Largest connected set returns a state when it should return an empty set

[MaaikeG]

The following should print the empty set [] but instead prints [3].

import numpy as np
from deeptime.markov import TransitionCountEstimator

estimator = TransitionCountEstimator(lagtime=1, count_mode='sliding')

full_counts_model = estimator.fit_fetch(np.asarray([0, 1, 2, 3]))
submodel = full_counts_model.submodel_largest(
        connectivity_threshold=1,
        directed=True)
print(submodel.state_symbols)

[clonker]

Yeah I think you are right. This is an error in the connectivity_threshold implementation which is not respected for self-connectivity (i.e. loops k -> k for state k). What do you think @thempel ?

[thempel]

Well... so one could say that the set of states consists of 4 independent, disconnected sets ([0], [1], [2], [3]). Since they all have the same size, submodel_largest will return a random one, in this case [3]. It's obviously a bit useless to have a 1-state submodel though, so maybe one should print some warning?

Some thoughts: I could imagine that returning empty sets may break something downstream. It's not technically wrong to have a 1-state model, so I wouldn't necessarily raise an error.

[clonker]

I would agree except for the connectivity threshold - if it is set to a value that is greater than what can be found on the count matrix diagonal then the one-state set should be discarded I think.

[clonker]

Like think about the 1x1 count matrix C=[[1]] and you set a connectivity threshold of 10... then the single connected component no longer fulfills the constraints given by connectivity threshold and there are (by that definition) no more connected sets.

[thempel]

As far as I remember, connectivity is only defined by transitions between different states, excluding self-transitions. In the graph sense: Two nodes are connected if there is an edge between them - the node does still exist in the graph if it's disconnected from everything else. So in the above trajectory, the connected sets with a connectivity threshold of >1 would still be [0], ..., [3].

[clonker]

Yeah to confirm: I just looked this up, singleton nodes are by definition connected components. Whether it is desirable to eliminate these if the weight of its loop is below connectivity threshold is a philosophical (and practical) consideration. Perhaps this should be documented somewhere more clearly.

[MaaikeG]

In that case, would it make sense to at least return the singleton set that contains the most samples?

[clonker]

If we define it to be that way then yes it would make sense, I don't see the the immediate benefit from it though, can you elaborate?

[MaaikeG]

If I want to restrict my samples to the largest connected set, I can imagine I would want to 'keep' as many samples as possible. But I guess it doesn't really matter because this is not a realistic use case. Just something I came accross while testing. So just updating the docs sounds good.

[clonker]

Alright, docs updated. In case of sets with more than one element it's not so clear how to order them anyways.