Is rotation necessary in PCA? If yes, Why? What will happen if you don’t rotate the components?

Data Science, AI and ML
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#1

Is rotation necessary in PCA? If yes, Why? What will happen if you don’t rotate the components?

#2

Yes, rotation (orthogonal) is necessary because it maximizes the difference between variance captured by the component. This makes the components easier to interpret. Not to forget, that’s the motive of doing PCA where, we aim to select fewer components (than features) which can explain the maximum variance in the data set. By doing rotation, the relative location of the components doesn’t change, it only changes the actual coordinates of the points.

If we don’t rotate the components, the effect of PCA will diminish and we’ll have to select more number of components to explain variance in the data set.

#3

It’s not nessecary, it’s a form of optimization or ease of computation.

If you do not rotate the components, the inherent attributes of the metric informational points of the underlying co-ordinate system, will sustain as they are.

The fundamental part of the alignment and the “reconstruction” of the Matrixes - inherently means to “adjust” a piece of the larger set of metric points.

Everything you see on your monitor is 2-dimensional in space, 1-dimensional in time, if there is depth, then there is more information to see. If you don’t rotate your POV, to see if there is 3-dimensional space to display, then you won’t know if there is hidden information.