ON CONSTRAINED PRINCIPAL COMPONENT ANALYSIS

Constrained generalised principal component analysis

Generalised Principal Component Analysis (GPCA) is a recently devised technique for fitting a multicomponent, piecewise-linear structure to data that has found strong utility in computer vision. Unlike other methods which intertwine the processes of estimating structure components and segmenting data points into clusters associated with putative components, GPCA estimates a multi-component stru...

Cone-Constrained Principal Component Analysis

Estimating a vector from noisy quadratic observations is a task that arises naturally in many contexts, from dimensionality reduction, to synchronization and phase retrieval problems. It is often the case that additional information is available about the unknown vector (for instance, sparsity, sign or magnitude of its entries). Many authors propose non-convex quadratic optimization problems th...

Ela Optimal Subspaces and Constrained Principal Component Analysis

The main result of this article allows formulas of analytic geometry to be elegantly unified, by readily providing parametric as well as cartesian systems of equations. These systems characterize affine subspaces in Rp passing through specified affine subspaces of lower dimension. The problem solved is closely related to constrained principal component analysis. A few interesting applications a...

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...

Tutorial on Principal Component Analysis