Abstract
Sparse and functional principal component analysis is a technique to extract sparse and smooth principal components from a matrix. In this paper, we propose a modified sparse and functional principal component analysis model for feature extraction. We measure the tuning parameters by their robustness against random perturbation, and select the tuning parameters by derivative-free optimization. We test our algorithm on the ADNI dataset to distinguish between the patients with Alzheimer's disease and the control group. By applying proper classification methods for sparse features, we get better result than classic singular value decomposition, support vector machine and logistic regression.
Acknowledgments
Prof. Bin Dong from Beijing International Center of Mathematical Research made great contribution to the idea of this paper. Sheng Hu from Peking University also offered help in the process of our work. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Zhengyang Fang http://orcid.org/0000-0003-1065-9258
Additional information
Funding
Notes on contributors
Zhengyang Fang
Zhengyang Fang is pursuing master's degrees in statistics at the University of Chicago. He received his Bachelor of Science in Mathematics from Peking University.
J. Y. Han
J. Y. Han is former graduate student in the department of biostatistics at University of Washington.
N. Simon
N. Simon is assistant professor in Department of Biostatistics at University of Washington.
X. H. Zhou
Dr X. H. Zhou is Boya Chair Professor in Beijing International Center for Mathematical Research and Chair of the Department of Biostatistics at Peking University. Previously he was Professor in the Department of Biostatistics at University of Washington.