stimuli using general purpose kernel adaptive filtering.  ...  ACKNOWLEDGMENT The authors would like to thank Ryan Burt for proofreading the manuscript.  ... 
doi:10.1155/2014/870160 pmid:24829569 pmcid:PMC4009155 fatcat:mpojdu3bgzc4dizd32l7vd7khq

Quantification of inter-trial non-stationarity in spike trains from periodically stimulated neural cultures

Il Park, Jose C. Principe
2010 2010 IEEE International Conference on Acoustics, Speech and Signal Processing  
A novel method for estimating point process divergence and its application for non-stationarity detection in spike trains is proposed.  ...  In neuroscience, non-stationarity detection of spike trains is useful for ensuring stability of experimental condition, and detecting plasticity.  ...  Hein and Bousquet proposed a family of such metric for probability measures which can be embedded isometrically in a Hilbert space, hence suggesting a family of reproducing kernel Hilbert space (RKHS)  ... 
doi:10.1109/icassp.2010.5494920 dblp:conf/icassp/ParkP10 fatcat:6odix2noxvgt3pc5dgngimx4uq

Restoring Behavior via Inverse Neurocontroller in a Lesioned Cortical Spiking Model Driving a Virtual Arm

Salvador Dura-Bernal, Kan Li, Samuel A. Neymotin, Joseph T. Francis, Jose C. Principe, William W. Lytton
2016 Frontiers in Neuroscience  
Here we employed a spiking network model of sensorimotor cortex trained to drive a realistic virtual musculoskeletal arm to reach a target.  ...  The inverse model was constructed using a kernel adaptive filtering method, and was used to predict the neural stimulation pattern required to recover the pre-lesion neural activity.  ...  We would like to thank Xianlian (Alex) Zhou and Andrzej Przekwas from CFD Research Corporation for providing the virtual arm, and Cliff C Kerr for code to simulate neurostimulation.  ... 
doi:10.3389/fnins.2016.00028 pmid:26903796 pmcid:PMC4746359 fatcat:lqhajjrd5bbzhbdl25owfcep7y

Population Encoding With Hodgkin–Huxley Neurons

Aurel A. Lazar
2010 IEEE Transactions on Information Theory  
For stimuli modeled as elements of Sobolev spaces the reconstruction algorithm minimizes a regularized quadratic optimality criterion.  ...  In the absence of a stimulus, the Hodgkin-Huxley neurons are assumed to be tonically spiking.  ...  The author would like to also thank the reviewers for their constructive comments.  ... 
doi:10.1109/tit.2009.2037040 pmid:24194625 pmcid:PMC3816091 fatcat:aarzutaq6vctbbxasxejqzc32e

RKHS Bayes Discriminant: A Subspace Constrained Nonlinear Feature Projection for Signal Detection

U. Ozertem, D. Erdogmus
2009 IEEE Transactions on Neural Networks  
The nonlinear projection filter is designed in a reproducing kernel Hilbert space leading to an analytical solution both for the filter and the optimal threshold.  ...  Results are compared with linear and kernel discriminant analysis, as well as classification algorithms such as support vector machine, AdaBoost and LogitBoost.  ...  Sanchez for providing neural spike data set.  ... 
doi:10.1109/tnn.2009.2021473 pmid:19497813 fatcat:ox335vzyxrb65pxzt3jonfngdy

Kernel Analysis for Estimating the Connectivity of a Network with Event Sequences

Taro Tezuka, Christophe Claramunt
2017 Journal of Artificial Intelligence and Soft Computing Research  
Specifically, a normalized positive definite kernel defined on spike trains was used.  ...  Synthetic data was generated using CERM (Coupled Escape-Rate Model), a model that generates various spike trains.  ...  Paiva et al. proposed a general framework that uses a reproducing kernel Hilbert space for analyzing spike trains [25, 26] .  ... 
doi:10.1515/jaiscr-2017-0002 fatcat:wvrnj4hb6ng3vf322qjlflzmua

A Reproducing Kernel Hilbert Space Framework for Information-Theoretic Learning

Jian-Wu Xu, A.R.C. Paiva, Il Park, J.C. Principe
2008 IEEE Transactions on Signal Processing  
This paper provides a functional analysis perspective of information-theoretic learning (ITL) by defining bottom-up a reproducing kernel Hilbert space (RKHS) uniquely determined by the symmetric nonnegative  ...  Index Terms-Cross-information potential, information-theoretic learning (ITL), kernel function, probability density function, reproducing kernel Hilbert space (RKHS).  ...  Then is said to be a reproducing kernel Hilbert space with reproducing kernel .  ... 
doi:10.1109/tsp.2008.2005085 fatcat:tn3bj75wdrdaxkupvbc4ug3nyi
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