Inferring individual perceptual experience from MEG: Robust statistics approach

1. . . R L Inferring individual perceptual experience from MEG: Robust statistics approach Andrey Zhdanov1,4, Talma Hendler1,2, Leslie Ungerleider3, Nathan Intrator4 1Functional Brain Imaging Unit, Tel Aviv Sourasky Medical Center 2Psychology Department and faculty of Medicine Tel Aviv University3Lab of Brain and Cognition, NIMH, NIH, Bethesda, USA 4School of Computer Science, Tel Aviv University Introduction Classifier Construction Inferring subjective experience from functional brain signals is one of the major goals of brain research. It has been attempted in several branches of neuroscience such as EEG-based brain-computer interfaces and fMRI data analysis. Here we introduce inference methodology that is based on machine learning techniques and apply it to infer perceived stimulus in magnetoencephalogram recordings. By assuming a timepoint-wise correspondence among the segmented signals and assigning each signal a target label (face or house) we formulate the stimulus inference problem as a classical high-dimensional machine learning problem. We then address the problem by using a regularized Fisher Linear Discriminant analysis (see above). Our investigation focuses on: 1. Selecting the optimal subset of MEG channels and timepoints 2. Selecting the optimal value of the regularization parameter λ 3. Investigating the relation between those values, in particular the structure of λ-time space. 4. Obtaining and interpreting the resulting MEG sensor weight maps. Fisher Linear Discriminant Fisher separation measure: The Fisher separation measure d between two sets of scalars {x1, x2, …, xn} and {y1, y2, …, ym} is given by where μx and μy are means and σx and σy are standard deviations of the two sets. Linear Discriminant Analysis (LDA): Given two sets of vectors X = {x1, x2, …, xn} and Y = {y1, y2, …, ym} we search for a direction p that maximizes the Fisher separation of the projections ofXandYonp:{p·x1, p·x2, …, p·xn} and {p·y1, p·y2, …, p·ym}. The solution is given by where Σ = Σx+ Σy is a sum of covariance matrices for X and Y and μx, μy – vector means of X and Y. Results A B C Curse of dimensionality and regularization: In many practical applications the dimension of the data is larger than the number of samples. In such cases the classical LDA problem is ill-posed – the covariance matrix Σ from (ii) is singular. In such cases some regularization of the problem is required. One commonly used regularization method is to replace Σ with regularized matrix Σ* where λ is a regularization parameter and I is an identity matrix. Optimal value of λ is usually estimated from the data using cross-validation. (A) Prediction accuracy of the regularized LDA classifier for each of the 10 subjects using signals from 274 sensors at a single timepoint. Error bars denote 1-std – wide margin around the average error. (B) Error rate as a function of regularization parameter for subject ZK. Solid blue line denotes the average error rate estimated by cross-validation, dotted lines mark 1-std – wide margin. The vertical line marks the minimum of the smoothed error rate (red line). Three plots below show the distribution of sensor weights corresponding to different values of the regularization parameter. (C) Error rate as a function of number of sensors used for classifier construction (for single timepoint) for subject TE. For comparison, red line depicts the error rate obtained by using all 274 sensors. Dotted lines mark 1-std – wide margin. All error estimates were obtained by 100-fold cross-validation. Experimental Setup • Mixed experiment design: • Visual categories were presented as events of either face or house. • Emotional valence of face was presented in 40 sec epochs of neutral or fear.10 sec blank separated between epochs. • The presentation duration of each category within epochs was a replay of prior perceptual experiences in a binocular rivalry paradigm for face competing with simultaneously presented house (Tong et al, 1998). Altogether the experiment lasted 15 minutes. • Data acquisition and preprocessing • 274-channel CTF MEG recording system • Signal sampled at 60Hz • Signals segmented into intervals [-0.3, 1] sec around the timepoint of stimulus switch. • We ignore distinction between neutral and negative epochs • Typically 50 - 70 events of each type per subject Conclusions Linear combination of MEG sensor signals created using regularized Fisher Discriminant Analysis was shown to be useful for inferring subjective experience. In addition, stable spatiotemporal patterns of discriminating weights that were discovered might produce an insight into the neurophysiologic mechanisms of perception. Optimization on spatio/temporal sensors provided a significant prediction results, suggesting more succinct interpretation of brain activity. We expect that further development of this technique may provide the means to detect not only externally-driven but also internally-driven events in in-vivo brain signals. Neutral epoch … … … … Negative epoch … … … … References 40 s 10 s Tong, F. et al. (1998) Binocular Rivalry and Visual Awareness in Human Extrastriate Cortex. Neuron 21, 753-759. Friedman, J.H. (1989) Regularized Discriminant Analysis. Journal of the American Statistical Association 84, 165-175 Acknowledgments: Dr. David Papo, Dr. Tom Holroyd, Mariam Eapen, Yonatan Weintraub, Israel Science Foundation, Bikura Foundation zhdanova@post.tau.ac.il