Semi-sparse PCA

Area of Science:

• Multivariate statistics
• Data analysis

Background:

• Exploratory Factor Analysis (EFA) often faces factor indeterminacy when observations exceed variables.
• Understanding and mitigating this indeterminacy is crucial for reliable data interpretation.

Purpose of the Study:

• To investigate new aspects of factor indeterminacy in EFA.
• To propose an alternative model for EFA estimation that results in determinate factors.

Main Methods:

• Considering EFA as a data matrix decomposition.
• Developing a new estimation approach and characterizing factor indeterminacy.
• Proposing a novel model akin to semi-sparse Principal Component Analysis (PCA).
• Implementing an alternating algorithm involving Procrustes problems.

Main Results:

• The new model provides determinate factors, unlike classical EFA.
• The model demonstrates versatility, acting as sparse PCA and low-rank-plus-sparse decomposition.
• Numerical examples confirm the model's performance and behavior on large datasets.

Conclusions:

• The proposed model offers a robust solution to factor indeterminacy in EFA.
• This approach enhances data analysis capabilities through its connection to sparse PCA and matrix decomposition.