It is commonly known that many techniques for data analysis based on the least squares criterion are very sensitive to outliers in the data. Gabriel and Odoroff (1984) suggested a resistant approach for lower rank approximation of matrices. In this approach, weights are used to diminish the influence of outliers on the low-dimensional representation. The present paper uses iterative majorization to provide for a general algorithm for such resistant lower rank approximations which guarantees convergence. It is shown that the weights can be chosen in different ways corresponding with different objective functions. Some possible extensions of the algorithm are discussed.
- lower rank approximation
- huber function
- biweight function
Verboon, P., & Heiser, W. (1994). Resistant lower rank approximation of matrices by iterative majorization. Computational Statistics & Data Analysis, 18(4), 457-476. https://doi.org/10.1016/0167-9473(94)90163-5