Kernel principal component analysis (KPCA) provides a concise set of basis vectors which capture nonlinear structures within large data sets, and is a central tool in data analysis and learning. To allow for nonlinear relations, typically a full n ⇥ n kernel matrix is constructed over n data points, but this requires too much space and time for large values of n. Techniques such as the Nyström ...

Principal component analysis (PCA) is widely used in dimensionality reduction. A lot of variants of PCA have been proposed to improve the robustness of the algorithm. However, the existing methods either cannot select the useful features consistently or is still sensitive to outliers, which will depress their performance of classification accuracy. In this paper, a novel approach called joint s...

We propose a subpattern-based principle component analysis (SpPCA). The traditional PCA operates directly on a whole pattern represented as a vector and acquires a set of projection vectors to extract global features from given training patterns. SpPCA operates instead directly on a set of partitioned subpatterns of the original pattern and acquires a set of projection sub-vectors for each part...

This paper discusses principal component analysis (PCA) of integral transforms (spectra and autocovariance functions) of time-domain signals. It is illustrated using acoustic emissions from mechanical equipment. It was found that acoustic signals from different stages of operation appeared as distinct clusters in the PCA analysis. The clusters moved when machinery faults were present and the mo...

Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure o...

In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance of the data. However, PCA has two major weaknesses. Firstly, it only considers linear correlations among variables (features), and secondly it is not suitable...

We consider the problem of finding lower dimensional subspaces in the presence of outliers and noise in the online setting. In particular, we extend previous batch formulations of robust PCA to the stochastic setting with minimal storage requirements and runtime complexity. We introduce three novel stochastic approximation algorithms for robust PCA that are extensions of standard algorithms for...

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; ...

A method for principal component analysis is proposed that is sparse and robust at the same time. The sparsity delivers principal components that have loadings on a small number of variables, making them easier to interpret. The robustness makes the analysis resistant to outlying observations. The principal components correspond to directions that maximize a robust measure of the variance, with...