PCA Analysis

What is it? Principle Component Analysis (PCA) transforms high-dimensional data into a lower-dimensional structure to improve data presentation, pattern recognition, and analysis. PCA determines which dimensions will result in the largest variability of measurements (e.g., expression of specific proteins) across all samples. It does not separate the different groups from each other as the method is unsupervised.

When is it used? This analysis is used when 1) there are a lot of variables to consider (e.g., expression of thousands of proteins), and 2) you want to ensure that the transformed measurements are independent of each other. PCA can help discover relationships between biomarkers that may not be intuitive.

How does it work?

PCA Analysis: Example

We analyze the protein profile of 1,000 proteins of 4 healthy patients and 4 cancer patients using an antibody-based microarray. This represents high-dimensional data since each sample is characterized by 1,000 variables (or biomarkers). Put another way, the sample point is located in a 1,000 dimension space. We want to find the biomarkers that are the most variable across the samples. We hope that, by doing so, we will be able to identify patterns (i.e., biomarkers that are expressed differently in healthy and diseased patients).

1. Center & scale data by subtracting the mean of each patient dataset from itself and dividing each patient dataset with its standard deviation, respectively. Now all datasets have a mean of 0 and a standard deviation of 1.
2. Create Principal Components (i.e., "Data Reduction").
   1. Determine # of Principal Components (PCs). The number of PCs is determined by the minimum number of samples or variables. In this case, the number of patients is lower than the number of proteins analyzed, so 8 PCs are made.
   2. Create PCs. Here, each sample has 8 PCs, where each PC value is a weighted summation of the 1,000 variables.