lfda: Local Fisher Discriminant Analysis in R

Fisher discriminant analysis (Scholkopft & Mullert, 1999) is a popular choice to reduce the dimensionality of the original dataset. It maximizes between-class scatter and minimizes within-class scatter. It works really well in practice but lacks some considerations for multimodality. Multimodality exists within many applications, such as disease diagnosis, where there may be multiple causes for a particular disease. In this situation, Fisher discriminant analysis cannot capture the multimodal characteristics of the clusters. To deal with multimodality, local-preserving projection (Niyogi, 2004) preserves the local structure of the data in that it keeps nearby data pairs in the original data space close in the embedding space. As a result, multimodal data could be embedded and its local structure will not be lost.