Sparse canonical correlation analysis from a predictive point of view

Canonical correlation analysis (CCA) describes the associations between two sets of variables by maximizing the correlation between linear combinations of the variables in each data set. However, in high-dimensional settings where the number of variables exceeds the sample size or when the variables are highly correlated, traditional CCA is no longer appropriate. This paper proposes a method for sparse CCA. Sparse estimation produces linear combinations of only a subset of variables from each data set, thereby increasing the interpretability of the canonical variates. We consider the CCA problem from a predictive point of view and recast it into a regression framework. By combining an alternating regression approach together with a lasso penalty, we induce sparsity in the canonical vectors. We compare the performance with other sparse CCA techniques in different simulation settings and illustrate its usefulness on a genomic data set

Robust Sparse Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal correlation. This paper discusses a method for Robust Sparse CCA. Sparse estimation produces canonical vectors with some of their elements estimated as exactly zero. As such, their interpretability is improved. We also robustify the method such that it can cope with outliers in the data. To estimate the canonical vectors, we convert the CCA problem into an alternating regression framework, and use the sparse Least Trimmed Squares estimator. We illustrate the good performance of the Robust Sparse CCA method in several simulation studies and two real data examples

Robust correlated and individual component analysis

© 1979-2012 IEEE.Recovering correlated and individual components of two, possibly temporally misaligned, sets of data is a fundamental task in disciplines such as image, vision, and behavior computing, with application to problems such as multi-modal fusion (via correlated components), predictive analysis, and clustering (via the individual ones). Here, we study the extraction of correlated and individual components under real-world conditions, namely i) the presence of gross non-Gaussian noise and ii) temporally misaligned data. In this light, we propose a method for the Robust Correlated and Individual Component Analysis (RCICA) of two sets of data in the presence of gross, sparse errors. We furthermore extend RCICA in order to handle temporal incongruities arising in the data. To this end, two suitable optimization problems are solved. The generality of the proposed methods is demonstrated by applying them onto 4 applications, namely i) heterogeneous face recognition, ii) multi-modal feature fusion for human behavior analysis (i.e., audio-visual prediction of interest and conflict), iii) face clustering, and iv) thetemporal alignment of facial expressions. Experimental results on 2 synthetic and 7 real world datasets indicate the robustness and effectiveness of the proposed methodson these application domains, outperforming other state-of-the-art methods in the field

Human action recognition with sparse classification and multiple-view learning

Employing multiple camera viewpoints in the recognition of human actions increases performance. This paper presents a feature fusion approach to efficiently combine 2D observations extracted from different camera viewpoints. Multiple-view dimensionality reduction is employed to learn a common parameterization of 2D action descriptors computed for each one of the available viewpoints. Canonical correlation analysis and their variants are employed to obtain such parameterizations. A sparse sequence classifier based on L1 regularization is proposed to avoid the problem of having to choose the proper number of dimensions of the common parameterization. The proposed system is employed in the classification of the Inria Xmas Motion Acquisition Sequences (IXMAS) data set with successful results.Publicad

Relative contributions of lesion location and lesion size to predictions of varied language deficits in post-stroke aphasia

Despite the widespread use of lesion-symptom mapping (LSM) techniques to study associations between location of brain damage and language deficits, the prediction of language deficits from lesion location remains a substantial challenge. The present study examined several factors which may impact lesion-symptom prediction by (1) testing the relative predictive advantage of general language deficit scores compared to composite scores that capture specific deficit types, (2) isolating the relative contribution of lesion location compared to lesion size, and (3) comparing standard voxel-based lesion-symptom mapping (VLSM) with a multivariate method (sparse canonical correlation analysis, SCCAN). Analyses were conducted on data from 128 participants who completed a detailed battery of psycholinguistic tests and underwent structural neuroimaging (MRI or CT) to determine lesion location. For both VLSM and SCCAN, overall aphasia severity (Western Aphasia Battery Aphasia Quotient) and object naming deficits were primarily predicted by lesion size, whereas deficits in Speech Production and Speech Recognition were better predicted by a combination of lesion size and location. The implementation of both VLSM and SCCAN raises important considerations regarding controlling for lesion size in lesion-symptom mapping analyses. These findings suggest that lesion-symptom prediction is more accurate for deficits within neurally-localized cognitive systems when both lesion size and location are considered compared to broad functional deficits, which can be predicted by overall lesion size alone. Keywords: Aphasia, Lesion-symptom prediction, Sparse canonical correlation analysis, Lesion siz

Face image super-resolution using 2D CCA

In this paper a face super-resolution method using two-dimensional canonical correlation analysis (2D CCA) is presented. A detail compensation step is followed to add high-frequency components to the reconstructed high-resolution face. Unlike most of the previous researches on face super-resolution algorithms that first transform the images into vectors, in our approach the relationship between the high-resolution and the low-resolution face image are maintained in their original 2D representation. In addition, rather than approximating the entire face, different parts of a face image are super-resolved separately to better preserve the local structure. The proposed method is compared with various state-of-the-art super-resolution algorithms using multiple evaluation criteria including face recognition performance. Results on publicly available datasets show that the proposed method super-resolves high quality face images which are very close to the ground-truth and performance gain is not dataset dependent. The method is very efficient in both the training and testing phases compared to the other approaches. © 2013 Elsevier B.V

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio