In this rather long post, we dove deep and looked at the two formulations of PCA: the Maximum Variance and Minimum Error Formulation. Therefore, care needs to be taken to standardise the data to avoid such issues. 3(b) shows the correct principal component when the scales are standardised. 3(a) where the Principal Component is not aligned properly because it is mislead by the unstandardised scale. So, PCA can be mislead by directions along which the variance appears high just because of the measurement scale. The principal directions from PCA are the ones along which the variance is the most. (b) PCA when the scales are standardised. (a) Principal Component is skewed because PCA is misled by the unstandardised data. i.e.,įig.3 PCA can get mislead by unstandardised data. Since we are only interested in the direction of the space, we set w1 to be of unit length. We define a vector w1â R^D as the direction of the lower dimensional space. Now let us consider the simplest case where M=1. Given the set of observations, n = 1, 2, â¦, N and x_n â R^D, our goal according to the maximum variance formulation is to find the orthogonal projection of x_n onto a space with dimensions M
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