Scaled correlation analysis: a better way to compute a cross‐correlogram

When computing a cross‐correlation histogram, slower signal components can hinder the detection of faster components, which are often in the research focus. For example, precise neuronal synchronization often co‐occurs with slow co‐variation in neuronal rate responses. Here we present a method – dubbed scaled correlation analysis – that enables the isolation of the cross‐correlation histogram of fast signal components. The method computes correlations only on small temporal scales (i.e. on short segments of signals such as 25 ms), resulting in the removal of correlation components slower than those defined by the scale. Scaled correlation analysis has several advantages over traditional filtering approaches based on computations in the frequency domain. Among its other applications, as we show on data from cat visual cortex, the method can assist the studies of precise neuronal synchronization.

[1]  C. Schroeder,et al.  A spatiotemporal profile of visual system activation revealed by current source density analysis in the awake macaque. , 1998, Cerebral cortex.

[2]  E. Schuman,et al.  Frequency-Dependent Signal Transmission and Modulation by Neuromodulators , 2008, Front. Neurosci..

[3]  Ovidiu F. Jurjuţ,et al.  The oscillation score: an efficient method for estimating oscillation strength in neuronal activity. , 2008, Journal of neurophysiology.

[4]  T. Sejnowski,et al.  Regulation of spike timing in visual cortical circuits , 2008, Nature Reviews Neuroscience.

[5]  Richard P. Runyon Fundamentals of behavioral statistics , 1968 .

[6]  C. Elger,et al.  Human memory formation is accompanied by rhinal–hippocampal coupling and decoupling , 2001, Nature Neuroscience.

[7]  Danko Nikolic,et al.  Real and Modeled Spike Trains: Where Do They Meet? , 2008, ICANN.

[8]  Matthieu Gilson,et al.  STDP Allows Fast Rate-Modulated Coding with Poisson-Like Spike Trains , 2011, PLoS Comput. Biol..

[9]  W. Singer,et al.  Stimulus-dependent synchronization of neuronal responses in the visual cortex of the awake macaque monkey , 1996, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[10]  H. Keselman,et al.  Multiple Comparison Procedures , 2005 .

[11]  W. Singer,et al.  Gamma-Phase Shifting in Awake Monkey Visual Cortex , 2010, The Journal of Neuroscience.

[12]  Miguel A. Labrador,et al.  The Mobile Phone , 2010 .

[13]  Wulfram Gerstner,et al.  Intrinsic Stabilization of Output Rates by Spike-Based Hebbian Learning , 2001, Neural Computation.

[14]  A. Bruns Fourier-, Hilbert- and wavelet-based signal analysis: are they really different approaches? , 2004, Journal of Neuroscience Methods.

[15]  D. Feldman,et al.  Spike Timing-Dependent Synaptic Depression in the In Vivo Barrel Cortex of the Rat , 2007, The Journal of Neuroscience.

[16]  Christophe Mulle,et al.  Activity‐dependent synaptic plasticity of NMDA receptors , 2010, The Journal of physiology.

[17]  M. Carandini Amplification of Trial-to-Trial Response Variability by Neurons in Visual Cortex , 2004, PLoS biology.

[18]  Xiao-Hua Zhou,et al.  Statistical Methods for Meta‐Analysis , 2008 .

[19]  Bruce D. McCandliss,et al.  The Relation of Brain Oscillations to Attentional Networks , 2007, The Journal of Neuroscience.

[20]  Maria Hansson,et al.  Coherence estimation between EEG signals using multiple window time-frequency analysis compared to Gaussian kernels , 2006, 2006 14th European Signal Processing Conference.

[21]  G. Laurent,et al.  Hebbian STDP in mushroom bodies facilitates the synchronous flow of olfactory information in locusts , 2007, Nature.

[22]  R. Fisher FREQUENCY DISTRIBUTION OF THE VALUES OF THE CORRELATION COEFFIENTS IN SAMPLES FROM AN INDEFINITELY LARGE POPU;ATION , 1915 .

[23]  Paul P. Foley,et al.  Explanations for Accuracy of the General Multivariate Formulas in Correcting for Range Restriction , 1994 .

[24]  Chun-I Yeh,et al.  Temporal precision in the neural code and the timescales of natural vision , 2007, Nature.

[25]  D. Tank,et al.  Intracellular dynamics of hippocampal place cells during virtual navigation , 2009, Nature.

[26]  Patrick D Roberts,et al.  Random walks for spike-timing-dependent plasticity. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  W. Singer,et al.  Visuomotor integration is associated with zero time-lag synchronization among cortical areas , 1997, Nature.

[28]  Florentin Wörgötter,et al.  Temporal Sequence Learning, Prediction, and Control: A Review of Different Models and Their Relation to Biological Mechanisms , 2005, Neural Computation.

[29]  Steven H. Kim Statistics and Decisions: An Introduction to Foundations , 1992 .

[30]  DeLiang Wang,et al.  Image Segmentation Based on Oscillatory Correlation , 1997, Neural Computation.

[31]  Daniel D. Lee,et al.  Equilibrium properties of temporally asymmetric Hebbian plasticity. , 2000, Physical review letters.

[32]  A. Riehle,et al.  The Local Field Potential Reflects Surplus Spike Synchrony , 2010, Cerebral cortex.

[33]  Deliang Wang,et al.  Global competition and local cooperation in a network of neural oscillators , 1995 .

[34]  Catherine Tallon-Baudry,et al.  The roles of gamma-band oscillatory synchrony in human visual cognition. , 2009, Frontiers in bioscience.

[35]  Danko Nikolić,et al.  Frequencies of gamma/beta oscillations are stably tuned to stimulus properties , 2010, Neuroreport.

[36]  A. Field Meta-analysis of correlation coefficients: a Monte Carlo comparison of fixed- and random-effects methods. , 2001, Psychological methods.

[37]  J. P. Jones,et al.  The two-dimensional spatial structure of simple receptive fields in cat striate cortex. , 1987, Journal of neurophysiology.

[38]  B. Mandelbrot,et al.  RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. , 1964, Biophysical journal.

[39]  Xiao-Jing Wang,et al.  What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance. , 2003, Journal of neurophysiology.

[40]  W. Singer,et al.  Synchrony Makes Neurons Fire in Sequence, and Stimulus Properties Determine Who Is Ahead , 2011, The Journal of Neuroscience.

[41]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

[42]  Gordon Pipa,et al.  NeuroXidence: reliable and efficient analysis of an excess or deficiency of joint-spike events , 2009, Journal of Computational Neuroscience.

[43]  Y. Dan,et al.  Spike-timing-dependent synaptic modification induced by natural spike trains , 2002, Nature.

[44]  A. Thiele,et al.  Comparison of spatial integration and surround suppression characteristics in spiking activity and the local field potential in macaque V1 , 2008, The European journal of neuroscience.

[45]  Roger E. Millsap,et al.  Sampling variance in attenuated correlation coefficients: A Monte Carlo study. , 1988 .

[46]  W. Singer,et al.  Modulation of Neuronal Interactions Through Neuronal Synchronization , 2007, Science.

[47]  T. Womelsdorf,et al.  Neuronal coherence during selective attentional processing and sensory–motor integration , 2006, Journal of Physiology-Paris.

[48]  Sonja Grün,et al.  Frontiers in Computational Neuroscience , 2022 .

[49]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[50]  Kikuro Fukushima,et al.  Relating Neuronal Firing Patterns to Functional Differentiation of Cerebral Cortex , 2009, PLoS Comput. Biol..

[51]  J. O’Keefe,et al.  Phase relationship between hippocampal place units and the EEG theta rhythm , 1993, Hippocampus.

[52]  W. Singer,et al.  Distributed Fading Memory for Stimulus Properties in the Primary Visual Cortex , 2009, PLoS biology.

[53]  Per Capita,et al.  About the authors , 1995, Machine Vision and Applications.

[54]  Marcelo A. Montemurro,et al.  Spike-Phase Coding Boosts and Stabilizes Information Carried by Spatial and Temporal Spike Patterns , 2009, Neuron.

[55]  N. C. Silver,et al.  Averaging Correlation Coefficients: Should Fishers z Transformation Be Used? , 1987 .

[56]  C. Gray The Temporal Correlation Hypothesis of Visual Feature Integration Still Alive and Well , 1999, Neuron.

[57]  C. Schroeder,et al.  Neuronal Oscillations and Multisensory Interaction in Primary Auditory Cortex , 2007, Neuron.

[58]  L. Abbott,et al.  Competitive Hebbian learning through spike-timing-dependent synaptic plasticity , 2000, Nature Neuroscience.

[59]  R. Traub,et al.  Inhibition-based rhythms: experimental and mathematical observations on network dynamics. , 2000, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[60]  C. Koch,et al.  The origin of extracellular fields and currents — EEG, ECoG, LFP and spikes , 2012, Nature Reviews Neuroscience.

[61]  M. Carandini,et al.  Orientation tuning of input conductance, excitation, and inhibition in cat primary visual cortex. , 2000, Journal of neurophysiology.

[62]  Christof Koch,et al.  Temporal Precision of Spike Trains in Extrastriate Cortex of the Behaving Macaque Monkey , 1999, Neural Computation.

[63]  Danko Nikolic,et al.  Model this! Seven empirical phenomena missing in the models of cortical oscillatory dynamics , 2009, 2009 International Joint Conference on Neural Networks.

[64]  P. J. Sjöström,et al.  Rate, Timing, and Cooperativity Jointly Determine Cortical Synaptic Plasticity , 2001, Neuron.

[65]  John M. Beggs,et al.  Neuronal Avalanches in Neocortical Circuits , 2003, The Journal of Neuroscience.

[66]  W. Singer,et al.  Precisely Synchronized Oscillatory Firing Patterns Require Electroencephalographic Activation , 1999, The Journal of Neuroscience.

[67]  Edward T. Bullmore,et al.  Broadband Criticality of Human Brain Network Synchronization , 2009, PLoS Comput. Biol..

[68]  Professor Dr. Guy A. Orban Neuronal Operations in the Visual Cortex , 1983, Studies of Brain Function.

[69]  W. Sannita Stimulus-specific oscillatory responses of the brain: a time/frequency-related coding process , 2000, Clinical Neurophysiology.

[70]  G. Bi,et al.  Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type , 1998, The Journal of Neuroscience.

[71]  A. Pouget,et al.  Neural correlations, population coding and computation , 2006, Nature Reviews Neuroscience.

[72]  Y. Dan,et al.  Spike timing-dependent plasticity: from synapse to perception. , 2006, Physiological reviews.

[73]  C. Gilbert,et al.  Synaptic physiology of horizontal connections in the cat's visual cortex , 1991, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[74]  Michael J. Burke,et al.  Averaging Correlations: Expected Values and Bias in Combined Pearson rs and Fisher's z Transformations , 1998 .

[75]  C. Gray,et al.  Stimulus-Dependent Neuronal Oscillations and Local Synchronization in Striate Cortex of the Alert Cat , 1997, The Journal of Neuroscience.

[76]  M. Scanziani,et al.  Instantaneous Modulation of Gamma Oscillation Frequency by Balancing Excitation with Inhibition , 2009, Neuron.

[77]  R. Zucker Calcium- and activity-dependent synaptic plasticity , 1999, Current Opinion in Neurobiology.

[78]  Farzan Nadim,et al.  Membrane Resonance in Bursting Pacemaker Neurons of an Oscillatory Network Is Correlated with Network Frequency , 2009, The Journal of Neuroscience.

[79]  E. De Schutter,et al.  Resonant Synchronization in Heterogeneous Networks of Inhibitory Neurons , 2003, The Journal of Neuroscience.

[80]  DeLiang Wang,et al.  Locally excitatory globally inhibitory oscillator networks , 1995, IEEE Transactions on Neural Networks.

[81]  P. Dayan,et al.  Matching storage and recall: hippocampal spike timing–dependent plasticity and phase response curves , 2005, Nature Neuroscience.

[82]  Danko Nikolic,et al.  Non-parametric detection of temporal order across pairwise measurements of time delays , 2007, Journal of Computational Neuroscience.

[83]  Petar M. Djuric,et al.  Spectrum Estimation and Modeling , 2009 .

[84]  J. Movshon,et al.  Spike train encoding by regular-spiking cells of the visual cortex. , 1996, Journal of neurophysiology.

[85]  Jane W Chan,et al.  The Cat Primary Visual Cortex , 2006 .

[86]  J. W. Tukey,et al.  The Measurement of Power Spectra from the Point of View of Communications Engineering , 1958 .

[87]  R. Malenka,et al.  Synaptic Plasticity: Multiple Forms, Functions, and Mechanisms , 2008, Neuropsychopharmacology.

[88]  Nambury S. Raju,et al.  Determining the Significance of Correlations Corrected for Unreliability and Range Restriction , 2003 .

[89]  J Bullier,et al.  Structural basis of cortical synchronization. II. Effects of cortical lesions. , 1995, Journal of neurophysiology.

[90]  Sonja Grün,et al.  Analysis of Parallel Spike Trains , 2010 .

[91]  R. Shapley,et al.  Suppression of neural responses to nonoptimal stimuli correlates with tuning selectivity in macaque V1. , 2002, Journal of neurophysiology.

[92]  Yuji Ikegaya,et al.  Synfire Chains and Cortical Songs: Temporal Modules of Cortical Activity , 2004, Science.

[93]  Sonja Grün,et al.  Unitary Events in Multiple Single-Neuron Spiking Activity: I. Detection and Significance , 2002, Neural Computation.

[94]  Haim Sompolinsky,et al.  Learning Input Correlations through Nonlinear Temporally Asymmetric Hebbian Plasticity , 2003, The Journal of Neuroscience.

[95]  Stefano Panzeri,et al.  The information content of Local Field Potentials: experiments and models , 2012, 1206.0560.

[96]  Yoshiki Kuramoto,et al.  Self-entrainment of a population of coupled non-linear oscillators , 1975 .

[97]  Bijan Pesaran,et al.  Temporal structure in neuronal activity during working memory in macaque parietal cortex , 2000, Nature Neuroscience.

[98]  Herman Aguinis,et al.  Sampling variance in the correlation coefficient under indirect range restriction : Implications for validity generalization , 1997 .

[99]  Kerry M. M. Walker,et al.  Linking Cortical Spike Pattern Codes to Auditory Perception , 2008, Journal of Cognitive Neuroscience.

[100]  Shan Yu,et al.  Higher-Order Interactions Characterized in Cortical Activity , 2011, The Journal of Neuroscience.

[101]  W. Singer,et al.  Neuronal avalanches in spontaneous activity in vivo. , 2010, Journal of neurophysiology.

[102]  Marian Tsanov,et al.  Intrinsic, Light-Independent and Visual Activity-Dependent Mechanisms Cooperate in the Shaping of the Field Response in Rat Visual Cortex , 2007, The Journal of Neuroscience.

[103]  Romesh D Kumbhani,et al.  Precision, reliability, and information-theoretic analysis of visual thalamocortical neurons. , 2007, Journal of neurophysiology.

[104]  C. Gray,et al.  Visually evoked oscillations of membrane potential in cells of cat visual cortex. , 1992, Science.

[105]  Tomoki Fukai,et al.  A Stochastic Method to Predict the Consequence of Arbitrary Forms of Spike-Timing-Dependent Plasticity , 2003, Neural Computation.

[106]  Miles A Whittington,et al.  Cellular mechanisms of neuronal population oscillations in the hippocampus in vitro. , 2004, Annual review of neuroscience.

[107]  W. Singer,et al.  Synchronization of oscillatory responses in visual cortex correlates with perception in interocular rivalry. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[108]  W. Singer,et al.  The gamma cycle , 2007, Trends in Neurosciences.

[109]  H. Stanley,et al.  Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. , 2007, Physical review letters.

[110]  Vijay K. Madisetti,et al.  The Digital Signal Processing Handbook , 1997 .

[111]  Z. Kuo The genesis of the cat's responses to the rat. , 1930 .

[112]  Pieter R. Roelfsema,et al.  How Precise is Neuronal Synchronization? , 1995, Neural Computation.

[113]  Christoph von der Malsburg,et al.  The Correlation Theory of Brain Function , 1994 .

[114]  Marc W Howard,et al.  Theta and Gamma Oscillations during Encoding Predict Subsequent Recall , 2003, The Journal of Neuroscience.

[115]  M. Diamond,et al.  Population Coding of Stimulus Location in Rat Somatosensory Cortex , 2001, Neuron.

[116]  Donald B. Percival,et al.  Spectral Analysis for Physical Applications , 1993 .

[117]  Victor A. F. Lamme,et al.  Neuronal synchrony does not represent texture segregation , 1998, Nature.

[118]  Todd K. Leen,et al.  Stochastic Perturbation Methods for Spike-Timing-Dependent Plasticity , 2012, Neural Computation.

[119]  W. Singer,et al.  Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[120]  J. Bullier,et al.  Cross-correlation study of the temporal interactions between areas V1 and V2 of the macaque monkey. , 1999, Journal of neurophysiology.

[121]  Y. Dan,et al.  Spike timing-dependent plasticity: a Hebbian learning rule. , 2008, Annual review of neuroscience.

[122]  Danko Nikolic,et al.  Spatiotemporal Structure in Large Neuronal Networks Detected from Cross-Correlation , 2006, Neural Computation.

[123]  V. Bringuier,et al.  Synaptic origin and stimulus dependency of neuronal oscillatory activity in the primary visual cortex of the cat. , 1997, The Journal of physiology.

[124]  R. Wurtz,et al.  Guarding the gateway to cortex: attention in visual thalamus , 2008, Nature.

[125]  Michael J. Berry,et al.  Weak pairwise correlations imply strongly correlated network states in a neural population , 2005, Nature.

[126]  W. Singer,et al.  Phase Sensitivity of Synaptic Modifications in Oscillating Cells of Rat Visual Cortex , 2004, The Journal of Neuroscience.

[127]  D. W. Wheeler,et al.  Brightness Induction: Rate Enhancement and Neuronal Synchronization as Complementary Codes , 2006, Neuron.

[128]  Wolf Singer,et al.  Neuronal Synchrony: A Versatile Code for the Definition of Relations? , 1999, Neuron.

[129]  Wulfram Gerstner,et al.  Coding properties of spiking neurons: reverse and cross-correlations , 2001, Neural Networks.

[130]  Partha P. Mitra,et al.  Sampling Properties of the Spectrum and Coherency of Sequences of Action Potentials , 2000, Neural Computation.

[131]  O. Bertrand,et al.  Oscillatory gamma activity in humans and its role in object representation , 1999, Trends in Cognitive Sciences.

[132]  Carlos D. Brody,et al.  Correlations Without Synchrony , 1999, Neural Computation.

[133]  W. Bair Spike timing in the mammalian visual system , 1999, Current Opinion in Neurobiology.

[134]  Roger E. Millsap,et al.  Sampling variance in the correlation coefficient under range restriction: A Monte Carlo study. , 1989 .

[135]  C. Gros,et al.  Complex and Adaptive Dynamical Systems , 2008, 0807.4838.

[136]  Pascal Fries,et al.  Assessing Neuronal Coherence with Single-Unit, Multi-Unit, and Local Field Potentials , 2006, Neural Computation.

[137]  Paul H. E. Tiesinga,et al.  The Possible Role of Spike Patterns in Cortical Information Processing , 2005, Journal of Computational Neuroscience.

[138]  George M. Alliger,et al.  Correction for Restriction of Range when Both X and Y are Truncated , 1984 .

[139]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[140]  Gustavo Deco,et al.  Optimal Information Transfer in the Cortex through Synchronization , 2010, PLoS Comput. Biol..

[141]  R. Reid,et al.  Low Response Variability in Simultaneously Recorded Retinal, Thalamic, and Cortical Neurons , 2000, Neuron.

[142]  Sheila Nirenberg,et al.  Decoding neuronal spike trains: How important are correlations? , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[143]  P. König A method for the quantification of synchrony and oscillatory properties of neuronal activity , 1994, Journal of Neuroscience Methods.

[144]  Alexander S. Ecker,et al.  Generating Spike Trains with Specified Correlation Coefficients , 2009, Neural Computation.

[145]  Yanling Yin,et al.  EEG default mode network in the human brain: Spectral regional field powers , 2008, NeuroImage.

[146]  G. V. Simpson,et al.  Phase Locking of Single Neuron Activity to Theta Oscillations during Working Memory in Monkey Extrastriate Visual Cortex , 2003, Neuron.

[147]  R. Desimone,et al.  Modulation of Oscillatory Neuronal Synchronization by Selective Visual Attention , 2001, Science.

[148]  Peter E. Latham,et al.  Pairwise Maximum Entropy Models for Studying Large Biological Systems: When They Can Work and When They Can't , 2008, PLoS Comput. Biol..

[149]  Wulfram Gerstner,et al.  Phenomenological models of synaptic plasticity based on spike timing , 2008, Biological Cybernetics.

[150]  D. Guitton,et al.  Cross-correlated and oscillatory visual responses of superficial-layer and tecto-reticular neurones in cat superior colliculus , 2000, Experimental Brain Research.

[151]  Alexa B. Roggeveen,et al.  Large-scale gamma-band phase synchronization and selective attention. , 2008, Cerebral cortex.

[152]  Terry Elliott,et al.  Discrete States of Synaptic Strength in a Stochastic Model of Spike-Timing-Dependent Plasticity , 2010, Neural Computation.

[153]  G L Gerstein,et al.  Mutual temporal relationships among neuronal spike trains. Statistical techniques for display and analysis. , 1972, Biophysical journal.

[154]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[155]  A. Tamhane,et al.  Multiple Comparison Procedures , 1989 .

[156]  Maria V. Sanchez-Vives,et al.  Cellular and network mechanisms of rhythmic recurrent activity in neocortex , 2000, Nature Neuroscience.

[157]  Rainer Goebel,et al.  Neural synchrony correlates with surface segregation rules , 2000, Nature.

[158]  N. Logothetis,et al.  Phase-of-Firing Coding of Natural Visual Stimuli in Primary Visual Cortex , 2008, Current Biology.

[159]  G. Buzsáki,et al.  Neuronal Oscillations in Cortical Networks , 2004, Science.

[160]  Mark C. W. van Rossum,et al.  Stable Hebbian Learning from Spike Timing-Dependent Plasticity , 2000, The Journal of Neuroscience.

[161]  H. Markram,et al.  Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs , 1997, Science.

[162]  Sonja Grün,et al.  Can Spike Coordination Be Differentiated from Rate Covariation? , 2008, Neural Computation.

[163]  H. Swadlow,et al.  Modulation of impulse conduction along the axonal tree. , 1980, Annual review of biophysics and bioengineering.

[164]  E R Kandel,et al.  The Contribution of Activity-Dependent Synaptic Plasticity to Classical Conditioning in Aplysia , 2001, The Journal of Neuroscience.

[165]  M. Young,et al.  Correlations, feature‐binding and population coding in primary visual cortex , 2003, Neuroreport.

[166]  G. Schneider,et al.  Detection and assessment of near-zero delays in neuronal spiking activity , 2006, Journal of Neuroscience Methods.

[167]  Thomas Burwick,et al.  Temporal Coding: Assembly Formation Through Constructive Interference , 2008, Neural Computation.

[168]  Danko Nikolić,et al.  A STOCHASTIC FRAMEWORK FOR THE QUANTIFICATION OF SYNCHRONOUS OSCILLATION IN NEURONAL NETWORKS , 2008 .