Effective Dimension Reduction with Prior Knowledge

In this talk, I will give a brief overview of research that we propose on dimension reduction and data reduction for effective and efficient data and visual analytics. I will then give some detailed discussion regarding effective dimension reduction that utilizes prior knowledge such as data clusters or nonnegatavity in the data. Dimension reduction is imperative for efficient representation of high dimensional data. The optimization criteria and role of some matrix
decompositions are examined in many commonly used dimension reduction methods such as Linear Discriminant Analysis (LDA), Principal Component Analysis (PCA), and Latent Semantic Indexing (LSI), and Nonnegative Matrix Factorization (NMF). In particular, we discuss how the generalized LDA based on the generalized singular value decomposition (LDA/GSVD), which is applicable even when the data set is extremely high dimensional and undersampled,
can be utilized in visualization of clustered data. We also propose some new directions for improving its efficiency and effectiveness. Some experimental results are presented in text classification, facial recognition, and fingerprint classification, demonstrating the effectiveness of the proposed directions.