A comparison of Euclidean metrics and their application in statistical inferences in the spike train space (original) (raw)
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Measuring representational distances–the spike-train metrics approach
2010
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.
The identity of sensory stimuli is encoded in the spatio-temporal patterns of responses of the neural population. For stimuli to be discriminated reliably, differences in population responses must be accurately decoded by downstream networks. Several methods to compare the pattern of responses and their differences have been used by neurophysiologist to characterize the accuracy of the sensory responses studied. Among the most widely used analysis, we note methods based on Euclidian distances or on spike metric distance such as the one proposed by van Rossum. Methods based on artificial neural network and machine learning (such as self-organizing maps) have also gain popularity to recognize and/or classify specific input patterns. In this brief report, we first compare these three strategies using dataset from 3 different sensory systems. We show that the input-weighting procedure inherent to artificial neural network allows the extraction of the information most relevant to the dis...
Analysis of Parallel Spike Trains, 2010
Important questions in neuroscience, such as how neural activity represents the sensory world, can be framed in terms of the extent to which spike trains differ from one another. Since spike trains can be considered to be sequences of stereotyped events, it is natural to focus on ways to quantify differences between event sequences, known as spike-train metrics. We begin by defining several families of these metrics, including metrics based on spike times, on interspike intervals, and on vector-space embedding. We show how these metrics can be applied to single-neuron and multineuronal data and then describe algorithms that calculate these metrics efficiently. Finally, we discuss analytical procedures based on these metrics, including methods for quantifying variability among spike trains, for constructing perceptual spaces, for calculating information-theoretic quantities, and for identifying candidate features of neural codes.
Current Opinion in Neurobiology, 2005
Quantifying similarity and dissimilarity of spike trains is an important requisite for understanding neural codes. Spike metrics constitute a class of approaches to this problem. In contrast to most signal-processing methods, spike metrics operate on time series of all-or-none events, and are, thus, particularly appropriate for extracellularly recorded neural signals. The spike metric approach can be extended to multineuronal recordings, mitigating the 'curse of dimensionality' typically associated with analyses of multivariate data. Spike metrics have been usefully applied to the analysis of neural coding in a variety of systems, including vision, audition, olfaction, taste and electric sense.
PLoS ONE, 2013
We analyzed the spike discharge patterns of two types of neurons in the rodent peripheral gustatory system, Na specialists (NS) and acid generalists (AG) to lingual stimulation with NaCl, acetic acid, and mixtures of the two stimuli. Previous computational investigations found that both spike rate and spike timing contribute to taste quality coding. These studies used commonly accepted computational methods, but they do not provide a consistent statistical evaluation of spike trains. In this paper, we adopted a new computational framework that treated each spike train as an individual data point for computing summary statistics such as mean and variance in the spike train space. We found that these statistical summaries properly characterized the firing patterns (e. g. template and variability) and quantified the differences between NS and AG neurons. The same framework was also used to assess the discrimination performance of NS and AG neurons and to remove spontaneous background activity or ''noise'' from the spike train responses. The results indicated that the new metric system provided the desired decoding performance and noise-removal improved stimulus classification accuracy, especially of neurons with high spontaneous rates. In summary, this new method naturally conducts statistical analysis and neural decoding under one consistent framework, and the results demonstrated that individual peripheral-gustatory neurons generate a unique and reliable firing pattern during sensory stimulation and that this pattern can be reliably decoded.
To which extend is the "neural code" a metric
Computing Research Repository, 2008
Here is proposed a review of the different choices to structure spike trains, using deterministic metrics. Temporal constraints observed in biological or computational spike trains are first taken into account The relation with existing neural codes (rate coding, rank coding, phase coding, ..) is then discussed.
A metric space approach to the information capacity of spike trains
A novel method is presented for calculating the information channel capacity of spike trains. This method works by fitting a χ-distribution to the distribution of distances between responses to the same stimulus: the χ-distribution is the length distribution for a vector of Gaussian variables. The dimension of this vector defines an effective dimension for the noise and by rephrasing the problem in terms of distance based quantities, this allows the channel capacity to be calculated. As an example, the capacity is calculated for a data set recorded from auditory neurons in zebra finch.
Metric-space analysis of spike trains: theory, algorithms and application
Network: Computation in Neural Systems, 1997
We present the mathematical basis of a new approach to the analysis of temporal coding. The foundation of the approach is the construction of several families of novel distances (metrics) between neuronal impulse trains. In contrast to most previous approaches to the analysis of temporal coding, the present approach does not attempt to embed impulse trains in a vector space, and does not assume a Euclidean notion of distance. Rather, the proposed metrics formalize physiologically based hypotheses for those aspects of the firing pattern that might be stimulus dependent, and make essential use of the point-process nature of neural discharges. We show that these families of metrics endow the space of impulse trains with related but inequivalent topological structures. We demonstrate how these metrics can be used to determine whether a set of observed responses has a stimulus-dependent temporal structure without a vector-space embedding. We show how multidimensional scaling can be used to assess the similarity of these metrics to Euclidean distances. For two of these families of metrics (one based on spike times and one based on spike intervals), we present highly efficient computational algorithms for calculating the distances. We illustrate these ideas by application to artificial data sets and to recordings from auditory and visual cortex. †
Correcting for the Sampling Bias Problem in Spike Train Information Measures
Journal of Neurophysiology, 2007
Panzeri S, Senatore R, Montemurro MA, Petersen RS. Correcting for the sampling bias problem in spike train information measures. Information Theory enables the quantification of how much information a neuronal response carries about external stimuli and is hence a natural analytic framework for studying neural coding. The main difficulty in its practical application to spike train analysis is that estimates of neuronal information from experimental data are prone to a systematic error (called "bias"). This bias is an inevitable consequence of the limited number of stimulusresponse samples that it is possible to record in a real experiment. In this paper, we first explain the origin and the implications of the bias problem in spike train analysis. We then review and evaluate some recent general-purpose methods to correct for sampling bias: the Panzeri-Treves, Quadratic Extrapolation, Best Universal Bound, Nemenman-Shafee-Bialek procedures, and a recently proposed shuffling bias reduction procedure. Finally, we make practical recommendations for the accurate computation of information from spike trains. Our main recommendation is to estimate information using the shuffling bias reduction procedure in combination with one of the other four general purpose bias reduction procedures mentioned in the preceding text. This provides information estimates with acceptable variance and which are unbiased even when the number of trials per stimulus is as small as the number of possible discrete neuronal responses. Abbott LF, Rolls ET, Tovee MJ. Representational capacity of face coding in monkeys. Cereb Cortex 6: 498 -505, 1996. Arabzadeh E, Panzeri S, Diamond ME. Whisker vibration information carried by rat barrel cortex neurons. J Neurosci 24: 6011-6020, 2004. Arabzadeh E, Zorzin E, Diamond ME. Neuronal encoding of texture in the whisker sensory pathway. PLoS Biol 3: e17, 2005. Averbeck BB, Latham PE, Pouget A. Neural correlations, population coding and computation. Nat Rev Neurosci 7: 358 -366, 2006. Borst A, Theunissen FE. Information theory and neural coding. Nat Neurosci 2: 947-957, 1999. de Ruyter van Steveninck R, Lewen GD, Strong SP, Koberle R, Bialek W. Reproducibility and variability in neural spike trains. Science 275: 1805-1808, 1997. Endres D, Foldiak P. Bayesian bin distribution inference and mutual information. IEEE Trans Inform Th 51: 3766 -3779, 2005. Gershon ED, Wiener MC, Latham PE, Richmond BJ. Coding strategies in monkey V1 and inferior temporal cortices.