Analysing time-series data

[wxmerkt]

Hi guys, Thank you very much for your hard work in developing and maintaining this excellent tool - it really is a breeze to work with!

We are currently working on problems involving time-series data (trajectories). In order to achieve this, we post-process the distance matrix D to set the distance between subsequent points (t and t+1) to 0. This works just fine with dense filtration and we obtain the results that we expect. With sparse/approximate filtration, however, this breaks (maybe because the 0 to be interpreted as a sparse entry?). As our datasets usually are larger than the synthetic ones we used to test, ripser.py often runs out of memory and we'd like to leverage the approximate filtration. Do you have any advice or perhaps best practices for dealing with time-series data and approximate filtration?

Thank you very much, Wolfgang

[ctralie]

Hello Wolfgang, Glad you've overall had a good experience with ripser.py so far!

Wow, this is quite an interesting case. Because in a metric space d(x, y) = 0 if and only if x=y, we never expect there to be zeros in the distance matrix. But I see why you would want to use them with trajectories to bully the filtration into adding the edges between subsequent points in time first. Unfortunately, zeros in a sparse matrix are interpreted to be infinity (edges that are never added). Because I can't think of a clean way to change the API to allow actual zeros in the sparse matrix (and because it may not be such a general thing to do), what I would recommend as a hack for the moment is to make the edges between t and t+1 a very small number, which is orders of magnitude below any other edges you have (so maybe something like 1e-14). That should get you basically the results you're seeing with dense matrices.

I hope that's a reasonable answer for now. I'm curious to see what you end up doing with time series, as I also do a lot of work on trajectories. Best, Chris

On Mon, Jul 8, 2019 at 6:53 AM Wolfgang Merkt [email protected] wrote:

Hi guys, Thank you very much for your hard work in developing and maintaining this excellent tool - it really is a breeze to work with!

We are currently working on problems involving time-series data (trajectories). In order to achieve this, we post-process the distance matrix D to set the distance between subsequent points (t and t+1) to 0. This works just fine with dense filtration and we obtain the results that we expect. With sparse/approximate filtration, however, this breaks (maybe because the 0 to be interpreted as a sparse entry?). As our datasets usually are larger than the synthetic ones we used to test, ripser.py often runs out of memory and we'd like to leverage the approximate filtration. Do you have any advice or perhaps best practices for dealing with time-series data and approximate filtration?

Thank you very much, Wolfgang

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[wxmerkt]

Hi Chris, Thank you very much for your quick response - I will try it (we have previously used 1e-6 instead of zero, and it only worked so-so). Do you mind sharing what approaches you use to represent trajectories when passing them to ripser.py?

Thank you very much - best, Wolfgang

[ctralie]

Hi Wolfgang, The results should be very close if you make them a number close to zero, so it's a bit alarming that they're not. Hopefully there's not another issue with sparse matrices lurking there!

So I have seen the trick you're using before, but I never personally use it when I apply TDA to trajectories. Instead, I represent local time information via sliding window embeddings. I have some notebooks on this here: https://github.com/ctralie/TDALabs Best, Chris

On Mon, Jul 8, 2019 at 9:21 AM Wolfgang Merkt [email protected] wrote:

Hi Chris, Thank you very much for your quick response - I will try it (we have previously used 1e-6 instead of zero, and it only worked so-so). Do you mind sharing what approaches you use to represent trajectories when passing them to ripser.py?

Thank you very much - best, Wolfgang

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[VladimirIvan]

Hi both, I have encountered a similar issue with the missing entries in a sparse matrix being interpreted as inf instead of a zero. I generated a distance matrix that has a large zero block:

The dense matrix produces the correct results at the cost of storage and probably additional computation.

I'd like to add myself as another future user of the feature to optionally to treat the undefined elements of a sparse matrix as zero.

Best, Vladimir

[ulupo]

@wxmerkt a bit late to the party here but, in my experience, things work out as I think you would like them to in ripser.py if you explicitly store zeros in your sparse matrices (this can be done in a number of scipy sparse formats, though not in all). I can show you an example if you like (perhaps this got solved in the meantime?).

When making pyflagser (docs), we had to face some similar conundrums concerning the expected format of sparse matrices. In the end, we settled for a design choice which is explained in the function flagser_weighted -- analogous to ripser (it computes the same persistence diagrams when directed=False is passed!). In brief, you can pass sparse adjacency matrices with explicitly stored zeros and they are treated as zero filtration parameters, not as absent edges. The absent edges, as @ctralie pointed out is the case also in ripser.py, are the non-stored entries in the sparse matrix (the "sparse zeros", if you will). But again, I think ripser.py does the same thing!

[ctralie]

Thank you Umberto, that is very helpful!

On Fri, Aug 21, 2020 at 11:55 AM Umberto Lupo [email protected] wrote:

@wxmerkt https://github.com/wxmerkt a bit late to the party here but, in my experience, things work out as I think you would like them to in ripser.py if you explicitly store zeros in your sparse matrices (this can be done in a number of scipy sparse formats). I can show you an example if you like (perhaps this got solved in the meantime?).

When making pyflagser https://github.com/giotto-ai/pyflagser (docs https://docs-pyflagser.giotto.ai/), we had to face some similar conundrums concerning the expected format of sparse matrices. In the end, we settled on a design choice which is explained in the function flagser_weighted https://docs-pyflagser.giotto.ai/generated/pyflagser.flagser_weighted.html#pyflagser.flagser_weighted -- analogous to ripser (it computes the same persistence diagrams when directed=False is passed!). In brief, you can pass sparse adjacency matrices with explicitly stored zeros and they are treated as zero filtration parameters, not as absent edges. The absent edges, as @ctralie https://github.com/ctralie pointed out is the case also in ripser.py, are the non-stored entries in the sparse matrix (the "sparse zeros", if you will).

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