Department of Food Science

Faculty of Science

University of Copenhagen

# Bootstrap based Confidence Limits in Principal Component Analysis

**Bootstrap based Confidence Limits in Principal Component Analysis**

The following code is a free MATLAB function to construct non-parametric bootstrap Bias-corrected and accelerated (BCa) confidence limits in PCA for scores and loadings. Further outputs are provided, e.g., bootstrap estimates of scores and loadings, standard error, and bias. Bootstrap confidence limits are useful to evaluate the uncertainty associated with samples or variables for outlier detection and variable selection.

In an experiment, NIR spectra of 2-Propanol/water mixtures were collected at two temperatures (data included in the download below):

The data were used to build non-parametric bootstrap BCa confidence intervals for PCA scores and loadings, where a PCA model with one PC was fitted to the bootstrap samples. The loading CIs are larger for the some variables compared to the others. The explanation is that the difference in the signal of the two sets is larger for those variables:

**Please refer to the below paper when using the function**:

H. Babamoradi, F. van den Berg, Å. Rinnan, Bootstrap based confidence limits in principal component analysis — A case study, Chemometrics Intellig. Lab. Syst. 120(2013)97-105

**Download: ** PCA bootstrap (May 31^{st}, 2013)