Fpmax

[harenbergsd]

Description

Added FPMax algorithm to frequent pattern mining. FPMax find maximal itemsets.

Related issues or pull requests

Related to #509

Pull Request Checklist

• Added a note about the modification or contribution to the ./docs/sources/CHANGELOG.md file (if applicable)
• Added appropriate unit test functions in the ./mlxtend/*/tests directories (if applicable)
• Modify documentation in the corresponding Jupyter Notebook under mlxtend/docs/sources/ (if applicable)
• Ran PYTHONPATH='.' pytest ./mlxtend -sv and make sure that all unit tests pass (for small modifications, it might be sufficient to only run the specific test file, e.g., PYTHONPATH='.' pytest ./mlxtend/classifier/tests/test_stacking_cv_classifier.py -sv)
• Checked for style issues by running flake8 ./mlxtend

[coveralls]

Coverage increased (+0.06%) to 92.104% when pulling 85816aa on harenbergsd:fpmax into b20e57c on rasbt:master.

[rasbt]

Do you know if that captures True and False values as well by chance?

[harenbergsd]

Yeah, in python, 1 == True (==1.0)

[rasbt]

haha, right, seems like my basic Python skill are getting a tad rusty

[rasbt]

Again, thanks so much for this very nice PR!

I can take care of the documentation part.

[harenbergsd]

Ok, cool, thanks!

[harenbergsd]

BTW, one design decision to discuss regarding max_len. It's not quite so clear what to do with max_len for this problem, where you are enumerating maximal itemsets. There are two options:

1. Given the set of all maximal itemsets, return those that are less than max_len
2. Given the set of all itemsets less than max_len, return those that are maximal

The latter is including max_len in the maximality constraint.

For example, if {a,b,c,d} and {c,d,e} are maximal itemsets. If you user gives a max_len of 3 the options would return:

1. {c,d,e}
2. {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}, {c,d,e}

I chose to go with the former, option (1), because with option (2) you can return itemsets that are not maximal wrt to the complete database. In other words, option (1) gives you subset of the complete set of solutions.

The other way would be fairly easy to implement as well, so if you think it's better, we can do it.

[rasbt]

Good point. I think there would be edge cases where someone would prefer one over the other. However, when I think of maximal itemsets, intuitively, I would think about it wrt the complete database as in scenario 1. I'd say we should go with 1, like you also suggest.

[rasbt]

Regarding what's currently implemented ... looking at the code (

mlxtend/mlxtend/frequent_patterns/fpmax.py

Line 86 in 9be453c

if max_len is None or len(largest_set) <= max_len:

), it looks like it's option 1, correct?

[harenbergsd]

Yep, option 1.

[rasbt]

Once the unit tests pass, I think this should be good to merge. Thanks a lot once again. Looks like quite some effort went into the code, and I particularly like the engineering best-practices regarding refactoring and encapsulation.