Principal Component Projection with Low-Degree Polynomials

Principal Component Projection Without Principal Component Analysis

We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal component analysis (PCA), our algorithm is the first with no runtime dependen...

Projection techniques for nonlinear principal component analysis

Sparse Principal Component Analysis via Variable Projection

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis. We discuss a robust and scalable algorithm for computing sparse principal component analysis. Specifically, we model SPCA as a matrix factorization problem with orthogonality constraints, and develop specialized optimization algorithms that partially minimize a subset of the variables (varia...

Robust Principal Component Analysis by Projection Pursuit

Different algorithms for principal component analysis (PCA) based on the idea of projection pursuit are proposed. We show how the algorithms are constructed, and compare the new algorithms with standard algorithms. With the R implementation pcaPP we demonstrate the usefulness at real data examples. Finally, it will be outlined how the algorithms can be used for robustifying other multivariate m...

Testing Low-Degree Polynomials over

We describe an efficient randomized algorithm to test if a given binary function is a low-degree polynomial (that is, a sum of low-degree monomials). For a given integer and a given real , the algorithm queries at !" # points. If is a polynomial of degree at most , the algorithm always accepts, and if the value of has to be modified on at least an fraction of all inputs in order to transform it...