Scaled Torus Principal Component Analysis

Torus Principal Component Analysis with an Application to RNA Structures

There are several cutting edge applications needing PCA methods for data on tori and we propose a novel torus-PCA method with important properties that can be generally applied. There are two existing general methods: tangent space PCA and geodesic PCA. However, unlike tangent space PCA, our torus-PCA honors the cyclic topology of the data space whereas, unlike geodesic PCA, our torus-PCA produ...

Torus Principal Component Analysis with Applications to Rna Structure

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...

Unsupervised Learning: Self-aggregation in Scaled Principal Component Space

Abstract We demonstrate that data clustering amounts to a dynamic process of self-aggregation in which data objects move towards each other to form clusters, revealing the inherent pattern of similarity. Self-aggregation is governed by connectivity and occurs in a space obtained by a nonlinear scaling of principal component analysis (PCA). The method combines dimensionality reduction with clust...

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...