Iolo Jones
@iolo_jones
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PhD student in geometry / geometric data analysis and ML @durham_uni
Durham
Joined February 2014
Really pleased to finally share my preprint: Diffusion Geometry (1/4) Diffusion geometry defines Riemannian geometry for data and probability spaces!
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RT @JoshuaABull: Very pleased to share that MuSpAn (Multiscale Spatial Analysis), @MuSpAn_Tweets, our Python package for quantitative spati…
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RT @docmilanfar: How are Kernel Smoothing in statistics, Data-Adaptive Filters in image processing, and Attention in Machine Learning relat…
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@amirvaxman_dgp Hi, yes I am! I’m using diffusion maps, which is essentially the same idea as laplacian eigenmaps, to estimate the laplacian like they describe. The point of diffusion geometry is to use that estimate to do all these other things, and generalise the theory to non-manifold data.
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RT @nicolefeng_: There are deep & wonderful connections between diffusion and geometry of manifolds, and it's great to see methods taking a…
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RT @DeGatchi: Today I spoke w/ @iolo_jones about the intuition behind intersecting riemannian geometry with diffusion and profound results…
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The code's now up on GitHub! See the intro notebook that works through the details and visualises each step of the algorithm
I'm super excited to have a new preprint - Manifold Diffusion Geometry Diffusion geometry *robustly* measures curvature, dimension, and tangent spaces of data!
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RT @cutezu_: Algorithms of differential geometry have existed for some time, but Iolo's Diffusion Geometry withstands noise and sparsity li…
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RT @ryansweb: This paper by @iolo_jones is amazing...Seriously. There are some very interesting novel approaches using diffusion geometry i…
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@SeattleStatSam Ah ok I see. I'm using the carré du champ formula to write the metric directly in terms of Laplacian - I wasn't aware of this 'locally inverse laplacian' formulation. I'll look at your work and see if there's a connection!
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@SeattleStatSam Hi! Algorithm 2 in that paper describes (a weighted version of) local PCA. This would probably deal better with noise than the standard version I'm comparing to here, but it's quite different from the DG approach of computing the metric directly and then diagonalising that.
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The preprint's available here The code will be available soon.
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