Metrics and similarities in modeling dependencies between continuous and nominal data

Classification theory analytical paradigm investigates continuous data only. When we deal with a mix of continuous and nominal attributes in data records, difficulties emerge. Usually, the analytical paradigm treats nominal attributes as continuous ones via numerical coding of nominal values (often a bit ad hoc). We propose a way of keeping nominal values within analytical paradigm with no pretending that nominal values are continuous. The core idea is that the information hidden in nominal values influences on metric (or on similarity function) between records of continuous and nominal data. Adaptation finds relevant parameters which influence metric between data records. Our approach works well for classifier induction algorithms where metric or similarity is generic, for instance k nearest neighbor algorithm or proposed here support of decision tree induction by similarity function between data. The k-nn algorithm working with continuous and nominal data behaves considerably better, when nominal values are processed by our approach. Algorithms of analytical paradigm using linear and probability machinery, like discriminant adaptive nearest-neighbor or Fisher’s linear discriminant analysis, cause some difficulties. We propose some possible ways to overcome these obstacles for adaptive nearest neighbor algorithm.