This paper illustrates how canonical correlation analysis can be used for designing efficient visual operators by learning. The approach is highly task oriented and what constitutes the relevant information is defined by a set of examples. The examples are pairs of images displaying a strong dependence in the chosen feature but are otherwise independent. Experimental results are presented illus...

This paper presents an approach that incorporates canonical correlation analysis for monocular 3D face tracking as a rigid object. It also provides the comparison between the linear and the non linear version (kernel) of the CCA. The 3D pose of the face is estimated from observed raw brightness shape-free 2D image patches. A parameterized geometric face model is adopted to crop out and to norma...

We study canonical correlation analysis (CCA) as a stochastic optimization problem. We show that regularized CCA is efficiently PAC-learnable. We give stochastic approximation (SA) algorithms that are instances of stochastic mirror descent, which achieve -suboptimality in the population objective in time poly( 1 , 1 δ , d) with probability 1− δ, where d is the input dimensionality.

A linear, discriminative, supervised technique for reducing feature vectors extracted from image data to a lower-dimensional representation is proposed. It is derived from classical Fisher linear discriminant analysis (LDA) and useful, for example, in supervised segmentation tasks in which high-dimensional feature vector describes the local structure of the image. In general, the main idea of t...

While kernel canonical correlation analysis (CCA) has been applied in many contexts, the convergence of finite sample estimates of the associated functions to their population counterparts has not yet been established. This paper gives a mathematical proof of the statistical convergence of kernel CCA, providing a theoretical justification for the method. The proof uses covariance operators defi...

In this paper, we propose the canonical correlation kernel (CCK), that seamlessly integrates the advantages of lower dimensional representation of videos with a discriminative classifier like SVM. In the process of defining the kernel, we learn a low-dimensional (linear as well as nonlinear) representation of the video data, which is originally represented as a tensor. We densely compute featur...

We have recently developed several ways of performing Canonical Correlation Analysis [1, 5, 7, 4] with probabilistic methods rather than the standard statistical tools. However, the computational demands of training such methods scales with the square of the number of samples, making these methods uncompetitive with e.g. artificial neural network methods [3, 2]. In this paper, we examine a rece...

We derive a new method of performing Canonical Correlation Analysis with Artiicial Neural Networks. We demonstrate its capability on a simple artiicial data set and then on a real data set where the results are compared with those achieved with standard statistical tools. We then extend the method to deal with a situation where there are two equal competing correlations within the datasets and ...

We consider two stochastic process methods for performing canonical correlation analysis (CCA). The first uses a Gaussian Process formulation of regression in which we use the current projection of one data set as the target for the other and then repeat in the opposite direction. The second uses a Dirichlet process of Gaussian models where the Gaussian models are determined by Probabilistic CC...

CCA is a powerful tool for analyzing paired multi-view data. However, when facing semi-paired multi-view data which widely exist in real-world problems, CCA usually performs poorly due to its requirement of data pairing between different views in nature. To cope with this problem, we propose a semi-paired variant of CCA named SemiPCCA based on the probabilistic model for CCA. Experiments with a...