New Machine Learning Methods for Neuroimaging

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1 New Machine Learning Methods for Neuroimaging Gatsby Computational Neuroscience Unit University College London, UK Dept of Computer Science University of Helsinki, Finland

2 Outline Resting-state networks in EEG/MEG Variants of independent component analysis (ICA) Testing ICA: Are the components reliable? Intersubject consistency provides an plausible null hypothesis Causal analysis / effective connectivity Directionality of connectivities estimated using non-gaussianity Analysis of differences between many connectivity matrices Dynamic connectivity, intersubject connectivity differences Decoding in EEG/MEG A pipeline using ICA, wide-band rhythmic activity

3 Outline Resting-state networks in EEG/MEG Testing ICA: Are the components reliable? Causal analysis / effective connectivity Analysis of differences between many connectivity matrices Decoding in EEG/MEG

4 The brain at rest EEG/MEG resting state analysis by ICA The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA The subject s brain is being measured while the subject has no task the subject receives no stimulation Measurements by functional magnetic resonance imaging (fmri) electroencephalography (EEG) magnetoencephalography (MEG) Why is this data so interesting? Not dependent on subjective choices in experimental design (e.g. stimulation protocol, task) Not much analysis has been done so far Completely new viewpoint: rich internal dynamics

The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA Is anything happening in the brain at rest?

5 The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA Is anything happening in the brain at rest? Some brain areas are actually more active at rest Default-mode network(s) in PET and fmri (Raichle 2001) Brain activity is intrinsic instead of just responses to stimulation How to analyse resting state in more detail? (Raichle, 2010 based on Shulman et al 1997)

6 The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA Independent component analysis (ICA) Supervised methods cannot be used: no teaching signal Assume a linear mixing model x i = j a ij s j (1) x i are observed variables, s j independent latent variables. ICA finds both a ij and s j by maximising sparsity of the s j. Sparsity = probability density has heavy tails and peak at zero: gaussian sparse

The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA ICA finds resting-state networks in fmri a) Medial and b)

7 The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA ICA finds resting-state networks in fmri a) Medial and b) lateral visual areas, c) Auditory system, d) Sensory-motor system, e) Default-mode network, f) Executive control, g) Dorsal visual stream (Beckmann et al, 2005) Very similar results obtained if subject watching a movie

8 How about EEG and MEG? The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA EEG and MEG are measurements of electrical activity in the brain Very high temporal accuracy (millisecond scale) Not so high spatial accuracy (less than in fmri) Typically characterized by oscillations, e.g. at around 10 Hz Up to 306 time series (signals), time points. Information very different from fmri

9 The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA Different sparsities of EEG/MEG data ICA finds components by maximizing sparsity, but sparsity of what? Depends on preprocessing and representation Assume we do wavelet or short-time Fourier transform We have different sparsities:

10 The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA Different sparsities of EEG/MEG data ICA finds components by maximizing sparsity, but sparsity of what? Depends on preprocessing and representation Assume we do wavelet or short-time Fourier transform We have different sparsities: Sparsity in time: Temporally modulated

11 The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA Different sparsities of EEG/MEG data ICA finds components by maximizing sparsity, but sparsity of what? Depends on preprocessing and representation Assume we do wavelet or short-time Fourier transform We have different sparsities: Sparsity in time: Temporally modulated Sparsity in frequency: narrow-band signals

12 The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA Different sparsities of EEG/MEG data ICA finds components by maximizing sparsity, but sparsity of what? Depends on preprocessing and representation Assume we do wavelet or short-time Fourier transform We have different sparsities: Sparsity in time: Temporally modulated Sparsity in frequency: narrow-band signals 2 1 Sparsity in space: Localised on cortex

13 Different sparsities of EEG/MEG data The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA ICA finds components by maximizing sparsity, but sparsity of what? Depends on preprocessing and representation Assume we do wavelet or short-time Fourier transform We have different sparsities: Sparsity in time: Temporally modulated Sparsity in frequency: narrow-band signals 2 1 Sparsity in space: Localised on cortex Plain ICA, Fourier-ICA, Spatial-ICA

14 EEG/MEG resting state analysis by ICA The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA Fourier-ICA: joint sparsity in time and frequency (Hyva rinen, Ramkumar, Parkkonen, Hari, NeuroImage, 2010) Aapo Hyva rinen

15 The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA Spatial sparsity (spatial ICA) Images observed at different time points are linear sums of source images = a11 +a a1n = a 21 = a n1 Maximizes spatial sparsity alone typical in fmri No assumption on temporal independence (Ramkumar et al, Human Brain Mapping, 2012)

16 Outline EEG/MEG resting state analysis by ICA The brain at rest Independent Component Analysis of fmri at rest Issues in ICA of EEG/MEG Different sparsities Fourier-ICA Spatial ICA Resting-state networks in EEG/MEG Testing ICA: Are the components reliable? Causal analysis / effective connectivity Analysis of differences between many connectivity matrices Decoding in EEG/MEG

17 Motivation Results Testing ICs: motivation ICA algorithms give a fixed number of components and do not tell which ones are reliable (statistically significant) How do we know that an estimated component is not just a random effect? Algorithmic artifacts also possible (local minima)

18 Motivation Results Testing ICs: motivation ICA algorithms give a fixed number of components and do not tell which ones are reliable (statistically significant) How do we know that an estimated component is not just a random effect? Algorithmic artifacts also possible (local minima) We develop a statistical test based on inter-subject consistency: Do ICA separately on several subjects A component is significant if it appears in two or more subjects in a sufficiently similar form We formulate a rigorous null hypothesis to quantify this idea (NeuroImage, 2011)

19 Motivation Results Testing ICs: results One IC Another IC b) Minimum norm estimate b) Minimum norm estimate 7 d) Modulation by stimulation 7 d) Modulation by stimulation 6 6 z score (neg) 5 4 z score (neg) beep spch v/hf v/bd tact 2 beep spch v/hf v/bd tact c) Fourier spectrum c) Fourier spectrum #6 # Frequency (Hz) Frequency (Hz)

20 Motivation Results Outline Resting-state networks in EEG/MEG Testing ICA: Are the components reliable? Causal analysis / effective connectivity Analysis of differences between many connectivity matrices Decoding in EEG/MEG

21 Introduction Structural equation models Simple measures of causal direction Results Causal analysis: Motivation Effective (directed) connectivity: Which area influences/drives which? Two fundamental approaches If time-resolution of measurements fast enough, we can use autoregressive modelling (Granger causality) Otherwise, we need structural equation models With EEG/MEG, we should first localize sources, e.g. by ICA Sources are often uncorrelated More meaningful to model dependencies of envelopes (amplitudes, variances)

22 Introduction Structural equation models Simple measures of causal direction Results Structural equation models How does an (externally imposed) change in one variable affect the others? x i = j i b ij x j + e i Difficult to estimate, not simple regression Classic methods fail in general

23 Introduction Structural equation models Simple measures of causal direction Results Structural equation models How does an (externally imposed) change in one variable affect the others? x4 x i = j i b ij x j + e i -0.3 x Difficult to estimate, not simple regression Classic methods fail in general Can be estimated if (Shimizu et al., JMLR, 2005) 1. the e i (t) are mutually independent 2. the e i (t) are non-gaussian, e.g. sparse 3. the b ij are acyclic: There is an ordering of x i where effects are all forward x x x7 x5 1 x6 0.37

24 Introduction Structural equation models Simple measures of causal direction Results Simple measures of causal direction The very simplest case: choose between regression models y = ρx + d (2) where d is independent of x, and symmetrically x = ρy + e (3) If data is Gaussian we can estimate ρ = E{xy} BUT: Both models have same likelihood! For non-gaussian data, approximate log-likelihood ratio as R = ρe{x g(y) g(x)y} (4) where g is a nonlinearity similar to those used in ICA Choose direction based on sign of R! (Hyvärinen and S.M. Smith, JMLR, 2013)

25 Introduction Structural equation models Simple measures of causal direction Results Sample of results on MEG (but for a different method) Black: positive influence, red: negative influence. Green: manually drawn grouping. Here, using GARCH model (Zhang and Hyvärinen, UAI2010)

26 Introduction Structural equation models Simple measures of causal direction Results Outline Resting-state networks in EEG/MEG Testing ICA: Are the components reliable? Causal analysis / effective connectivity Analysis of differences between many connectivity matrices Decoding in EEG/MEG

27 Motivation PCA of connectivity matrices Problem with PCA approach New decomposition after PCA Results on fcmri : Motivation Often the data consists of a number of connectivity matrices from different time windows from different subjects Differences or changes in connectivity can be of great interest dynamic connectivity intersubject differences Contrast with spatial ICA for fmri which analyses static connectivity. commonalities over subjects

28 Motivation PCA of connectivity matrices Problem with PCA approach New decomposition after PCA Results on fcmri Basic approach by PCA of connectivity matrices Compute connectivity matrix C t in many time windows t = 1,..., T e.g. sliding windows to analyse dynamice connectivity or, from different subjects Vectorize each C t, subtract means and do PCA on those vectors. Each obtained principal component is converted back to a matrix.

29 Motivation PCA of connectivity matrices Problem with PCA approach New decomposition after PCA Results on fcmri PCA on connectivity matrices (Leonardi et al, 2013)

30 Motivation PCA of connectivity matrices Problem with PCA approach New decomposition after PCA Results on fcmri Our approach: Motivation A principal component K of connectivity patterns are big and complex. How to visualize and analyse them further? Solution: Use linear components in the original data space. Conventional approach: Take a matrix principal component K and use rank-one approximation K = ww T. (Possibly repeated a couple of times.) However, Cannot really analyse connectivities between brain areas. Mainly connectivity inside one area (cliques). In real data, eigenstructure of K is quite unconventional:

31 Motivation PCA of connectivity matrices Problem with PCA approach New decomposition after PCA Results on fcmri New decomposition of PCA matrices Assume we are given a principal component (PC) of connectivity matrices, K Analyse matrix PC by two orthogonal linear components by optimizing: max w = v =1,w T v=0 w T Kv (5) where each vector w and v is a spatial pattern. Equivalent to approximation of K as wv T + vw T. Orthogonality of w and v essential, otherwise w = v and we get classic rank-one approximation by eigen-value decomposition.

32 Motivation PCA of connectivity matrices Problem with PCA approach New decomposition after PCA Results on fcmri Theorem on approximating matrix principal component Consider optimization problem on last slide max w T Kv (6) w = v =1,w T v=0 where K obtained from PCA of connectivity matrices. Theorem 1 The solution is w = 1 2 (e max + e min ), v = 1 2 (e max e min ) (7) where e max and e min are the eigenvectors corresponding to the smallest and largest eigenvalues of K. Important point: eigenvectors themselves do not give w, v.

33 Motivation PCA of connectivity matrices Problem with PCA approach New decomposition after PCA Results on fcmri Experiments on fmri: Methods Publicly available data set 1000 Functional connectomes 103 subjects used 177 brain regions One connectivity matrix for each subject Matlab code available; paper in Neural Computation, 2016.

34 Motivation PCA of connectivity matrices Problem with PCA approach New decomposition after PCA Results on fcmri Experiments on fmri: Results, PC #1 w v w: Task-positive network (?), v: Default-mode network

35 Motivation PCA of connectivity matrices Problem with PCA approach New decomposition after PCA Results on fcmri Experiments on fmri: Results, PC #2 w v w: Default-mode network, v: Frontal executive network

36 Motivation PCA of connectivity matrices Problem with PCA approach New decomposition after PCA Results on fcmri Outline Resting-state networks in EEG/MEG Testing ICA: Are the components reliable? Causal analysis / effective connectivity Analysis of differences between many connectivity matrices Decoding in EEG/MEG

37 Decoding EEG/MEG Our Spectral Decoding Toolbox Example results Decoding EEG/MEG based on envelopes Consider data with a stimulation or a task but not phase-locked ERPs e.g. watching a movie, practising mindfulness Decoding popular in fmri, and evoked EEG/MEG but less widely used for rhythmic activity in EEG/MEG few methods available For one-sec time windows, how to decode stimulation/task? We develop a method for decoding rhythmic activity (Kauppi et al, NIMG, 2013) with MATLAB package

38 Decoding EEG/MEG Our Spectral Decoding Toolbox Example results Principles of our Spectral Decoding Toolbox (SpeDeBox) Data can be wide-band (theta + alpha + beta, etc.) Algorithm finds optimal frequency band(s) Decoding based on envelopes / energies We learn two kinds of weights: Spatial pattern (weights) Spectral profile (weights) We use components given by ICA Avoids problems with extremely high-dim cortical projections Yet works on brain sources instead of sensors

39 Decoding EEG/MEG Our Spectral Decoding Toolbox Example results Example of SpeDeBox in action Data with four stimulation modalities: visual, auditory, tactile, rest

40 Decoding EEG/MEG Our Spectral Decoding Toolbox Example results Conclusion Exploratory analysis by ICA can give information about internal dynamics during rest activity not directly related to stimulation responses when stimulation too complex

41 Decoding EEG/MEG Our Spectral Decoding Toolbox Example results Conclusion Exploratory analysis by ICA can give information about internal dynamics during rest activity not directly related to stimulation responses when stimulation too complex We present various methods Finding EEG/MEG sources by different variants of ICA Analyzing their effective connectivity

42 Decoding EEG/MEG Our Spectral Decoding Toolbox Example results Conclusion Exploratory analysis by ICA can give information about internal dynamics during rest activity not directly related to stimulation responses when stimulation too complex We present various methods Finding EEG/MEG sources by different variants of ICA Analyzing their effective connectivity Significance (by consistency) should also be analyzed

43 Decoding EEG/MEG Our Spectral Decoding Toolbox Example results Conclusion Exploratory analysis by ICA can give information about internal dynamics during rest activity not directly related to stimulation responses when stimulation too complex We present various methods Finding EEG/MEG sources by different variants of ICA Analyzing their effective connectivity Significance (by consistency) should also be analyzed Dynamic connectivity from many connectivity matrices Further analysis going beyond PCA

44 Decoding EEG/MEG Our Spectral Decoding Toolbox Example results Conclusion Exploratory analysis by ICA can give information about internal dynamics during rest activity not directly related to stimulation responses when stimulation too complex We present various methods Finding EEG/MEG sources by different variants of ICA Analyzing their effective connectivity Significance (by consistency) should also be analyzed Dynamic connectivity from many connectivity matrices Further analysis going beyond PCA Alternative approach: Decoding of rhytmic EEG/MEG

Independent Component Analysis

A Short Introduction to Independent Component Analysis with Some Recent Advances Aapo Hyvärinen Dept of Computer Science Dept of Mathematics and Statistics University of Helsinki Problem of blind source