Modified “Rule N” Procedure for Principal Component (EOF) Truncation

Approximation of N-Way Principal Component Analysis for Organ Data

We apply multilinear principal component analysis to dimension reduction and classification of human volumetric organ data, which are expressed as multiway array data. For the decomposition of multiway array data, tensor-based principal component analysis extracts multilinear structure of the data. We numerically clarify that low-pass filtering after the multidimensional discrete cosine transfo...

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...

A modified principal component technique based on the LASSO

Sketching for Principal Component Regression

Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large scale data. In this paper, we propose efficient algorithms for computing approximate PCR solutions that are, on one hand, high quality approximations to the...

DUAL PRINCIPAL COMPONENT PURSUIT Dual Principal Component Pursuit

We consider the problem of outlier rejection in single subspace learning. Classical approaches work with a direct representation of the subspace, and are thus efficient when the subspace dimension is small. Our approach works with a dual representation of the subspace and hence aims to find its orthogonal complement; as such it is particularly suitable for high-dimensional subspaces. We pose th...