# Problem with Understanding “correlated attributes into a set of values of uncorrelated attributes” in PCA

I am studying PCA. I have a problem in understanding the following concept:

What is meant by transforming "correlated attributes into a set of values of uncorrelated attributes" in Principal Component Analysis?

Principal Component Analysis (PCA) is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated attributes into a set of values of uncorrelated attributes called principal components.

as discussed in the article Weight by PCA (emphasis mine)?

• It looks like you are not aware that you can accept an answer if you are the asker. It is part of protocol and etiquette to try accepting the best answer that has answered your question by clicking on the check mark beside the answer. – John L. Apr 12 '19 at 14:54

It looks like you are using RapidMiner documentation as a medium to study. If that is case, then the best answer to your question and probably to some other questions of yours should be, I believe, a recommendation of related textbook, tutorial or lecture notes.

For the current question, I recommend you to read a tutorial on Principal Components Analysis by Lindsay I Smith, a tutorial that is self-contained and easy to read.

Now let me get back to you question, assuming we have gone through that tutorial up to and including section 3.1 or any equivalent materials.

What is meant by transforming "correlated attributes into a set of values of uncorrelated attributes" in Principal Component Analysis"?

That just means, given existing $$x$$ axis and $$y$$ axis, and a set of data points with their coordinates (a set of observations of possibly correlated attributes), PCA will produce their eigenvectors and, using these eigenvectors as the new $$x$$ axis and $$y$$ axis as well as moving the origin to the center of the data points, obtain the new coordinates of those data points (principal components). The crux of the PCA is that the new $$x$$ coordinates and the new $$y$$ coordinates of the data points are 2 uncorrelated variables (uncorrelated attributes) in the sense that their covariance is 0. I am talking about 2-dimensional data for simplicity; PCA applies to 3 or more dimension the same way. In higher dimensions, the new coordinates of the data points are a set of variables every pair between which are uncorrelated.

All these concepts become very much alive and easy to understand once you have gone through several end-to-end computations. That is probably the fastest way to understand these concepts.

• Thanks. I would go through the tutorial and try to evaluate the co-variance matrix. Really you are right mathematical evaluation can improve the concepts. – user2994783 Nov 7 '18 at 5:26