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Does PCA assume normal distribution?
No, it is NOT true that the basis of PCA uses an assumption that the data are normally distributed. PCA is based on the ideas of linear-relationships or linear combinations, and of variances and correlations.
Are principal components Gaussian?
PCA has different interpretations and different applications. In this paradigm, since the original r.v.’s are Gaussian distributed, their linear combinations will also be Gaussian distributed, and uncorrelated principal components will also be independent.
Does PCA assume independence?
When you apply PCA to the matrix, the variables could be correlated, however the observations should be independent! This is why for time course data, people usually apply function PCA instead.
How does the PCA compare to the Gaussian dataset?
Suppose I have two datasets, “A” and “B”, where “A” corresponds to randomly sampled points taken from a Gaussian, while “B” corresponds to points randomly sampled from another distribution (say Poisson). How does the PCA (A) compare to the PCA (B)?
When does PCA assume normal distribution of features?
PCA does assume normal distribution of features See p.55 SAS book 1 or Rummel, 1970 2 or Mardia, 1979 3. If you expect the PCs to be independent, then PCA might fail to live to your expectations.
How does PCA guarantee that the PCs are independent?
Thus, under the assumption that the original dataset is Gaussian distributed, PCA guarantees that the PCs are independent. Someone correct me if I’m wrong, but the PCA process itself doesn’t assume anything about the distribution of your data. The PCA algorithm is simple –
When does a PCA fail in a skewed distribution?
But it can fail when we consider skewed or asymmetric distributions. Now recall that PCA tries to maximize the variance in the projected dimension. If X is normal, then X w is still normal, i.e. still symmetric and variance works well. But if X is not normal, like Poisson, the variance of X w need not be very descriptive.