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...

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...

'Kernel' principal component analysis (PCA) is an elegant nonlinear generalisation of the popular linear data analysis method, where a kernel function implicitly defines a nonlinear transformation into a feature space wherein standard PCA is performed. Unfortunately, the technique is not 'sparse', since the components thus obtained are expressed in terms of kernels associated with every trainin...

Principal component analysis (PCA) is a popular dimensionality reduction algorithm. However, it is not easy to interpret which of the original features are important based on the principal components. Recent methods improve interpretability by sparsifying PCA through adding an L1 regularizer. In this paper, we introduce a probabilistic formulation for sparse PCA. By presenting sparse PCA as a p...

1. Preliminaries Theorem A-1. (Theorem 3.1, (Chang, 2012)) Let A ∈ Rm×n be of full column rank with QR factorization A = QR, ∆A be a perturbation in A, and A + ∆A = (Q + ∆Q)(R + ∆R) be the QR-factorization of A + ∆A. Let PA and PA⊥ be the orthogonal projectors onto the range of A and the orthogonal complement of the range of A, respectively. LetQ⊥ be an orthonormal matrix such that matrix [Q,Q⊥...