本研究之目標為檢定成對的隨機影像是否相關。由於影像資料的高維度，將影像向量化後做典型相關分析會有低檢定力或甚至無法適用的問題。在這個研究中，我們將研究在典型相關分析下保留相關性訊息的維度縮減問題。其一為先將影像資料投影到平滑函數所構成的空間中再執行典型相關分析，其二為考慮多線性結構的典型相關分析。當維度縮減的子空間捕捉到部分的相關性結構，且其維度又相對小的時候，我們設想這些典型相關分析的延伸方法可以有不錯的檢定力。 ;The goal is to test the dependency between paired random images. A simple idea is to apply the canonical correlation analysis (CCA) after reshaping images into vectors. However, the test would be very low power, even not applicable, since the dimensions of images are usually much larger than those in a typical CCA study. In this project, we will study informative dimension reduction methods for CCA to deal with the large dimension problem. One is to project the images to the subspaces spanned by smooth functions and then to apply CCA on the projected data. The second one is to apply CCA with multilinear constraints. The test power would be good when the signal captured by the subspaces is strong and the dimensions of the subspaces are relative low.
