Principal component analysis on chemical abundances spaces

Continuous-time flows on quotient spaces for principal component analysis

A novel matrix flow for principal or minor component analysis is constructed. The development is based on decompositions of the set of full-rank n× p matrices into orbits of Lie group actions.

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

On Bayesian principal component analysis

A complete Bayesian framework for Principal Component Analysis (PCA) is proposed in this paper. Previous model-based approaches to PCA were usually based on a factor analysis model with isotropic Gaussian noise. This model does not impose orthogonality constraints, contrary to PCA. In this paper, we propose a new model with orthogonality restrictions, and develop its approximate Bayesian soluti...

Principal Component Analysis in Very High-dimensional Spaces

Principal component analysis (PCA) is widely used as a means of dimension reduction for high-dimensional data analysis. A main disadvantage of the standard PCA is that the principal components are typically linear combinations of all variables, which makes the results difficult to interpret. Applying the standard PCA also fails to yield consistent estimators of the loading vectors in very high-...