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appended answer 26323 as supplemental
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François G. Dorais
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I want to make a diffusion kernel, which involves $e^{\beta A}$, where A is a large matrix (25k by 25k). It is an adjacency matrix, so it's symmetric and very sparse.

Does anyone have a recommendation of a tool to solve this? I use the term "tool" loosely - if you know that transforming it in this way first or whatever is useful then I'd like to know that.


I am going with a hack - since the kernel "diffuses" relatively quickly, I just take only the neighbourhood around the two vertices that I want. This gives me a much reduced adjacency matrix which I can then raise e to without difficulty.

I'm not familiar enough with the kernel function though to know how severely this is screwing up my results, and it's imperfect at best, so I'm still interested if anyone has a better idea.

I want to make a diffusion kernel, which involves $e^{\beta A}$, where A is a large matrix (25k by 25k). It is an adjacency matrix, so it's symmetric and very sparse.

Does anyone have a recommendation of a tool to solve this? I use the term "tool" loosely - if you know that transforming it in this way first or whatever is useful then I'd like to know that.

I want to make a diffusion kernel, which involves $e^{\beta A}$, where A is a large matrix (25k by 25k). It is an adjacency matrix, so it's symmetric and very sparse.

Does anyone have a recommendation of a tool to solve this? I use the term "tool" loosely - if you know that transforming it in this way first or whatever is useful then I'd like to know that.


I am going with a hack - since the kernel "diffuses" relatively quickly, I just take only the neighbourhood around the two vertices that I want. This gives me a much reduced adjacency matrix which I can then raise e to without difficulty.

I'm not familiar enough with the kernel function though to know how severely this is screwing up my results, and it's imperfect at best, so I'm still interested if anyone has a better idea.

s/exponent/exponential/
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Xodarap
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Exponent Exponential of large matrices

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j.c.
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Xodarap
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