Jack of all trades, Master of None: The trade-offs in sparse PCA methods for diverse purposes

Sparse algorithms are becoming increasingly popular in data science research because they can identify and select the most relevant variables in a dataset while minimizing overfitting. However, sparse algorithms present unique challenges when dealing with social data, such as data integration (heterogeneity) and the need to account for complex social interactions and dynamics. Throughout this thesis, I focused on researching the sparse Principal Component Analysis (sPCA) problem. I have explored and developed sPCA algorithms that can effectively identify and select the essential features in a dataset, reducing its dimensionality or underlying factors in the data. Specifically, I examined sPCA methods that utilize sparsity-inducing penalties and cardinality constraints to achieve sparsity in the solution.