Kristoffer Hougaard Madsen

Approximate L 0 constrained non-negative matrix and tensor factorization

Non-negative matrix factorization (NMF), i.e. V ap WH where both V, W and H are non-negative has become a widely used blind source separation technique due to its part based representation. The NMF decomposition is not in general unique and a part based representation not guaranteed. However, imposing sparseness both improves the uniqueness of the decomposition and favors part based representation. Sparseness in the form of attaining as many zero elements in the solution as possible is appealing from a conceptional point of view and corresponds to minimizing reconstruction error with an L0 norm constraint. In general, solving for a given L0 norm is an NP hard problem thus convex relaxation to regularization by the L1 norm is often considered, i.e., minimizing (1/2||V - WH||F 2 + lambda||H||1).An open problem is to control the degree of sparsity lambda imposed. We here demonstrate that a full regularization path for the L1 norm regularized least squares NMF for fixed W can be calculated at the cost of an ordinary least squares solution based on a modification of the least angle regression and selection (LARS) algorithm forming a non-negativity constrained LARS (NLARS). With the full regularization path, the L1 regularization strength lambda that best approximates a given L0 can be directly accessed and in effect used to control the sparsity of H. The MATLAB code for the NLARS algorithm is available for download.

Shifted Non-Negative Matrix Factorization

Non-negative matrix factorization (NMF) has become a widely used blind source separation technique due to its part based representation and ease of interpretability. We currently extend the NMF model to allow for delays between sources and sensors. This is a natural extension for spectrometry data where a shift in onset of frequency profile can be induced by the Doppler effect. However, the model is also relevant for biomedical data analysis where the sources are given by compound intensities over time and the onset of the profiles have different delays to the sensors. A simple algorithm based on multiplicative updates is derived and it is demonstrated how the algorithm correctly identifies the components of a synthetic data set. Matlab implementation of the algorithm and a demonstration data set is available.

P314 Two distinct phenotypes of corticomotor hand representation in human motor cortex

Objective Transcranial magnetic stimulation (TMS) can be used to map the corticomotor representations of hand muscles in the precentral motor-cortex (PMC). The spatial peak of the corticomotor representations is often not located in the primary motor cortex (M1HAND), but shows an anterior shift towards the dorsal premotor cortex (PMd). Here we used magnetic resonance imaging (MRI) to test the hypothesis that the PMC shows different structural and functional properties in individuals with a clear “premotor” representation compared to individuals with a preponderant “primary-motor” representation of hand muscles. Methods MRI-measurements and neuronavigated-TMS were performed on twenty-four volunteers (mean age: 24.3xa0 ± xa00.9 SE, 12 women). Participants underwent structural MRI to evaluate cortical thickness and curvature of the PMC. We also performed fMRI to evaluate precentral functional activation in the hand-knob during a simple motor task. Sulcus-shape based TMS-mapping was used to obtain mediolateral and posterior-anterior corticomotor excitability profiles of the left abductor-digiti-minimi and first-dorsal-interosseus muscles. Results In 14 out of 24 individuals (58%), TMS mapping disclosed a clear spatial peak in the stimulation lines overlying the PMd, whereas the remaining 10 subjects (42%) showed maximal motor responses more posteriorly along M1HAND. During fMRI, the “premotor” group displayed a stronger task-related activation in the PMd relative to the “primary-motor” group ( p xa0=xa00.002). No difference between two groups was evident for curvature and cortical thickness. Conclusion The results confirm that many individuals have a more premotor corticomotor representation of small hand muscles when measured with TMS. This premotor phenotype in terms of corticomotor representation is associated with a stronger premotor activation during simple movements. This association supports the notion of two distinct functional phenotypes of corticomotor hand representations in human PMC: a primary motor and a premotor phenotype.

ID 345 – “What”, “When”, “Whether” – The electrophysiological correlates of voluntary action in virtual environment

The study of (Libet, 1985) gave rise to active discussion among scientists over the nature of the will and volition, suggesting that intention to perform voluntary action can be predicted from prior neural activity. (Brass and Haggart, 2008) proposed three different classes of voluntary decisions: ”what” type of action to perform, “when” to act, and “whether” to act or not. Those distinct decisions might involve different neural pathways and anatomical regions, including medial pFC, ACC, preSMA and SMA, PMC, and parietal cortex. In our study, we repeatedly confront participants with the three classes of decisions in a natural, yet still strictly controlled experimental setup, involving navigating a car through a virtual environment. For each participant we acquired high-resolution EEG data with 128-channel Biosemi ActiveTwo system, structural MR brain image (3T Philips), and recorded electrode coordinates with Localite neuro-navigation system. We demonstrate electrophysiological differences in activation of brain regions related to different classes of decisions, in terms of spatial distribution and time-frequency modulation. The event-related modulation of EEG signals, along with subject-specific T1 images, session-specific electrode coordinates, and set of spatial filters are then used to localize decision-relevant neuroanatomical sources distributed over frontal and posterior cortical regions.