Fast Subspace Approximation Via Greedy Least-Squares

Fast Subspace Approximation via Greedy Least-Squares

In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let P ⊂ R be a given set of M points. The techniques developed herein find an O(n logM)-dimensional subspace that is guaranteed to always contain a near-best fit n-dimensional hyperplane H for P with respect to the cumulative projection error (∑ x∈P ‖x−ΠHx‖ p 2 )1...

Fast General Norm Approximation via Iteratively Reweighted Least Squares

This paper describes an efficient method for general norm approximation that appears frequently in various computer vision problems. Such a lot of problems are differently formulated, but frequently require to minimize the sum of weighted norms as the general norm approximation. Therefore we extend Iteratively Reweighted Least Squares (IRLS) that is originally for minimizing single norm. The pr...

Penalized Least Squares Regression: Fast Computation via EÆ ient Approximation

Unified LASSO Estimation via Least Squares Approximation

We propose a method of least squares approximation (LSA) for unified yet simple LASSO estimation. Our general theoretical framework includes ordinary least squares, generalized linear models, quantile regression, and many others as special cases. Specifically, LSA can transfer many different types of LASSO objective functions into their asymptotically equivalent least-squares problems. Thereaft...

Subspace Least Squares Multidimensional Scaling

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and reconstruction of non-rigid shapes. In this regard, MDS can be thought of as a shape from metric algorithm, consisting of finding a configuration of p...