Utilizing notes from the last lecture, it's interesting to see that we can decompose human movements into different signals, and therefore PCA is a solution to analyze these signals to be able to blend the movements. This was used in 16B to analyze the audio signals and I didn't realize how it could be applied to visual signals as well since it didn't seem like it could be simplified that like.
wangdotjason
@rsha256 It is approximately equal because PCA is a way to trade complexity in the model for accuracy in an optimal way. Only the components that are most significant are kept, which doesn't produce a perfectly accurate result, but requires much less computation.
ncastaneda02
Another thing I find interesting about PCA is that it is provably optimal with respect to the frobenius norm, it isn't the only solution for dimensionality reduction and in fact many other methods are used. Linear Discriminant Analysis and Factor analysis are two other popular techniques for this same problem - but provide broader benefits at the cost of requiring a more specific type of data. Just interesting to see how sometimes a broad hammer like PCA isn't optimal for some problems, despite being mathematically optimal.
Why is this approx equal and not actually equal?
Utilizing notes from the last lecture, it's interesting to see that we can decompose human movements into different signals, and therefore PCA is a solution to analyze these signals to be able to blend the movements. This was used in 16B to analyze the audio signals and I didn't realize how it could be applied to visual signals as well since it didn't seem like it could be simplified that like.
@rsha256 It is approximately equal because PCA is a way to trade complexity in the model for accuracy in an optimal way. Only the components that are most significant are kept, which doesn't produce a perfectly accurate result, but requires much less computation.
Another thing I find interesting about PCA is that it is provably optimal with respect to the frobenius norm, it isn't the only solution for dimensionality reduction and in fact many other methods are used. Linear Discriminant Analysis and Factor analysis are two other popular techniques for this same problem - but provide broader benefits at the cost of requiring a more specific type of data. Just interesting to see how sometimes a broad hammer like PCA isn't optimal for some problems, despite being mathematically optimal.