Abstract
We propose a multiscale weighted principal component regression (MWPCR) framework for the use of high dimensional features with strong spatial features (e.g., smoothness and correlation) to predict an outcome variable, such as disease status. This development is motivated by identifying imaging biomarkers that could potentially aid detection, diagnosis, assessment of prognosis, prediction of response to treatment, and monitoring of disease status, among many others. The MWPCR can be regarded as a novel integration of principal components analysis (PCA), kernel methods, and regression models. In MWPCR, we introduce various weight matrices to prewhitten high dimensional feature vectors, perform matrix decomposition for both dimension reduction and feature extraction, and build a prediction model by using the extracted features. Examples of such weight matrices include an importance score weight matrix for the selection of individual features at each location and a spatial weight matrix for the incorporation of the spatial pattern of feature vectors. We integrate the importance score weights with the spatial weights in order to recover the low dimensional structure of high dimensional features. We demonstrate the utility of our methods through extensive simulations and real data analyses of the Alzheimer's disease neuroimaging initiative (ADNI) data set.