Does PCA assume Gaussian distribution?
PCA doesn’t assume the dataset to be Gaussian distributed.
Are principal components statistically independent?
In contrary to PCA, ICA identifies non-Gaussian components which are modelled as a linear combination of the biological features. These components are statistically independent, i.e. there is no overlapping information between the components.
Do you need normal distribution for PCA?
The data needs not be normally distributed but linear to use PCA.
Do you need to assume Gaussian distribution for PCA?
Assuming that the dataset is Gaussian distributed would guarantee that the PCs are independent. Most of the sources I have found (e.g. wikipedia) don’t list Gaussian distribution as a requirement of PCA. I found 2 more versions of Shlens’ tutorial: version 2 and version 3.02.
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.
Which is the formula for multivariate Gaussian density?
To get an intuition for what a multivariate Gaussian is, consider the simple case where n = 2, and where the covariance matrix Σ is diagonal, i.e., x = x1 x2 µ = µ1 µ2 Σ = σ2 1 0 0 σ2 2 In this case, the multivariate Gaussian density has the form, p(x;µ,Σ) = 1 2π σ2 1 0 0 σ2 2 1/2 exp − 1 2 x1 −µ1 x2 −µ2 T σ2 1 0 0 σ2 2 −1 x1 −µ1 x2 −µ2 ! = 1 2π(σ2
Which is the only probability distribution fully described by the variance?
The formalism of sufficient statistics captures the notion that the mean and the variance entirely describe a probability distribution. The only zero-mean probability distribution that is fully described by the variance is the Gaussian distribution. In order for this assumption to hold, the probability distribution of x i must be Gaussian.