TY - JOUR
T1 - MWPCR
T2 - Multiscale Weighted Principal Component Regression for High-Dimensional Prediction
AU - Zhu, Hongtu
AU - Shen, Dan
AU - Peng, Xuewei
AU - Liu, Leo Yufeng
N1 - Publisher Copyright:
© 2017 American Statistical Association.
PY - 2017/7/3
Y1 - 2017/7/3
N2 - 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 of score weights with the spatial weights 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) dataset. Supplementary materials for this article are available online.
AB - 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 of score weights with the spatial weights 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) dataset. Supplementary materials for this article are available online.
KW - Alzheimer
KW - Feature
KW - Principal component analysis
KW - Regression
KW - Spatial
KW - Supervised
UR - http://www.scopus.com/inward/record.url?scp=85032476911&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85032476911&partnerID=8YFLogxK
U2 - 10.1080/01621459.2016.1261710
DO - 10.1080/01621459.2016.1261710
M3 - Article
C2 - 29151657
AN - SCOPUS:85032476911
SN - 0162-1459
VL - 112
SP - 1009
EP - 1021
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 519
ER -