Classification using non-standard metrics

A large variety of supervised or unsupervised learning algorithms is based on a metric or similarity measure of the patterns in input space. Often, the standard euclidean metric is not sufficient and much more efficient and powerful approximators can be constructed based on more complex similarity calculations such as kernels or learning metrics. This procedure is benefitial for data in euclidean space and it is crucial for more complex data structures such as occur in bioinformatics or natural language processing. In this article, we review similarity based methods and its combination with similarity measures which go beyond the standard Euclidian metric. Thereby, we focus on general unifying principles of learning using non-standard metrics and metric adaptation.