FisherS return nan value when ID is pretty large

[marsggbo]

def test_ID_estimator(D, name='TwoNN', *args, **kwargs):
  ids = []
  Ns = [64, 128, 256, 512, 1024, 2048]
  for N in Ns:
    data = np.zeros((N,3*32*32))
    data[:,:D] = skdim.datasets.hyperBall(n = N, d = D, radius = 2, random_state = 666)
    _id = eval(f"skdim.id.{name}")(*args,**kwargs).fit_transform(X=data)
    ids.append(_id)
    print(f'{name}', N, _id)

Results

test_ID_estimate(10, name='FisherS')
>>>
FisherS 64 11.258882790713601
FisherS 128 12.293955630520735
FisherS 256 10.300845319222297
FisherS 512 10.0622264687654
FisherS 1024 10.117248646587507
FisherS 2048 10.083245836860842

test_ID_estimate(20, name='FisherS')
>>>
FisherS 64 nan
FisherS 128 25.11715241495022
FisherS 256 19.984501791074795
FisherS 512 20.91391435506641
FisherS 1024 19.95265685270067
FisherS 2048 19.77165730041636

test_ID_estimate(50, name='FisherS')
>>>
FisherS 64 nan
FisherS 128 nan
FisherS 256 nan
FisherS 512 nan
FisherS 1024 nan
FisherS 2048 49.44956027057592

test_ID_estimate(100, name='FisherS')
>>>
FisherS 64 nan
FisherS 128 nan
FisherS 256 nan
FisherS 512 nan
FisherS 1024 nan
FisherS 2048 nan

[marsggbo]

Should I modify some arguments of FisherS?

[j-bac]

FisherS has theoretical restrictions on maximum detectable ID depending on dataset cardinality (you can look at Figure 1-E in https://arxiv.org/pdf/2001.11739.pdf). ESS or DANCo should be more robust in such situations. Maybe TwoNN also

In such a case for FisherS you can tune alphas parameter values further down. E.g. instead of the default
alphas = np.arange(0.6, 1, 0.02)[None] you can use alphas = np.arange(0.3, 1, 0.02)[None]