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.