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A reproducing kernel Hilbert space framework for spike train signal processing
 Neural Comp
, 2009
"... This paper 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 descr ..."
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Cited by 22 (11 self)
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This paper 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, called the crossintensity (CI) kernels, is further analyzed in detail. This particular inner product family encapsulates the statistical description from conditional intensity functions of spike trains. The problem of their estimation is also addressed. 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. Finally, as an application example, the presented RKHS framework is used to derive from simple principles a clustering algorithm for spike trains.
Quantifying Statistical Interdependence by Message Passing on Graphs  PART II: MultiDimensional Point Processes
, 2009
"... Stochastic event synchrony is a technique to quantify the similarity of pairs of signals. First, “events” are extracted from the two given time series. Next, one tries to align events from one time series with events from the other. The better the alignment, the more similar the two time series are ..."
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Cited by 20 (12 self)
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Stochastic event synchrony is a technique to quantify the similarity of pairs of signals. First, “events” are extracted from the two given time series. Next, one tries to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. In Part I, onedimensional events are considered, this paper (Paper II) concerns multidimensional events. Although the basic idea is similar, the extension to multidimensional point processes involves a significantly harder combinatorial problem, and therefore, it is nontrivial. Also in the multidimensional, the problem of jointly computing the pairwise alignment and SES parameters is cast as a statistical inference problem. This problem is solved by coordinate descent, more specifically, by alternating the following two steps: (i) one estimates the SES parameters from a given pairwise alignment; (ii) with the resulting estimates, one refines the pairwise alignment. The SES parameters are computed by maximum a posteriori (MAP) estimation (Step 1), in
A comparison of binless spike train measures
, 2009
"... Several binless spike train measures which avoid the limitations of binning have been recently been proposed in the literature. This paper presents a systematic comparison of these measures in three simulated paradigms designed to address specific situations of interest in spike train analysis where ..."
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Cited by 12 (1 self)
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Several binless spike train measures which avoid the limitations of binning have been recently been proposed in the literature. This paper presents a systematic comparison of these measures in three simulated paradigms designed to address specific situations of interest in spike train analysis where the relevant feature may be in the form of firing rate, firing rate modulations and/or synchrony. The measures are first disseminated and extended for ease of comparison. It is also discussed how the measures can be used to measure dissimilarity in spike trains’ firing rate despite their explicit formulation for synchrony.
A fast Lp spike alignment metric
"... Abstract. The metrization of the space of neural responses is an ongoing research program seeking to find natural ways to describe, in geometrical terms, the sets of possible activities in the brain. One component of this program are the spike metrics, notions of distance between two spike trains re ..."
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Cited by 9 (1 self)
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Abstract. The metrization of the space of neural responses is an ongoing research program seeking to find natural ways to describe, in geometrical terms, the sets of possible activities in the brain. One component of this program are the spike metrics, notions of distance between two spike trains recorded from a neuron. Alignment spike metrics work by identifying “equivalent ” spikes in one train and the other. We present an alignment spike metric having Lp underlying geometrical structure; the L2 version is Euclidean and is suitable for further embedding in Euclidean spaces by Multidimensional Scaling methods or related procedures. We show how to implement a fast algorithm for the computation of this metric based on bipartite graph matching theory. 1.
Inner products for representation and learning in the spike
, 2010
"... In many neurophysiological studies and braininspired computation paradigms, there is still a need for new spike train analysis and learning algorithms because current methods tend to be limited in terms of the tools they provide and are not easily extended. This chapter presents a general framework ..."
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Cited by 6 (4 self)
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In many neurophysiological studies and braininspired computation paradigms, there is still a need for new spike train analysis and learning algorithms because current methods tend to be limited in terms of the tools they provide and are not easily extended. This chapter presents a general framework to develop spike train machine learning methods by defining inner product operators for spike trains. 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. The inner products utilize functional representations of spike trains, which we motivate from two perspectives: as a biologicalmodeling problem, and as a statistical description. The biologicalmodeling approach highlights the potential biological mechanisms taking place at the neuron level and that are quantified by the inner product. On the other hand, by interpreting the representation from a statistical perspective, one relates to other work in the literature. Moreover, the statistical description characterizes which information can be detected by the spike train inner product. The applications of the given inner products for development of machine learning methods are demonstrated in two
Measuring representational distances  the spiketrain metrics approach
, 2009
"... A fundamental problem in studying population codes is how to compare population activity patterns. Population activity patterns are not just spatial, but spatiotemporal. Thus, a principled approach to the problem of the comparison of population activity patterns begins with the comparison of the te ..."
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Cited by 5 (1 self)
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A fundamental problem in studying population codes is how to compare population activity patterns. Population activity patterns are not just spatial, but spatiotemporal. Thus, a principled approach to the problem of the comparison of population activity patterns begins with the comparison of the temporal activity patterns of a single neuron, and then, to the extension of the scope of this comparison to populations spread across space. Since 1926 when Adrian and Zotterman reported that the firing rates of somatosensory receptor cells depend on stimulus strength, it has become apparent that a significant amount of the information propagating through the sensory pathways is encoded in neuronal firing rates. However, while it is easy to define the average firing rate for a cell over the lengthy presentation of a timeinvariant stimulus, it is more difficult to quantify the temporal features of spike trains. With an experimental data set extracting a timedependent rate function is model dependent since calculating it requires a choice of a binning or smoothing procedure.
Príncipe. Spectral clustering of synchronous spike trains
 In Proc. IEEE Int. Joint Conf. on Neural Networks, IJCNN2007
, 2007
"... Abstract — In this paper a clustering algorithm that learns the groups of synchronized spike trains directly from data is proposed. Clustering of spike trains based on the presence of synchronous neural activity is of high relevance in neurophysiological studies. In this context such activity is tho ..."
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Cited by 4 (4 self)
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Abstract — In this paper a clustering algorithm that learns the groups of synchronized spike trains directly from data is proposed. Clustering of spike trains based on the presence of synchronous neural activity is of high relevance in neurophysiological studies. In this context such activity is thought to be associated with functional structures in the brain. In addition, clustering has the potential to analyze large volumes of data. The algorithm couples a distance between two spike trains recently proposed in the literature with spectral clustering. Finally, the algorithm is illustrated in sets of computer generated spike trains and analyzed for the dependence on its parameters and accuracy with respect to features of interest. I.
Neural network based pattern matching and spike detection tools and services – in the carmen neuroinformatics project
 Neural. Netw
, 2008
"... CARMEN neuroinformatics project ..."
Reproducing Kernel Hilbert Spaces for Point Processes, with Applications to Neural Activity Analysis
, 2008
"... having accepted me as his student, and for his experienced guidance and advice. His incentive to creativity, breath of knowledge, and critical reaching thinking are, I believe, some of the most valuable lessons I will retain from my doctoral education. Without him, this dissertation would not have b ..."
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Cited by 3 (1 self)
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having accepted me as his student, and for his experienced guidance and advice. His incentive to creativity, breath of knowledge, and critical reaching thinking are, I believe, some of the most valuable lessons I will retain from my doctoral education. Without him, this dissertation would not have been possible. I also thank Dr. John G. Harris, for serving as my committee member, his interest in my research, and providing an essential practical perspective to much of my work. I also thank Dr. Justin C. Sanchez for his valuable time to read and comment on many of the results shown here. His expertise on neural activity analysis and often complementary perspective can be encountered throughout this dissertation. I also thank Dr. Jianbo Gao for all the advice and interest in serving in my committee. I am forever indebted to Dr. Francisco Vaz, for first creating the opportunity for me to come to CNEL and for all the help in obtaining funding from FCT. I will never forget that without Dr. Vaz’s assistance, I would have missed the wonderful opportunity to get a Ph.D. at the University of Florida. My friends and colleagues at CNEL deserve credit for many of the joys and for
Evaluating dependence in spike train metric spaces
 in IJCNN 2011 (accepted
"... Abstract — Assessing dependence between two sets of spike trains or between a set of input stimuli and the corresponding generated spike trains is crucial in many neuroscientific applications, such as in analyzing functional connectivity among neural assemblies, and in neural coding. Dependence bet ..."
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Cited by 3 (3 self)
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Abstract — Assessing dependence between two sets of spike trains or between a set of input stimuli and the corresponding generated spike trains is crucial in many neuroscientific applications, such as in analyzing functional connectivity among neural assemblies, and in neural coding. Dependence between two random variables is traditionally assessed in terms of mutual information. However, although well explored in the context of real or vector valued random variables, estimating mutual information still remains a challenging issue when the random variables exist in more exotic spaces such as the space of spike trains. In the statistical literature, on the other hand, the concept of dependence between two random variables has been presented in many other ways, e.g. using copula, or using measures of association such as Spearman’s ρ, and Kendall’s τ. Although these methods are usually applied on the real line, their simplicity, both in terms of understanding and estimating, make them worth investigating in the context of spike train dependence. In this paper, we generalize the concept of association to any abstract metric spaces. This new approach is an attractive alternative to mutual information, since it can be easily estimated from realizations without binning or clustering. It also provides an intuitive understanding of what dependence implies in the context of realizations. We show that this new methodology effectively captures dependence between sets of stimuli and spike trains. Moreover, the estimator has desirable small sample characteristic, and it often outperforms an existing similar metric based approach. I.