Dimensionality is an issue that can arise in every scientific field. Generally speaking, the difficulty lies on how to visualize a high dimensional function or data set. Aside from the differences that underlie the various scientific contexts, such kinds of questions do have a common root in Statistics. This is the driving force for the study of high dimensional data analysis. This course will discuss several statistical methodologies useful for exploring voluminous data. They include Principal Component Analysis, Clustering and Classification, Tree-structured analysis, Sliced inverse regression (SIR) and principal Hessian direction (PHD). SIR and PHD are two novel dimension reduction methods, useful for the extraction of geometric information underlying noisy data of several dimensions. The theory of SIR/PHD will be discussed in depth. It will be used as the backbone for the entire course. Examples from various application areas will be given. They include social/economic problems like unemployment rates, biostatistics problems like clinic trials with censoring, machine learning problems like handwritten digital recognition; quality control problems like performance measurement of digital to analogic converters; biomedical problems like functional Magnet Resonance Imaging, and bioinformatics problems like micro-array gene expression.

cultivate student ability in problem solving using data analysis techniques

intelligent data analysis, Michael Berthold and David J. Hand