Factor analysis writes an observation as , where the low-dimensional latent variable describes shared variation. In the isotropic Gaussian model and independently, the observation has covariance .
In factor analysis with one factor and fixed noise variance , let be the current loading vector, , and . The expectation-maximization algorithm update isThe conditional factor means are and their variances are ; maximizing the expected complete-data log-likelihood gives the formula.
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Factor analysis is a statistical method used to identify underlying relationships between variables in a dataset. Its primary goal is to reduce the dimensionality of the data while retaining as much variance as possible. Essentially, factor analysis helps to uncover latent (hidden) factors that can explain the observed correlations among variables. ### Key Components of Factor Analysis: 1. **Variables**: The original observable variables in the dataset (e.g., survey responses, test scores).