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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.  ...  Finally, as an application example, the presented RKHS framework is used to derive from simple principles a clustering algorithm for spike trains.  ...  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

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  ...  This paper presents a novel real-time dynamic framework for quantifying time-series structure in spoken words using spikes.  ...  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

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.  ...  However, for the most part, such attempts still remain a mere curiosity for both computational neuroscientists and signal processing experts.  ...  DISCUSSION Spike train kernels enable signal processing and machine learning of spike trains by providing a feature space for computation.  ... 
doi:10.1109/msp.2013.2251072 fatcat:lxwgwxt7nzhazg5hroo254bdve

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.  ...  However, for the most part, such attempts still remain a mere curiosity for both computational neuroscientists and signal processing experts.  ...  DISCUSSION Spike train kernels enable signal processing and machine learning of spike trains by providing a feature space for computation.  ... 
doi:10.1002/9781118628522.ch10 fatcat:qwnlvtl45rgsnpuag6c6tanksy

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 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  
This provides a common mathematical framework for incorporating signals from different domains. The approach is applied to the problem of neural decoding and control.  ...  In this paper, we propose a tensor-product-kernel-based framework to integrate the multiscale activity and exploit the complementary information available in multiscale neural activity.  ...  ACKNOWLEDGMENT The authors would like to thank Ryan Burt for proofreading the manuscript.  ... 
doi:10.1155/2014/870160 pmid:24829569 pmcid:PMC4009155 fatcat:mpojdu3bgzc4dizd32l7vd7khq

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

Repairing lesions via kernel adaptive inverse control in a biomimetic model of sensorimotor cortex

Kan Li, Salvador Dura-Bernal, Joseph T. Francis, William W. Lytton, Jose C. Principe
2015 2015 7th International IEEE/EMBS Conference on Neural Engineering (NER)  
In this paper we propose a kernel adaptive filtering (KAF) approach to repair lesions via microstimulation in a biomimetic spiking neural network of sensorimotor cortex.  ...  For real brains, this is especially challenging and often unfeasible.  ...  Reproducing kernel Hilbert space (RKHS) for spike trains A spike train or sequence of M ordered spike times, i.e., s = {t m ∈ T : m = 1, · · · , M } in the interval T = [0, T ], can be viewed as a realization  ... 
doi:10.1109/ner.2015.7146663 dblp:conf/ner/LiDFLP15 fatcat:7dolhxe475dxhognemy52aj4vi

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

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

Iterative learning cascaded multiclass kernel based support vector machine for neural spike data classification

Amir Zjajo, Rene van Leuken
2015 2015 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB)  
In this paper, we develop an iterative learning framework based on multiclass kernel support vector machine (SVM) for adaptive classification of neural spikes.  ...  Since obtained classification function is highly parallelizable, the problem is sub-divided and parallel units are instantiated for the processing of each sub-problem via energy-scalable kernels.  ...  k=l, and (k, l)=0 for k l and map it to a reproducing kernel Hilbert space such that the dot product obtains the same value as the function .  ... 
doi:10.1109/cibcb.2015.7300278 dblp:conf/cibcb/ZjajoL15 fatcat:s5zd4wtwarciph6gr2f33xh7da

Nonparametric likelihood based estimation of linear filters for point processes [article]

Niels Richard Hansen
2014 arXiv   pre-print
We consider models for multivariate point processes where the intensity is given nonparametrically in terms of functions in a reproducing kernel Hilbert space.  ...  The likelihood function involves a time integral and is consequently not given in terms of a finite number of kernel evaluations.  ...  Acknowledgements The neuron spike data was provided by Associate Professor, Rune W. Berg, Department of Neuroscience and pharmacology, University of Copenhagen.  ... 
arXiv:1304.0503v3 fatcat:yuhg3zyqujgfbel2ukifx3wosi

Functional Identification of Spike-Processing Neural Circuits

Aurel A. Lazar, Yevgeniy B. Slutskiy
2014 Neural Computation  
We introduce a novel approach for a complete functional identification of biophysical spike-processing neural circuits.  ...  Employing the reproducing kernel Hilbert space (RKHS) of trigonometric polynomials to describe input stimuli, we quantitatively describe the relationship between underlying circuit parameters and their  ...  Acknowledgments The authors would like to thank the reviews for suggestions for improving the quality of the presentation of this paper.  ... 
doi:10.1162/neco_a_00543 pmid:24206386 fatcat:z6zfamofd5hodhtrx6ak2u3dnm

Consistent Recovery of Sensory Stimuli Encoded with MIMO Neural Circuits

Aurel A. Lazar, Eftychios A. Pnevmatikakis
2010 Computational Intelligence and Neuroscience  
The reconstructed signal satisfies a consistency condition: when passed through the same neuron, it triggers the same spike train as the original stimulus.  ...  We formulate the reconstruction as a spline interpolation problem for scalar as well as vector valued stimuli and show that the recovery has a unique solution.  ...  A. Pnevmatikakis was also supported by the Onassis Public Benefit Foundation. The authors would like to thank the reviewers for their suggestions for improving the presentation of this paper.  ... 
doi:10.1155/2010/469658 pmid:19809513 pmcid:PMC2754078 fatcat:5niast5ln5c6pkrbh4c2qdmjqi

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  ...  We apply these kernels to construct measures of divergence between two point processes, and use them for hypothesis testing, that is, to observe if two sets of spike trains originate from the same underlying  ...  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
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