Extensions of Factor Analysis

This chapter describes shortly the ideas behind factor analysis and how it has been extended. It also describes how the model in this thesis is related to other work in the field.

In factor analysis, regularities in the observations are assumed to be caused by hidden factors or sources. The problem setting in all the factor-analysis like models is to find those factors and the mapping to the data. These models are generative which means that they describe a random process which is thought to have generated the data. Generative models have some useful properties. The learning criterion is easy to formulate and thus includes no heuristics. The models can be combined and their performances can be compared. They also offer a straightforward way to handle missing values.

The data is in this case a collection of real-valued vectors x(t), where $t \in \{1,2,\dots,T\}$ is the time index for the observation. In static analysis, the dependencies between consequent time indices are neglected and the data could be permutated, still giving the same result as opposed to dynamical analysis. The mean of the data is assumed to be a zero vector to simplify the equations.