Graph Frequency Analysis of Learning Progression Name Mentor: Faculty Sponsor:

Investigations into Human Learning fMRI signals for regional brain activities (Hardwick, Rottschy, Miall, & Eickhoff, 2013) Functional connections for brain signal relationships (Dayan & Cohen, 2011) Combine analysis to uncover new information (Siebenhühner, Weiss, Coppola, Weinberger, & Bassett, 2013, Bassett et al., 2013) Currently global analysis Investigations into Human Learning Functional magnetic resonance imaging (fMRI) signals are widely used to describe activities occurring at brain regions Reference image- for regional activity Functional connections between brain regions determine significant relationships associated with brain signals In a study analyzing fMRI time-series data, a global-scale coherence matrix was created to represent the spatial relationship between brain regions over the course of learning. This underlying network uncovered key features that were observed to adapt over time through meso-scale temporal analysis Key information lost through global scale analysis (Hardwick, Rottschy, Miall, & Eickhoff, 2013)

Brain Signals as Graph Networks and Features Graph Signal Processing Applications (Gadde & Ortega, 2015; Thanou, Shuman, & Frossard, 2014) fMRI signals = activity at brain regions (temporal) Brain = network of connected nodes (spatial) Analysis preserves information Be able to relate how key frequency signatures change over course of learning Brain Signals as Graph Networks and Features Idea to use graph networks and features over networks as used in applications like exploiting it to improve classification Reference images See how signal changes over graph in these two domains Want to preserve information- especially time (Richiardi, Achard, Bunke, & Van De Ville, 2013)

Multi-dimensional Analysis: Product Graph Multidimensional: Spatial and Temporal Information collected over period of time related to past and future points Preserving information (Sandryhaila & Moura, 2014) Multi-dimensional Analysis: Product Graph Use image to explain product graph in context Connected nodes for preserving relationships (Sandryhaila & Moura, 2014)

Information on graph signal processing methods for time series data and graphs (Richiardi, Achard, Bunke, & Van De Ville, 2013) Understand brain region relationships (Sporns, 2011) Support and add to prior information Using Prior Knowledge

Verification Methods Documentation Vary frequency analysis range Certain ranges where new information exposed Repeatability Using two different data sets Verification Methods Frequency analysis in terms of variability over a brain region and time Don’t want all frequency ranges to expose same information- no significance

Bassett, D. S. , Wymbs, N. F. , Rombach, M. P. , Porter, M. A  Bassett, D. S., Wymbs, N. F., Rombach, M. P., Porter, M. A., Mucha, P. J., & Grafton, S. T. (2013). Task-based core-periphery organization of human brain dynamics. PLoS Computational Biology, 9(9), e1003171. http://doi.org/10.1371/journal.pcbi.1003171 Dayan, E., & Cohen, L. G. (2011). Neuroplasticity subserving motor skill learning. Neuron, 72(3), 443–54. http://doi.org/10.1016/j.neuron.2011.10.008 Gadde, A., & Ortega, A. (2015). A probabilistic interpretation of sampling theory of graph signals. In 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (Vol. 2015-Augus, pp. 3257–3261). IEEE. http://doi.org/10.1109/ICASSP.2015.7178573 Hardwick, R. M., Rottschy, C., Miall, R. C., & Eickhoff, S. B. (2013). A quantitative meta-analysis and review of motor learning in the human brain. NeuroImage, 67, 283–97. http://doi.org/10.1016/j.neuroimage.2012.11.020 O. Sporns, Networks of the Brain. MIT press, 2011. Richiardi, J., Achard, S., Bunke, H., & Van De Ville, D. (2013). Machine Learning with Brain Graphs: Predictive Modeling Approaches for Functional Imaging in Systems Neuroscience. IEEE Signal Processing Magazine, 30(3), 58–70. http://doi.org/10.1109/MSP.2012.2233865 Sandryhaila, A., & Moura, J. M. F. (2014). Big Data Analysis with Signal Processing on Graphs: Representation and processing of massive data sets with irregular structure. IEEE Signal Processing Magazine, 31(5), 80–90. http://doi.org/10.1109/MSP.2014.2329213 Siebenhühner, F., Weiss, S. A., Coppola, R., Weinberger, D. R., & Bassett, D. S. (2013). Intra- and inter-frequency brain network structure in health and schizophrenia. PloS One, 8(8), e72351. http://doi.org/10.1371/journal.pone.0072351 Thanou, D., Shuman, D. I., & Frossard, P. (2014). Learning Parametric Dictionaries for Signals on Graphs. IEEE Transactions on Signal Processing, 62(15), 3849–3862. http://doi.org/10.1109/TSP.2014.2332441 Bibliography