How to Decipher a Biplots Observation

Hi all, I made a biplot based on my data set (10000x9). Each of the 9 category is labeled as such on the biplots. I used the data cursor to point to a point (red dots) on the biplot and it shows me:

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Scores

Component 1: 0.2323

Component 2: -0,3763

Observation: 508

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I m trying to understand what is the observation number correspond to? How do I find out the data that corresponds to these PC score?

Thank you for your time.

Best, James

Answer 1

[Eric Lin]

The "Observation" number simply corresponds to the row number of the original data point. That is, you will have 10,000 observations given your data set. Note that the component scores shown in the data tip may not match the scores returned by "pca" according to the "biplot" documentation:

biplot scales the scores so that they fit on the plot: It divides each score by the maximum absolute value of all scores, and multiplies by the maximum coefficient length of coefs. Then biplot changes the sign of score coordinates according to the sign convention for the coefs.

In R2015a, the exact transformation steps can be seen in lines 198 and 199 of "biplot.m":

      maxCoefLen = sqrt(max(sum(coefs.^2,2)));
      scores = bsxfun(@times, maxCoefLen.*(scores ./ max(abs(scores(:)))), colsign);

Answer 2

[James Ooi]

Thank you Eric. Your explanation is very detailed and I appreciate it!