Multi-Level Canonical Correlation Analysis for Standard-Dose PET Image Estimation

A Multi-level Canonical Correlation Analysis Scheme for Standard-Dose PET Image Estimation

Multi-View Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a method for finding linear relations between two multidimensional random variables. This paper presents a generalization of the method to more than two variables. The approach is highly scalable, since it scales linearly with respect to the number of training examples and number of views (standard CCA implementations yield cubic complexity). The method i...

Minimax Estimation in Sparse Canonical Correlation Analysis

Canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables. This paper considers the problem of estimating the leading canonical correlation directions in high dimensional settings. Recently, under the assumption that the leading canonical correlation directions are sparse, various procedures have been proposed for...

Multi-view Regression Via Canonical Correlation Analysis

In the multi-view regression problem, we have a regression problem where the input variable (which is a real vector) can be partitioned into two different views, where it is assumed that either view of the input is sufficient to make accurate predictions — this is essentially (a significantly weaker version of) the co-training assumption for the regression problem. We provide a semi-supervised ...

Supplement to “minimax Estimation in Sparse Canonical Correlation Analysis”

In this appendix, we prove Theorem 4 and Lemmas 7 – 12 in order. A.1. Proof of Theorem 4. We first need a lemma for perturbation bound of square root matrices. Lemma 16. Let A, B be positive semi-definite matrices, and then for any unitarily invariant norm ï¿¿·ï¿¿, ï¿¿A 1/2 − B 1/2 ï¿¿ ≤ 1 σ min (A 1/2) + σ min (B 1/2) ï¿¿A − Bï¿¿. Proof. The proof essentially follows the idea of [27]. Let D = ...