A Correlation-Based Distance Function for Nearest Neighbor Classification

The Nearest Neighbor rule is a well-known classification me-thod largely studied in the pattern recognition community, both for its simplicity and its performance. The definition of the distance function is central for obtaining a good accuracy on a given data set and different distance functions have been proposed to increase the performance. This paper proposes a new distance function based on the correlation of fuzzy sets, called Fuzzy Correlation-based Difference Metric. The proposed distance function is a generalization of the Value Difference Metric and applies to both nominal and continuous attributes in a uniform way. Fuzzy sets are used to represent numeric attributes. A uninorm operator is used to aggregate local differences. Experimental results using an standard $\mathit{k}$-NN algorithm show a significant improvement in comparison to other distance functions proposed before.