lfda: Local Fisher Discriminant Analysis in R
Yuan Tang, Wenxuan Li · The Journal of Open Source Software · 2019
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.