Coarse Graining of Data via Inhomogeneous Diffusion Condensation
Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here, we consider multiple levels of abstraction via a multiresolution geometry of data points at different granularities. To construct this geometry we define a time-inhomogeneous diffusion process that effectively condenses data points together to uncover nested groupings at larger and larger granularities. This inhomogeneous process creates a deep cascade of intrinsic low pass filters in the data that are applied in sequence to gradually eliminate local variability while adjusting the learned data geometry to increasingly coarser resolutions. We provide visualizations to exhibit our method as a "continuously-hierarchical" clustering with directions of eliminated variation highlighted at each step. The utility of our algorithm is demonstrated via neuronal data condensation, where the constructed multiresolution data geometry uncovers the organization, grouping, and connectivity between neurons.
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Nathan Brugnone (add twitter)
Alex Gonopolskiy (add twitter)
Mark W. Moyle (edit)
Manik Kuchroo (add twitter)
David van Dijk (edit)
Kevin R. Moon (add twitter)
Daniel Colon-Ramos (edit)
Guy Wolf (add twitter)
Matthew J. Hirn (add twitter)
Smita Krishnaswamy (edit)
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07/10/19 06:05PM
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dacolon: Excited to share our first collaboration w @KrishnaswamyLab, in which we used a powerful condensation algorithm they developed and demonstrated its utility for #connectome data, revealing underlying systematic organization of C. elegans nervous system https://t.co/KMUDBovnj8
arxiv_cshc: Coarse Graining of Data via Inhomogeneous Diffusion Condensation https://t.co/4HIWG0q9NI
arxiv_cscv: Coarse Graining of Data via Inhomogeneous Diffusion Condensation https://t.co/t2Y5EGpjS4
arxiv_cshc: Coarse Graining of Data via Inhomogeneous Diffusion Condensation https://t.co/4HIWG0q9NI
mincle: . @KrishnaswamyLab also pointing to https://t.co/bdANIGzTbS
KrishnaswamyLab: Don't cluster your data, slowly condense it! And check out our preprint on our "Diffusion Condensation" method: https://t.co/EdrUMnRJFp
arxiv_cshc: Coarse Graining of Data via Inhomogeneous Diffusion Condensation https://t.co/4HIWG0q9NI
arxiv_cscv: Coarse Graining of Data via Inhomogeneous Diffusion Condensation https://t.co/t2Y5EGGUJC
arxiv_cshc: Coarse Graining of Data via Inhomogeneous Diffusion Condensation https://t.co/4HIWG0q9NI
arxiv_cscv: Coarse Graining of Data via Inhomogeneous Diffusion Condensation https://t.co/t2Y5EGpjS4
arxivml: "Coarse Graining of Data via Inhomogeneous Diffusion Condensation", Nathan Brugnone, Alex Gonopolskiy, Mark W. Moyl… https://t.co/np0svrYq71
Memoirs: Coarse Graining of Data via Inhomogeneous Diffusion Condensation. https://t.co/8P1P9HWqBB
arxiv_cs_LG: Coarse Graining of Data via Inhomogeneous Diffusion Condensation. Nathan Brugnone, Alex Gonopolskiy, Mark W. Moyle, Manik Kuchroo, David van Dijk, Kevin R. Moon, Daniel Colon-Ramos, Guy Wolf, Matthew J. Hirn, and Smita Krishnaswamy https://t.co/kIGDR1dWR7
arxiv_cshc: Coarse Graining of Data via Inhomogeneous Diffusion Condensation https://t.co/4HIWG0q9NI
arxiv_cscv: Coarse Graining of Data via Inhomogeneous Diffusion Condensation https://t.co/t2Y5EGpjS4
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