Dictionary Learning under Symmetries via Group Representations

The dictionary learning problem can be viewed as a data-driven process to learn a suitable transformation so that data is sparsely represented directly from example data. In this paper, we examine the problem of learning a dictionary that is invariant under a pre-specified group of transformations. Natural settings include Cryo-EM, multi-object tracking, synchronization, pose estimation, etc. We specifically study this problem under the lens of mathematical representation theory. Leveraging the power of non-abelian Fourier analysis for functions over compact groups, we prescribe an algorithmic recipe for learning dictionaries that obey such invariances. We relate the dictionary learning problem in the physical domain, which is naturally modelled as being infinite dimensional, with the associated computational problem, which is necessarily finite dimensional. We establish that the dictionary learning problem can be effectively understood as an optimization instance over certain matrix orbitopes having a particular block-diagonal structure governed by the irreducible representations of the group of symmetries. This perspective enables us to introduce a band-limiting procedure which obtains dimensionality reduction in applications. We provide guarantees for our computational ansatz to provide a desirable dictionary learning outcome. We apply our paradigm to investigate the dictionary learning problem for the groups SO(2) and SO(3). While the SO(2)-orbitope admits an exact spectrahedral description, substantially less is understood about the SO(3)-orbitope. We describe a tractable spectrahedral outer approximation of the SO(3)-orbitope, and contribute an alternating minimization paradigm to perform optimization in this setting. We provide numerical experiments to highlight the efficacy of our approach in learning SO(3)-invariant dictionaries, both on synthetic and on real world data.Comment: 29 pages, 2 figure

Developing CRISPR/Cas9-Mediated Fluorescent Reporter Human Pluripotent Stem-Cell Lines for High-Content Screening

Application of the CRISPR/Cas9 system to knock in fluorescent proteins to endogenous genes of interest in human pluripotent stem cells (hPSCs) has the potential to facilitate hPSC-based disease modeling, drug screening, and optimization of transplantation therapy. To evaluate the capability of fluorescent reporter hPSC lines for high-content screening approaches, we targeted EGFP to the endogenous OCT4 locus. Resulting hPSC–OCT4–EGFP lines generated expressed EGFP coincident with pluripotency markers and could be adapted to multi-well formats for high-content screening (HCS) campaigns. However, after long-term culture, hPSCs transiently lost their EGFP expression. Alternatively, through EGFP knock-in to the AAVS1 locus, we established a stable and consistent EGFP-expressing hPSC–AAVS1–EGFP line that maintained EGFP expression during in vitro hematopoietic and neural differentiation. Thus, hPSC–AAVS1–EGFP-derived sensory neurons could be adapted to a high-content screening platform that can be applied to high-throughput small-molecule screening and drug discovery campaigns. Our observations are consistent with recent findings indicating that high-frequency on-target complexities appear following CRISPR/Cas9 genome editing at the OCT4 locus. In contrast, we demonstrate that the AAVS1 locus is a safe genomic location in hPSCs with high gene expression that does not impact hPSC quality and differentiation. Our findings suggest that the CRISPR/Cas9-integrated AAVS1 system should be applied for generating stable reporter hPSC lines for long-term HCS approaches, and they underscore the importance of careful evaluation and selection of the applied reporter cell lines for HCS purposes