# Feature Selection Algorithm for Attributes with Logical Relationships (like "AND")

I'm looking at datasets where the the attributes and the target class have a logical relationsships. All attributes and the target class are binary.

Here's an example: Neither feature#1 nor feature#2 have a significant correlation with the target class. But the conjunction feature#1 AND feature#2 is correlated with the target class.

Are there any Feature Selection Algorithms able to cope with situations like that? I'm thinking that frequent itemsets could be useful. It would be tremendously helpful, if anyone could point me to a related paper.

Cheers!

• As features can be extracted from some models, there are many choices. Feb 13, 2017 at 15:03
• Sure, but there has to be a ranking of feature importance of some kind for that. For polynomial models those are usually the coefficient weights. For a decision tree one could use the information gain for each feature. But what can I do, when the features show a correlation to the target class only in conjunction with each other but not individually? That case is rather hard to represent with polynomial models oder DTs... Feb 13, 2017 at 16:04
• I don't have the answer but any reliable way to do this will get computationally expensive pretty fast without some loose heuristics Feb 13, 2017 at 16:55
• I don't see why L_1 regularization shouldn't pick this up.
– Emre
Feb 13, 2017 at 17:09
• @Emre Because conjunctions require non-continous functions in a model. Feb 14, 2017 at 15:22

Emergent pattern mining could be useful for you. In classification, emergent patterns are subsets of features which differentiate one class from the others. Look at Example 1.1 in the paper. Two feature subests, denoted $X$ and $Y$, are EPs because $X$ has large support in one class and small support in the other, and vice versa for $Y$. The nifty thing about EP mining is that it considers subsets of features instead of individual features.
Mining patterns in this way could address your problem of feature1 and feature2 having no correlation with the target class alone, but the combination feature1 AND feature2 having high correlation with the target class.