How to draw (intuitively) the first and second principal component in PCA methods?
In the case of 2d data, the first principal component will be aligned along the direction of major continuity, and the second will be perpendicular to that, aligned along the least continuous direction. Generally just the eigen vectors at the mean x / mean y.

Sort of like so (sorry for the poor drawing)



My favorite reference on pca is A TUTORIAL ON PRINCIPAL COMPONENT ANALYSIS by Jon Shlens: pdf His example is in figure 2.

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