Schrödinger principal-component analysis: On the duality between principal-component analysis and the Schrödinger equation

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...

Compression of Breast Cancer Images By Principal Component Analysis

The principle of dimensionality reduction with PCA is the representation of the dataset ‘X’in terms of eigenvectors ei ∈ RN  of its covariance matrix. The eigenvectors oriented in the direction with the maximum variance of X in RN carry the most      relevant information of X. These eigenvectors are called principal components [8]. Ass...

Compression of Breast Cancer Images By Principal Component Analysis

The principle of dimensionality reduction with PCA is the representation of the dataset ‘X’in terms of eigenvectors ei ∈ RN  of its covariance matrix. The eigenvectors oriented in the direction with the maximum variance of X in RN carry the most      relevant information of X. These eigenvectors are called principal components [8]. Ass...

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...