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Thank you very much for working on this.

Some thoughts:

• Focus the module on two distinct tasks : find_neighbors and find_motifs for all type for similarity search estimators. Similarly to the fit/ predict interface we already know well, here, we first fit and then either find_motifs or find_neighbors ("predict" keyword don't make much sense here). We give a collection to use as database in fit, and a single series in find_neighbors or find_motifs to use as query for the search.

That is an interesting problem. Here is my view:

For whole series similarity search fit requires a dataset of time series of equal length, and find_neighbors would get one or many query series of this length.

For subsequence similarity search fit requires a single time series, and find_neighbors commonly gets a single query sequence which length is shorter than the single series length. It would be fine however, to extend it to multiple short sequences.

There is only one whole series consensus motif search paper, which would be the use case of whole matching and motif discovery. The input to fit would be the whole dataset, and find_motif has no input series X. not sure, what an input series X should trigger.

Most papers solve the problem of motif discovery in a single long time series, defined as subsequences of the time series. Here, fit gets a single series, and find_motif has no input series X.

• Distinguish between two kind of similarity search tasks with the two submodules, SeriesSearch and SubsequencesSearch. The SubsequencesSearch focuses on tasks for which the goal is to find motifs or neighbors in subsequences of time series (e.g. Matrix Profiles, Motiflets, etc.). the SeriesSearch focuses on task using whole series (e.g. Indexes such as LSH, iSAX, etc.)

• Have base classes for families of method to limit code duplication (e.g. BaseMatrixProfile, and STOMP, where most existing code was ported), so the we can focus on implementing the computational logic when adding new estimators.

What is the difference between BaseMatrixProfile and STOMP?

At least for Motiflets, we cannot use STOMP/MP, as it only gives a 1-NN profile, but we need k-NN profiles. Same problem would be the case, if you want to solve k-nearest neighbors similarity search.

Questions to answers for motif search :

• Do we want to make providing X optional in find_motifs ? Providing X means that we search for subsequences in X that are motifs in the collection given in fit. Not providing X would mean that we search for motifs in the collection given in fit only. I think it would make sense to make it optional, but would love some comment from people actually doing motif discovery.

I think that X is not meaningful for motif discovery.

Thanks for the inputs @patrickzib😄

For whole series similarity search fit requires a dataset of time series of equal length, and find_neighbors would get one or many query series of this length.

Completely in line with this, but what about the case of unequal length series, with, for example, elastic distance measures? Wouldn't that be a plausible use case? (all whole series estimators don't have to support it)

For subsequence similarity search fit requires a single time series, and find_neighbors commonly gets a single query sequence which length is shorter than the single series length. It would be fine however, to extend it to multiple short sequences.

For this case, I'm defining a length parameter during __init__, and accept a 2D subsequence of shape (n_channels, length) for find_neighbors, ensuring that length is not bigger than the length of any series given in fit. However, any reason why you think we should restrain ourselves to a single series for fit ?

There is only one whole series consensus motif search paper, which would be the use case of whole matching and motif discovery. The input to fit would be the whole dataset, and find_motif has no input series X. not sure, what an input series X should trigger.

This is the tricky one for me too. I'm not sure how giving X during find_motifs on whole series would fit any use case.

Most papers solve the problem of motif discovery in a single long time series, defined as subsequences of the time series. Here, fit gets a single series, and find_motif has no input series X.

I've been kinda frustrated by this limitation for practical use cases, wouldn't it be fine to loop on series of a collection with the motif discovery methods and then merge the results ? That's how I implemented STOMP for now for example. For each subsequence in X, it computes the distance profile to all series in a collection, and keep the top k among all of them (also storing the sample ID and timepoint ID).

What is the difference between BaseMatrixProfile and STOMP?
At least for Motiflets, we cannot use STOMP/MP, as it only gives a 1-NN profile, but we need k-NN profiles. Same problem would be the case, if you want to solve k-nearest neighbors similarity search.

BaseMatrixProfile (which inherit BaseSubsequenceSearch) is simply a base class that defines abstract compute_matrix_profile and compute_distance_profile methods to be implemented by child classes such as STOMP and the likes (STUMP, etc...). The logic for finding neighbors / motifs is then handled in the BaseMatrixProfile. I wanted to leave the door open to alternative methods and not just focus on matrix profiles, hence the split.

As stated above, I already extended STOMP to support k-NN profiles for collections (multivariate and unequal length compatible).

I suppose that in this context, motiflets would either inherit from BaseMatrixProfile if you need to implement methods like compute_matrix_profile and compute_distance_profile. Otherwise, It would inherit from BaseSubsequenceSearch and make its own methods to answer the find_neighbors/find_motifs tasks. (I would need to read the paper again!)

Note that it's possible to simply raise a "NotImplementedError" or something similar if an estimator would only support neighbors or motifs search.

My goal here is to find a base class structure that enables us to move most common code to there and focus on the computational optimisations of each method in the child classes.

I think that X is not meaningful for motif discovery.

In the context of motif search in a single series I agree, but wouldn't there be some interest when dealing with a collection ? For example find motifs in the collection at the condition that they are similar to a subsequence in X ? (This is pure speculation)

Completely in line with this, but what about the case of unequal length series, with, for example, elastic distance measures? Wouldn't that be a plausible use case? (all whole series estimators don't have to support it)

Sure. I did not think of this.

For subsequence similarity search fit requires a single time series, and find_neighbors commonly gets a single query sequence which length is shorter than the single series length. It would be fine however, to extend it to multiple short sequences.

For this case, I'm defining a length parameter during __init__, and accept a 2D subsequence of shape (n_channels, length) for find_neighbors, ensuring that length is not bigger than the length of any series given in fit. However, any reason why you think we should restrain ourselves to a single series for fit ?

Simplicity :) But I agree that you could have multiple series in fit, too - this would mimic the Shapelet use case, I suppose?

Most papers solve the problem of motif discovery in a single long time series, defined as subsequences of the time series. Here, fit gets a single series, and find_motif has no input series X.

I've been kinda frustrated by this limitation for practical use cases, wouldn't it be fine to loop on series of a collection with the motif discovery methods and then merge the results ? That's how I implemented STOMP for now for example. For each subsequence in X, it computes the distance profile to all series in a collection, and keep the top k among all of them (also storing the sample ID and timepoint ID).

Sorry, yes, that is what the authors refer to as consensus motif:
https://www.cs.ucr.edu/~eamonn/consensus_Motif_ICDM_Long_version.pdf

BaseMatrixProfile (which inherit BaseSubsequenceSearch) is simply a base class that defines abstract compute_matrix_profile and compute_distance_profile methods to be implemented by child classes such as STOMP and the likes (STUMP, etc...).

I see. I personally do not like to use the terms matrix-profile for simple k-NN distances or k-NN indices though. It was a brilliant re-framing of EK, such that all 1-NN algorithms are now suddenly an instance of matrix profile. Yet, the concept is much older.

As stated above, I already extended STOMP to support k-NN profiles for collections (multivariate and unequal length compatible).

Great.

I think that X is not meaningful for motif discovery.

In the context of motif search in a single series I agree, but wouldn't there be some interest when dealing with a collection ? For example find motifs in the collection at the condition that they are similar to a subsequence in X ? (This is pure speculation)

I would not say that this is impossible, but I have not seen it. :)

Simplicity :) But I agree that you could have multiple series in fit, too - this would mimic the Shapelet use case, I suppose?

I'm not 100% sure what you mean, but in a sense yes ? For example with a brute force neighbour search, just compute the distance of the subsequence given in find_neighbors to all candidates subsequences in all series of the collection given in fit, and take the k best overall, (considering neighbouring matches/self matches if specified by parameters).

I see. I personally do not like to use the terms matrix-profile for simple k-NN distances or k-NN indices though. It was a brilliant re-framing of EK, such that all 1-NN algorithms are now suddenly an instance of matrix profile. Yet, the concept is much older.

I'm not against the idea of a different naming, especially if methods labelled differently from MPs would fit in the base class without much change of parameter/interface. Would you have any proposal? Something like BaseNeighborhoodSearch ?