In the paper Factor Analysis (FA) and Nuisance Attribute Projection (NAP) are reviewed, analyzed and compared. Since nowadays FA become a part of most state-of-the-art recognition systems (used e.g. in the concept of i-vectors or PLDA models) it is of relevance to examine different insights into the problem. NAP was chosen as a counterpart to FA as an advanced PCA like method often utilized in speaker recognition systems along with FA. It is demonstrated how can be both FA and NAP expressed as solutions of Least Squares (LS), the consequences of the LS formulation are discussed, and it is shown in what extent does the solutions of NAP and FA overlap.

Index Terms: NAP, FA, PCA, least squares