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Archetypal analysis (AA) is a versatile data analysis method to cluster distinct features within a data set. Here, we demonstrate a framework showing the power of AA to spatio-temporally resolve events in calcium imaging, an imaging modality commonly used in neurobiology and neuroscience to capture neuronal communication patterns. After validation of our AA-based approach on synthetic data sets, we were able to characterize neuronal communication patterns in recorded calcium waves. Clinical relevance– Transient calcium events play an essential role in brain cell communication, growth, and network formation, as well as in neurodegeneration. To reliably interpret calcium events from personalized medicine data, where patterns may differ from patient to patient, appropriate image processing and signal analysis methods need to be developed for optimal network characterization.
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Probabilistic methods for approximate archetypal analysis
Abstract Archetypal analysis (AA) is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of AA in practice is the inherent computational complexity of the existing algorithms. In this paper, we provide a novel approximation approach to partially address this issue. Utilizing probabilistic ideas from high-dimensional geometry, we introduce two preprocessing techniques to reduce the dimension and representation cardinality of the data, respectively. We prove that provided data are approximately embedded in a low-dimensional linear subspace and the convex hull of the corresponding representations is well approximated by a polytope with a few vertices, our method can effectively reduce the scaling of AA. Moreover, the solution of the reduced problem is near-optimal in terms of prediction errors. Our approach can be combined with other acceleration techniques to further mitigate the intrinsic complexity of AA. We demonstrate the usefulness of our results by applying our method to summarize several moderately large-scale datasets.
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- PAR ID:
- 10335149
- Date Published:
- Journal Name:
- Information and Inference: A Journal of the IMA
- ISSN:
- 2049-8772
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1093/imaiai/iaac008
