This paper proposes three feature extraction (FE) methods based on density estimation for hyperspectral images (HSIs). The methods are a mixture of factor analyzers (MFA), deep MFA (DMFA), and supervised MFA (SMFA). The MFA extends the Gaussian mixture model to allow a low-dimensionality representation of the Gaussians. DMFA is a deep version of MFA and consists of a two-layer MFA, i.e, samples from the posterior distribution at the first layer are input to an MFA model at the second layer. SMFA consists of single-layer MFA and exploits labeled information to extract features of HSI effectively. Based on these three FE methods, the paper also proposes a framework that automatically extracts the most important features for classification from an HSI. The overall accuracy of a classifier is used to automatically choose the optimal number of features and hence performs dimensionality reduction (DR) before HSI classification. The performance of MFA, DMFA, and SMFA FE methods are evaluated and compared to five different types of unsupervised and supervised FE methods by using four real HSIs datasets.