Title: A high-dimensional quadratic classifier by data transformation for strongly spiked eigenvalue models
Authors: Kazuyoshi Yata - University of Tsukuba (Japan) [presenting]
Aki Ishii - Tokyo University of Science (Japan)
Makoto Aoshima - University of Tsukuba (Japan)
Abstract: High-dimensional classification is considered. Any high-dimensional data is classified into two disjoint models: the strongly spiked eigenvalue (SSE) model and the non-SSE (NSSE) model. In actual high-dimensional data, one often finds a non-sparse structure which contains strongly spiked eigenvalues. That structure fits the SSE model. There are several studies providing high-dimensional classifiers. However, it should be noted that one cannot usually obtain a consistency property of the classifiers under the SSE model. It is because the classifiers are heavily influenced by the strongly spiked eigenvalues. In order to overcome the difficulty, a data transformation technique that transform the SSE model to the non-SSE model has been previously developed. We propose a quadratic classification procedure by using the data transformation. We prove that our proposed classification procedure has a consistency property for misclassification rates under the SSE model. We discuss performances of our classification procedure in simulations and real data analyses using microarray data sets.