Distance functions

[hugo-pires]

Hello and congratulations for your work

Is it possible to use other distance than the euclidean one? And, in your opinion, would it make any sense?

Thank you

[seanlaw]

@hugo-pires Thank you for your question and welcome to the STUMPY community? Can you please elaborate on what "other distances" you are interested in using?

Natively, STUMPY supports z-normalized Euclidean distance and, when you set normalize=False, this changes it to "non-normalized Euclidean distance". The reason why this is fast is because there is special relationship between each distance along the pairwise distance matrix (i.e., D[i, j]) and its nearest diagonal neighbor (i.e., D[i-1, j-1]). Please see Section IV A of this Matrix Profile II paper for more information.

Now, regarding your question about whether or not other distances "make any sense", that really depends on your objective. In z-normalized Euclidean distances, the matrix profile is really finding the one nearest neighbor subsequence with the same shape (i.e., it doesn't depend on amplitude) while, in non-normalized Euclidean distance, the amplitude matters. Ultimately, the original matrix profile researchers, who have thought about this stuff way more than I have, have found z-normalization to be generally applicable and that it is now fast to compute all of the pairwise distances with it. With other distances, these facts may not hold true.

[hugo-pires]

Thank you. I don't have any case yet but I thought that, as you may consider the window length as a parameter, the Minkowski distance p exponent could be also considered. But It is just a guess and I am not a specialist on the matter.

[seanlaw]

Thank you. I don't have any case yet but I thought that, as you may consider the window length as a parameter, the Minkowski distance p exponent could be also considered. But It is just a guess and I am not a specialist on the matter.

So, adding Minkowski distance has been requested in the past and this feature was successfully added to the main branch just two days ago:

d3b68b4

And it should be available in the next STUMPY release. So, you will be able to do something like:

import numpy as np
import stumpy

T = np.random.rand(100)
m = 5
mp = stumpy.stump(T, m, normalize=False, p=1.0)

And this would compute the matrix profiles using Manhattan distance rather than Euclidean distance (without z-normalization). If you'd like to clone the repo and test it out, I'd appreciate any feedback/criticism!