multivariate time series analysis bijan pesaran center for neural science new york university
DESCRIPTION
Multivariate data, Imaging data types MEG/EEG/LFP fMRI Optical imaging Need to find spatial projection to reduce dimensionality Combine spectral and multivariate toolsTRANSCRIPT
![Page 1: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/1.jpg)
Multivariate time series analysisBijan PesaranCenter for Neural ScienceNew York University
![Page 2: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/2.jpg)
Overview
Singular value decomposition
Application to space-time data
Application to space-frequency data
Periodic stacking method
![Page 3: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/3.jpg)
Multivariate data, Imaging data types
MEG/EEG/LFP fMRI Optical imaging
Need to find spatial projection to reduce dimensionality
Combine spectral and multivariate tools
![Page 4: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/4.jpg)
Singular value decomposition Eigenvalue decomposition Calculates directions/modes in data space that
contain maximum variance
Singular valuespectrum
Spatialmode
Temporalmode
![Page 5: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/5.jpg)
Application to space-time data
![Page 6: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/6.jpg)
Spatial and temporal correlations modes of spatial correlation matrix
modes of temporal correlation matrix
![Page 7: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/7.jpg)
Truncation defines subspace
Noise tailfor a pxq
matrix
fMRI data set with 1877x500data points, sampled at 5 Hz for 10 s.
2
![Page 8: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/8.jpg)
Spectrum of temporal modes
Reveals physiological features across multiple modes
![Page 9: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/9.jpg)
Application to space-frequency data
![Page 10: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/10.jpg)
A geometric interpretation Project time series into a subspace Use an orthogonal basis set Local-in-frequency projection operator
Ttktk WfPXWfX ;;~,
![Page 11: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/11.jpg)
Advantages of local-in-frequencybasis Combine information across this basis
Ensemble averaging
Choose properties of this basis Select time and frequency
Project onto multiple different subspaces centered on different frequencies
![Page 12: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/12.jpg)
Space-frequency decomposition Local-in-frequency projection
Dimensionality reduction
![Page 13: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/13.jpg)
Multivariate Coherence, Assess degree of low-dimensionality
fMRI data set
![Page 14: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/14.jpg)
Complex-valued spatial modes
Spatial segregation of physiological modes.
1st order modes
![Page 15: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/15.jpg)
fMRI example
Presence or absence of visual stimulus Digitization rate: 5 Hz Duration: 110 s Visual stimulation with red LED patterns (8
Hz).
![Page 16: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/16.jpg)
Visual response in fMRI signal
No stimulus - dashed
Visual stimulus - solid
![Page 17: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/17.jpg)
Visual response in fMRI signal
No stimulus
Visual stimulus
Spatially restricted visual response Coronal slice at the occipital pole
![Page 18: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/18.jpg)
Optical imaging example Isolated procerebral lobe of Limax Presence of voltage sensitive dye Digitization rate: 75 Hz Duration: 23 s 600 um by 200 um
![Page 19: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/19.jpg)
Optical imaging response
Limax procerebral lobe during olfactory stimulation
![Page 20: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/20.jpg)
Principal spatial modes
![Page 21: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/21.jpg)
Quantifying traveling waves Express leading spatial mode
2.5 Hz 1.25 and 2.5 Hz
x
y
![Page 22: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/22.jpg)
LFP example Rubino et al. 2007 Electrode arrays in M1 and PMd of awake
monkey Digitization rate: 1 kHz Duraction Visual instructional cue response
![Page 23: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/23.jpg)
Phase gradients in M1 PMd
M1 M1 PMd
Activity between 10 - 45 Hz
![Page 24: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/24.jpg)
Waves reflect anatomical connections
![Page 25: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/25.jpg)
Periodic stacking
If you have repeated measurements of the response to multiple stimuli, you can order your data to take advantage of the multitaper harmonic analysis methods that we have been shown.
1 2 1 2 1 2
Extraction of the average and differential dynamical response in stimulus-locked experimental data. J Neurosci Methods. 2005 Feb 15;141(2):223-9.
![Page 26: Multivariate time series analysis Bijan Pesaran Center for Neural Science New York University](https://reader035.vdocuments.us/reader035/viewer/2022062504/5a4d1b927f8b9ab0599c1d33/html5/thumbnails/26.jpg)
Odd harmonics - differences between responsesEven harmonics - average dynamics
Generalization to N stimuli: N’th harmonics are average dynamics, the rest are differences amongst the stimuli