Well-Known Incremental PCA Algorithm

The article introduces a well-known incremental PCA approach, which serves as an efficient dimensionality reduction technique that obtains principal components incrementally. Unlike conventional PCA methods, incremental PCA can update principal component analysis results as new data arrives without recalculating the entire dataset. This method proves particularly valuable for large-scale datasets as it significantly reduces computational time and storage requirements. The implementation typically involves maintaining a covariance matrix approximation and updating it using efficient rank-one updates or singular value decomposition (SVD) techniques. Algorithmically, it processes data chunks sequentially while preserving the eigenspace structure through methods like weighted covariance updates or online SVD. As such, it has found extensive applications in machine learning pipelines, image processing systems, and natural language processing frameworks where streaming data handling is crucial.