标签：EM Analysis mu 算法 因子分析 Factor mathcal Sigma sim

Factor Analysis

目录

• Factor Analysis
  • Background
  • Marginal and Conditional Distribution of Gaussian
  • Factor Analysis Model

Background

when m (number of samples) < n (dimension of samples), the covariance matrix might be singular. So it is necessary to find a way without having to fit a full covariance matrix.

Marginal and Conditional Distribution of Gaussian

\[x = [x1,x2]^T \]

\(x \sim \mathcal{N}(\mu,\Sigma)\)

marginal distribution \(x_1 \sim \mathcal{N}(\mu_1,\Sigma_{11})\)

conditional distribution $x_1|x_2 \sim \mathcal{N}(\mu_{1|2},\Sigma_{1|2}) $ and

\[\mu_{1|2} = \mu_1 + \Sigma_{12}\Sigma_{22}^{-1}(x_2-\mu_2) \\ \Sigma_{1|2}=\Sigma_{11}-\Sigma_{12}\Sigma_{22}^{-1}\Sigma_{21} \]

Factor Analysis Model

\[z \sim \mathcal{N}(0,I) \\ x|z \sim \mathcal{N}(\mu+\Lambda z,\Psi) \]

标签：EM,Analysis,mu,算法,因子分析,Factor,mathcal,Sigma,sim
From： https://www.cnblogs.com/BUAA-Stargazer/p/16617340.html