Iteratively Reweighted Least Squares Algorithms for L1-Norm Principal Component Analysis
This work addresses the need for robust PCA methods in data analysis by improving L1-norm PCA, but it is incremental as it builds on existing algorithms with enhanced performance.
The paper tackled the problem of L1-norm principal component analysis (PCA) by proposing exact reweighted and approximate algorithms based on iteratively reweighted least squares, and the computational experiments showed that these algorithms consistently performed best compared to benchmark methods.
Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the fitting error of the reconstructed data, we propose an exact reweighted and an approximate algorithm based on iteratively reweighted least squares. We provide convergence analyses, and compare their performance against benchmark algorithms in the literature. The computational experiment shows that the proposed algorithms consistently perform best.