Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2017 Feb 27;18(3):521–536. doi: 10.1093/biostatistics/kxw050

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

© The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

PMC Copyright notice

Fig. 1. — Top panel. For one randomly sampled subject, 50 contiguous time points and 200 contiguous voxels were randomly selected. For the resulting dataset , five PCs were identified, and PCA leverage was computed for each time point , displayed in the column on the left. After centering and scaling , each observed value was increased by one unit and PCs and scores recomputed. The matrix displayed on the right shows the resulting change in the fitted value , where . Although some variation is seen across voxels, the observed change in fitted values is overall quite similar to the leverage. Other randomly sampled subjects show similar patterns, supporting the analogy with regression (where the relationship is exact) and the concept of PCA leverage as a measure of influence in PCA. Bottom panel. We performed the analysis described above for randomly sampled subjects, then computed the average change in fitted values across voxels. We performed the analysis with , and PCs retained. The plot displays the PCA leverage and average change in fitted values for each subject, as well as a linear smoother across subjects. PCA leverage and the average change in fitted values are nearly equal, again supporting PCA leverage as a measure of influence in PCA.

Inline graphic — Top panel. For one randomly sampled subject, 50 contiguous time points and 200 contiguous voxels were randomly selected. For the resulting dataset , five PCs were identified, and PCA leverage was computed for each time point , displayed in the column on the left. After centering and scaling , each observed value was increased by one unit and PCs and scores recomputed. The matrix displayed on the right shows the resulting change in the fitted value , where . Although some variation is seen across voxels, the observed change in fitted values is overall quite similar to the leverage. Other randomly sampled subjects show similar patterns, supporting the analogy with regression (where the relationship is exact) and the concept of PCA leverage as a measure of influence in PCA. Bottom panel. We performed the analysis described above for randomly sampled subjects, then computed the average change in fitted values across voxels. We performed the analysis with , and PCs retained. The plot displays the PCA leverage and average change in fitted values for each subject, as well as a linear smoother across subjects. PCA leverage and the average change in fitted values are nearly equal, again supporting PCA leverage as a measure of influence in PCA.