Principal component analysis

In many cases, the dimensionality of the input dataset X is high and so is the complexity of every related machine learning algorithm. Moreover, the information is seldom spread uniformly across all the features and, as discussed in the previous chapter, there will be high entropy features together with low entropy ones, which, of course, don't contribute dramatically to the final outcome. In general, if we consider a Euclidean space, we have:

So each point is expressed using an orthonormal basis made of m linearly independent vectors. Now, considering a dataset X, a natural question arises: is it possible to reduce ...

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