Lohmann, G.

Volz, K.

von Cramon, D.

English

MPG.PuRe

Single trial analysis using non-negative matrix factorizationsNMF decompositionsConsider an experimental setup in which one or more stimuli are presented re-peatedly and in a possibly randomized order. We assume that m trials of the same event type are given. The m trial vectors of length n form the columns of the input matrix V. Non-negative matrix factorization (NMF) produces a decompo-sition of the formIn our context, typical values are m=40 (number of trials) n=12 (number of timesteps per trial), and r=3 (number of basis functions).MAXPLANCKINSTITUTEIntroductionDiscussionGabriele Lohmann, Kirsten Volz  D. & Yves von Cramon  Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germanyemail:lohmann@cbs.mpg.de• We found that NMF may help to uncover hidden structure in single trial data. In the fMRI data reported here, three clusters of trials were found.• We found that the city recognition value correlated with cluster membership so that we can assume that the decomposition revealed meaningful information.• We also found that a low recognition value correlated with a deactivation in aFMC. A possible interpretation might be that a deactivation of the Recognition Heuristic leads to a suppression of the default mode network.REFERENCES[1]Volz, et al. (in press), Why you think Milan is larger than Modena: The neural correlates of the recognition heuristic, J Cogn Neurosci.[2] Lee & Seung (1999), Learning the parts of objects by non-negative matrix factorization, Nature, 401:788-791.The reaction to a stimulus may differ across trials of the same stimulus type.For instance, the stimuli may consist of sentences that evoke different reactions depending on their content. If those reactions are not predictable then the differ-ences between trials cannot be described by the experimental design. Rather, they can only be inferred by differences in the BOLD responses that they evoke.Idea: 1. Use a new matrix decomposition method (NMF) to uncover such hidden  struc ture in the data.2. Use the NMF decomposition to investigate the interaction between trials in   across different brain regions.=1 mn1 111rr1 mnWVHdata vectorsweights(encodings)basisfunctionsThe AlgorithmThe algorithm for obtaining an NMF decomposition ([2]):Application to single trial data• In this experiments, participants were presented with two city names and had to indicate which city they thought was larger.• If a subject recognizes the city name he/she is more likely to think that it is large (``recognition heuristic'').• Since we cannot know which heuristic or strategy a subject employs in each trial there may be hidden information in the single trial data.Activation map of the fMRI experiment by Volz et al.[1]. The single trial data were obtained from voxels in the anterior frontomedian cortex (aFMC) and the precuneus (PCU).-2-1.5-1-0.5 0 0.5 1 1.5 2 0  2  4  6  8  10seconds-2-1.5-1-0.5 0 0.5 1 1.5 2 0  2  4  6  8  10seconds-2-1.5-1-0.5 0 0.5 1 1.5 2 0  2  4  6  8  10secondsSingle trial data in aFMC of one subject, before and after application of NMF.Comparisons of trials between brain regions aFMC (red) and PCU (blue) averaged across 12 subjects.The thick lines show averages, the thin lines the corresponding standard errors based on the inter-subject variance.-0.75-0.5-0.25 0 0.25 0.5 0.75 0  3  6  9  12basis 0-0.75-0.5-0.25 0 0.25 0.5 0.75 0  3  6  9  12basis 1-0.75-0.5-0.25 0 0.25 0.5 0.75 0  3  6  9  12basis 2Synthetic Data-0.3 0 0.3 0.6 0  3  6  9  12data 60 70 80 90 100 110 120 130 140 150 0  3  6  9  12W 0.3 0.4 0.5 0.6 0.7 0.8 0  5  10  15  20  25  30H-1.2-0.9-0.6-0.3 0 0.3 0.6 0.9 1.2 1.5 0  3  6  9  12data 60 70 80 90 100 110 120 130 140 0  3  6  9  12W 0.3 0.4 0.5 0.6 0.7 0.8 0  5  10  15  20  25  30H-0.9-0.6-0.3 0 0.3 0.6 0.9 0  3  6  9  12-0.6-0.4-0.2 0 0.2 0.4 0.6 0  3  6  9  12-1.5-1.2-0.9-0.6-0.3 0 0.3 0.6 0.9 1.2 1.5 0  5  10  15  20  25  30A synthetically generated set of 10 trials:more noise added...compared to PCA:

Single trial analysis using non-negative matrix factorizations

http://hdl.handle.net/11858/00-001M-0000-0010-D9EC-3

Single trial analysis using non-negative matrix factorizations

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