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

2. 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)

3. 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)

4. 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)

5. 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

6. 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

7. 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), e
Dayan, E., & Cohen, L. G. (2011). Neuroplasticity subserving motor skill learning. Neuron, 72(3), 443–54.
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 Augus, pp. 3257–3261). IEEE.
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.
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.
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.
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), e
Thanou, D., Shuman, D. I., & Frossard, P. (2014). Learning Parametric Dictionaries for Signals on Graphs. IEEE Transactions on Signal Processing, 62(15), 3849–
Bibliography