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Can anyone describe what is the the factor that make principal component analysis widely used for dimensional reduction?

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The other reason not covered by @Kant is that the principal components are orthogonal. This is important because there are infinite many possible ways to create a new transformation otherwise.

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  • $\begingroup$ Thank You @Student T for your answer.. Why it is important on orthogonal component? Do have any notes regarding this so i can learn about this. $\endgroup$ – bbadyalina Dec 21 '16 at 6:32
  • $\begingroup$ @bbadyalina Read any book about PCA. You'd need orthogonal to extract as much information (or variance) as possible with each axis. This is useful for dimensional reduction because you want your first principal component take up the most variance. $\endgroup$ – HelloWorld Dec 21 '16 at 6:33
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The intuitive answer is that when you want to reduce the number of dimensions you wish to preserve as much information as possible from the original dataset. The information metric that we are most interested in preserving is the extent of variation present in the dataset. PCA attempts to preserve the variation by choosing the new dimensions such that the amount of variation preserved is the maximum.

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  • $\begingroup$ Thank You @Kant for your answer, other than that is there any other benefit using PCA in dimensionality reduction? $\endgroup$ – bbadyalina Dec 21 '16 at 3:45

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