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Factor analysis methods have been widely used in neuroimaging to transfer high dimensional imaging data into low dimensional, ideally interpretable representations. However, most of these methods overlook the highly nonlinear and complex temporal dynamics of neural processes when factorizing their imaging data. In this paper, we present deep Markov factor analysis (DMFA), a generative model that employs Markov property in a chain of low dimensional temporal embeddings together with spatial inductive assumptions, all related through neural networks, to capture temporal dynamics in functional magnetic resonance imaging (fMRI) data, and tackle their high spatial dimensionality, respectively. Augmented with a discrete latent, DMFA is able to cluster fMRI data in its low dimensional temporal embedding with regard to subject and cognitive state variability, therefore, enables validation of a variety of fMRI-driven neuroscientific hypotheses. Experimental results on both synthetic and real fMRI data demonstrate the capacity of DMFA in revealing interpretable clusters and capturing nonlinear temporal dependencies in these high dimensional imaging data.
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Learning Manifolds from Dynamic Process Data
Scientific data, generated by computational models or from experiments, are typically results of nonlinear interactions among several latent processes. Such datasets are typically high-dimensional and exhibit strong temporal correlations. Better understanding of the underlying processes requires mapping such data to a low-dimensional manifold where the dynamics of the latent processes are evident. While nonlinear spectral dimensionality reduction methods, e.g., Isomap, and their scalable variants, are conceptually fit candidates for obtaining such a mapping, the presence of the strong temporal correlation in the data can significantly impact these methods. In this paper, we first show why such methods fail when dealing with dynamic process data. A novel method, Entropy-Isomap, is proposed to handle this shortcoming. We demonstrate the effectiveness of the proposed method in the context of understanding the fabrication process of organic materials. The resulting low-dimensional representation correctly characterizes the process control variables and allows for informative visualization of the material morphology evolution.
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- Award ID(s):
- 1910539
- PAR ID:
- 10145314
- Date Published:
- Journal Name:
- Algorithms
- Volume:
- 13
- Issue:
- 2
- ISSN:
- 1999-4893
- Page Range / eLocation ID:
- 30
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/a13020030
