Based on the fact that distance metrics learned from the data reflect the actual similarity between objects better than the geometric distance, in this research I developed two distance functions learned from the data. The first one deals with complete datasets (datasets without missing values) while the second one deals with incomplete datasets (datasets with missing values). I integrated these distance within the frame work of several data mining algorithms from different types: KNN classifier for classification. For clustering I developed two algorithms: k-Means and Mean Shift clustering algorithms, and for active learning I developed a new approach for selective sampling.