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I have 2D data set, X of size [m*2]. Now, I want to find the directions of maximum variations in the data set. Let's say I plot my 2-d data, how can I visually identify directions where there is maximum variation in the data set? I got to know eigen values and eigen vectors are used for my above objective but don't know how to proceed after identifying them.

Directions of maximum variations are represented as in this figure. In the figure, the small circular dots represents data set, black lines represents directions of maximum variation of the data set and the intersection of the black lines represent the mean coordinates.

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  • $\begingroup$ how many dimensions / parameters does your dataset have? I'm assuming it's a 2D dataset with "m" values? Also, how do you define "variation"? $\endgroup$ – Siddharth Bhat Jun 9 '16 at 11:25
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Hint: Apply PCA see here on the covariance matrix constructed from your dataset. Choose first principal component (top eigen vector) to visualize the maximum variation in your dataset.

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  • $\begingroup$ After finding out the eigen values and the eigen vectors, wiki says "we must orthogonalize the set of eigenvectors, and normalize each to become unit vectors" . How to do this? and how to plot in order to get the vectors (shown as black lines in above figure)? $\endgroup$ – NareshR Jun 9 '16 at 12:19

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