Analogical Relevance Index

Focusing on the most significant features of a dataset is useful both in machine learning (ML) and data mining. In ML, it can lead to a higher accuracy, a faster learning process, and ultimately a simpler and more understandable model. In data mining, identifying significant features is essential not only for gaining a better understanding of the data but also for visualization. In this paper, we demonstrate a new way of identifying significant features inspired by analogical proportions. Such a proportion is of the form of "a is to b as c is to d", comparing two pairs of items (a, b) and (c, d) in terms of similarities and dissimilarities. In a classification context, if the similarities/dissimilarities between a and b correlate with the fact that a and b have different labels, this knowledge can be transferred to c and d, inferring that c and d also have different labels. From a feature selection perspective, observing a huge number of such pairs (a, b) where a and b have different labels provides a hint about the importance of the features where a and b differ. Following this idea, we introduce the Analogical Relevance Index (ARI), a new statistical test of the significance of a given feature with respect to the label. ARI is a filter-based method. Filter-based methods are ML-agnostic but generally unable to handle feature redundancy. However, ARI can detect feature redundancy. Our experiments show that ARI is effective and outperforms well-known methods on a variety of artificial and some real datasets.

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