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Okay so let me give you just a few more examples Michael of how PCA and ICA differ and I'm going to do this mainly by talking about certain things that I see a does and this is really just for your edification but I think it really helps to think about those sort of underlying models and how they differ by thinking about how they react differently to different kinds of data so just here's a couple of examples the one we covered right away was the blind source separation problem and of course we what we recall is that I say in some sense was designed to solve the blind source separation problem and in fact ICA does an excellent job at solving the blind source separation problem meanwhile PCA does a terrible job at solving the blind source separation problem and that's just because it's assuming these kind of Gaussian distribution of blind source route in it it's actually a directional and what I mean by that is you recall I drew this sort of matrix before where we had features this way and we had samples of those features like sound time samples of sound this way it turns out that for PCA it doesn't matter whether I give you this matrix or I give you the transpose of this matrix it ends up finding the same answer and that should make sense right because it's just basically finding a new rotation of the data and these are effectively just rotations of each other for the purposes of if you just kind of think about it geometrically in space I see on the other hand gives you completely different answers if you give it this versus giving it this so ICA is highly directional in PCA much lesser but ICA because it's making this kind of fundamental assumption does end up generating some really cool results so I'm going to give you another example of one that's like the blind source separation one in fact I'm going to give you two okay so imagine you had a bunch of inputs of faces okay so here's my input faces I gave you bunches and bunches and bunches of faces what do you think PCA would do what do you think the first principal component of PCA would be over pictures of thousands and thousands and thousands of faces overall darkness of the image actually that's exactly right the first thing that PCA tends to do with images were actually talking pictures not just sketches here is it finds the direction of maximal variance and that tends to be brightness or luminance which kind of makes sense because that's typically the kind of thing that gets very the most so in fact the first thing people often do when they're trying to use PCA on faces is they normalize all of that away because the first principal component isn't terribly helpful it's just kind of giving you.