We are interested in building topological learning methods, i.e. statistical and machine learning tools that utilize the topological structures and features in neuroimaging data depicted by TDA. Our goal is to obtain fresh insight into brain network disorders, such as epilepsy and post-stroke aphasia, with topological learning of multimodal neuroimaging data. Our research areas are outlined below with annotations on select publications.
Topological signal processing and inference
Wang, Y., Behroozmand, R., Johnson, L.P., Bonilha, L. Fridriksson, J. (2020). Topological signal processing in neuroimaging studies, Workshop Proceedings of the 17th IEEE International Symposium on Biomedical Imaging (ISBI).
Exact permutation test on event-related potential (ERP) response
Wang, Y., Behroozmand, R., Johnson, L.P., Bonilha, L., Fridriksson, J.. Topological signal processing and inference of event-related potential response. In revision.
Wang, Y., Behroozmand, R., Johnson, L.P., Fridriksson, J. (2020). Topology highlights neural deficits in post-stroke aphasia, Proceedings of the 17th IEEE International Symposium on Biomedical Imaging (ISBI) 754 - 757.
Wang, Y., Ombao, H., Chung, M.K. (2019). Statistical persistent homology of brain signals. Proceedings of the 44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 1125 – 1129.
In this paper, we made a breakthrough on the computational speed of permutation testing on persistence landscapes in signals. We developed an exact permutation test on the areas under the layers of two persistence landscapes, utilizing an exact topological inference (ETI) approach by Chung et al (2019, Network Neuroscience) that computes the p-value of Kolmogorov-Smirnov test exactly through a fast combinatorial routine.
Standard permutation test on single-trial EEG signals
Wang, Y., Ombao, H., Chung, M.K. (2018). Topological data analysis of single-trial electroencephalographic signals. Annals of Applied Statistics. 12(3):1506-1534. An earlier version of this paper received the Distinguished Student Paper Award by International Biometric Society Eastern North American Region Meeting (ENAR).
In this paper, we advanced the first permutation-based framework for inference on persistence landscapes on EEG signals. Due to the practical constraint of having only one trial in the data, the framework resamples in the spectral domain instead of the temporal domain to preserve topological features in waveforms. Drawback is that the standard random permutation procedure used in the method is too slow, taking hours on end to converge for a few minutes of EEG recording sampled at 100 Hz.
Brain NEtwork Analysis
Lee, H., Ma, Z., Wang, Y., Chung, M.K. (2017). Topological distances between networks and its application to brain imaging. arXiv:1701.04171.
Wang, Y., Chung, M.K., Bachhuber, D.R.W., Schaefer, S.M., Van Reekum, C.M., Davidson, R.J. (2015). LARS network filtration in the study of EEG brain connectivity. Proceedings of the 12th IEEE International Symposium on Biomedical Imaging (ISBI) 30 – 33.
Human growth modeling
Werner, H.M., Miller, C.A., Tillman, K.K., Wang, Y., Vorperian, H.K. (2021). Growth and sexual dimorphism of the hyoid bone and its relationship to the mandible from birth to 19 years: A three-dimensional computed tomography study. Anatomical Record.
Kelly, M.P., Vorperian, H.K., Wang, Y., Tillman, K.K., Werner, H.M., Chung, M.K., Gentry, L.R. (2017). Characterizing mandibular growth using three-dimensional imaging techniques and anatomic landmarks. Archives of Oral Biology. 77:27-38.
Wang, Y., Chung, M.K., Vorpeiran, H.K. (2016). Composite growth model applied to human oral and pharyngeal structures and identifying the contribution of growth types. Statistical Methods in Medical Research. 25:1975-1990.