Sets Of Multidimensional Variables Research Articles

Spatio-Spectral CCA (SS-CCA): A novel approach for frequency recognition in SSVEP-based BCI

BackgroundSteady-state visually evoked potentials (SSVEP) are one of the most important paradigms in the BCI Domain. Among the best methods for detecting frequency in the SSVEP-based BCI is the Canonical Correlation Analysis (CCA), which calculates canonical correlation between two sets of multidimensional variables, the electroencephalogram (EEG) and reference signals. Despite its efficiency and widespread application, CCA algorithm has some limitations. One major limitation of CCA is to only consider the spatial domain information of the signal. New methodHowever, regarding frequency of signal as another critical feature of the signals, combining both spatial and frequency domain information can significantly improve the performance of frequency recognition. Although several previous studies about CCA algorithm, could improve its performance, they have not addressed CCA algorithm's limitation. To address this concern, in the current study, we presented Spatio-Spectral CCA (SS-CCA) algorithm, which is inspired from Common Spatio-Spectral Patterns (CSSP) algorithm. In the SS-CCA algorithm, we added a time delay to the EEG signal, in order to simultaneously optimize spatial and frequency information and obtain the canonical variables. Accordingly, for correlation coefficient’s calculations, more information from EEG signal is utilized. ResultsFinally, SS-CCA algorithm which is used as the base model of Filter Bank CCA (FBCCA), and Filter Bank SS-CCA algorithms, can help increase the frequency recognition performance. In order to evaluate the proposed method, 35-subject benchmark dataset were used. Proposed algorithm yielded mean accuracy 98.33 across all subjects. Comparison with existing methodsOur classification accuracy and Information Transfer Rate (ITR) results showed that the performance of the above-mentioned method improves in comparison to the CCA. ConclusionsIn conclusion, using the proposed SS-CCA algorithm instead of the CCA, in all our experiments the CCA-based methods were improved.

SA26 - SPARSE CANONICAL CORRELATION IN APPLICATION TO BIPOLAR PSYCHOTIC PHENOTYPES AND SCHIZOPHRENIA GENOME-WIDE SIGNIFICANT GENETIC LOCI

Background The aetiology of Bipolar Disorder (BD) and Schizophrenia (SZ) involves a complex gene-environment interplay and this involves common risk alleles that are shared across the disorders. Bipolar disorder is heterogeneous in presentation and we and others have postulated that the particular clinical presentation is in part determined by the particular risk alleles carried. To investigate this, we have employed sparse Canonical Correlation Analysis (sCCA), to seek patterns of correlation between psychotic symptoms and schizophrenia risk alleles in a large (N=3903) deeply phenotyped sample of subjects with BD. Methods Canonical Correlation Analysis (CCA) seeks linear relationships between two sets of multi-dimensional variables. In the psychiatric genetics field, this approach can be adapted to enable the analysis of both phenotype and genetic variables in one framework. This has the advantage of minimizing the number of statistical tests required. A recent extension of CCA to sparse canonical correlation analysis (sCCA) allows application of the general approach to high dimensional genomic data (Witten et al., 2009). sCCA has advantages compared to CCA in terms of precision of parameter estimates and statistical power. We employed sCCA to analyse 30 psychotic symptoms assessed with the OPerational CRITeria checklist (OPCRIT) and 82 independent genome-wide significant SNPs that were identified by the SZ PGC2 study (The Psychiatric Genomics Consortium, 2014) for which we had data in our BD sample. We applied the sCCA as a purely data driven approach to individual OPCRIT psychotic symptoms and also to groups of OPCRIT psychotic symptoms (“positive”, “negative”, “disorganised”) defined by a previously published factor analysis study of schizophrenia. Results sCCA analysis of the individual OPCRIT items with the set of significantly associated with SZ 82 sCCA analysis based on individual psychotic symptoms revealed a significant association (p=0.045) with the largest weights attributed to delusions of influence, bizarre behaviour and grandiose delusions and an indel SNP on chromosome 3 (3:180594593, build 37). sCCA analysis on the same set of SNPs and OPCRIT symptom groups confirmed association with the same SNP and the “disorganised” group of OPCRIT symptoms (p=0.01). The results also show significant association when we use less stringent p-value thresholds in SZ. In this case the most heavily weighted SNP remains 3:180594593, but other SNPs also contribute to the analysis. Discussion Our results suggest the CCA canonical correlation approach might be a useful tool to explore phenotype-genotype relationships. It can be applied to generate data-driven hypotheses with the potential to provide further insights into the complex architecture of psychiatric disorders. To the best of our knowledge, this is the first study to apply this approach in analysing phenotypes and genotypes together. sCCA offers the potential to be extended to include a larger number of fine grained systematic descriptors of BD, and for testing for correlation with genetic profiles from other co-morbid disorders.

Robust kernel canonical correlation analysis with applications to information retrieval

Canonical correlation analysis (CCA) is a powerful statistical tool quantifying correlations between two sets of multidimensional variables. CCA cannot detect nonlinear relationship, and it is costly to derive canonical variates for high-dimensional data. Kernel CCA, a nonlinear extension of the CCA method, can efficiently exploit nonlinear relations and reduce high dimensionality. However, kernel CCA yields the so called over-fitting phenomenon in the high-dimensional feature space. To handle the shortcomings of kernel CCA, this paper develops a novel robust kernel CCA algorithm (KCCA-ROB). The derived method begins with reformulating the traditional generalized eigenvalue–eigenvector problem into a new framework. Under this novel framework, we develop a stable and fast algorithm by means of singular value decomposition (SVD) method. Experimental results on both a simulated dataset and real-world datasets demonstrate the effectiveness of the developed method.

Sparse and smooth canonical correlation analysis through rank-1 matrix approximation

Canonical correlation analysis (CCA) is a well-known technique used to characterize the relationship between two sets of multidimensional variables by finding linear combinations of variables with maximal correlation. Sparse CCA and smooth or regularized CCA are two widely used variants of CCA because of the improved interpretability of the former and the better performance of the later. So far, the cross-matrix product of the two sets of multidimensional variables has been widely used for the derivation of these variants. In this paper, two new algorithms for sparse CCA and smooth CCA are proposed. These algorithms differ from the existing ones in their derivation which is based on penalized rank-1 matrix approximation and the orthogonal projectors onto the space spanned by the two sets of multidimensional variables instead of the simple cross-matrix product. The performance and effectiveness of the proposed algorithms are tested on simulated experiments. On these results, it can be observed that they outperform the state of the art sparse CCA algorithms.

Kernel canonical correlation analysis via gradient descent

Kernel canonical correlation analysis (CCA) is a powerful statistical tool characterizing nonlinear relations between two sets of multidimensional variables. It has been widely used in many branches of science and technology, e.g. bioinfomatics, multi-media information retrieval, cross-language document retrieval, fMRI (functional magnetic resonance imaging). Previous algorithms focus on sparsity analysis of kernel CCA. In this paper, from another viewpoint, we address a new gradient descent kernel CCA algorithm, which is based on the relation between kernel CCA and linear systems of equations. Meanwhile, stability analysis of the algorithm is addressed by means of suitable error decomposition formula and compact operator theory. Theoretical analysis is elegantly investigated in terms of choices of regularization parameter and step size. Experimental results on real-world datasets demonstrate the effectiveness of the algorithm for content-based image retrieval task. The results indicate that the proposed algorithm is stable and the performance is comparable with several state-of-the-art CCA algorithms.

Complete canonical correlation analysis with application to multi-view gait recognition

Canonical correlation analysis (CCA) is a well-known multivariate analysis method for quantifying the correlations between two sets of multidimensional variables. However, for multi-view gait recognition, it is difficult to directly apply CCA to deal with two sets of high-dimensional vectors because of computational complexity. Moreover, in such situation, the eigenmatrix of CCA is usually singular which makes the direct implementation of the CCA algorithm almost impossible. In practice, PCA or singular value decomposition is employed as a preprocessing step to solve these problems. Nevertheless, this strategy may discard dimensions that contain important discriminative information and correlation information. To overcome the shortcomings of CCA when dealing with two sets of high-dimensional vectors, we develop a novel method, named complete canonical correlation analysis (C3A). In our method, we first reformulate the traditional CCA so that we can avoid the computing of the inverse of a high-dimensional matrix. With the help of this reformulation, C3A further transforms the singular generalized eigensystem computation of CCA into two stable eigenvalue decomposition problems. Moreover, a feasible and effective method is proposed to alleviate the computational burden of high dimensional matrix for typical gait image data. Experimental results on two benchmark gait databases, CASIA gait database and the challenge USF gait database, demonstrate the effectiveness of the proposed method.

Canonical correlation analysis for gene-based pleiotropy discovery.

Genome-wide association studies have identified a wealth of genetic variants involved in complex traits and multifactorial diseases. There is now considerable interest in testing variants for association with multiple phenotypes (pleiotropy) and for testing multiple variants for association with a single phenotype (gene-based association tests). Such approaches can increase statistical power by combining evidence for association over multiple phenotypes or genetic variants respectively. Canonical Correlation Analysis (CCA) measures the correlation between two sets of multidimensional variables, and thus offers the potential to combine these two approaches. To apply CCA, we must restrict the number of attributes relative to the number of samples. Hence we consider modules of genetic variation that can comprise a gene, a pathway or another biologically relevant grouping, and/or a set of phenotypes. In order to do this, we use an attribute selection strategy based on a binary genetic algorithm. Applied to a UK-based prospective cohort study of 4286 women (the British Women's Heart and Health Study), we find improved statistical power in the detection of previously reported genetic associations, and identify a number of novel pleiotropic associations between genetic variants and phenotypes. New discoveries include gene-based association of NSF with triglyceride levels and several genes (ACSM3, ERI2, IL18RAP, IL23RAP and NRG1) with left ventricular hypertrophy phenotypes. In multiple-phenotype analyses we find association of NRG1 with left ventricular hypertrophy phenotypes, fibrinogen and urea and pleiotropic relationships of F7 and F10 with Factor VII, Factor IX and cholesterol levels.

Sparse Canonical Correlation Analysis: New Formulation and Algorithm

In this paper, we study canonical correlation analysis (CCA), which is a powerful tool in multivariate data analysis for finding the correlation between two sets of multidimensional variables. The main contributions of the paper are: 1) to reveal the equivalent relationship between a recursive formula and a trace formula for the multiple CCA problem, 2) to obtain the explicit characterization for all solutions of the multiple CCA problem even when the corresponding covariance matrices are singular, 3) to develop a new sparse CCA algorithm, and 4) to establish the equivalent relationship between the uncorrelated linear discriminant analysis and the CCA problem. We test several simulated and real-world datasets in gene classification and cross-language document retrieval to demonstrate the effectiveness of the proposed algorithm. The performance of the proposed method is competitive with the state-of-the-art sparse CCA algorithms.

Local CCA alignment and its applications

Canonical correlation analysis (CCA) is a well-known technique for finding the correlations between two sets of multi-dimensional variables. It projects both sets of variables into a lower-dimensional space in which they are maximally correlated. One popular use of CCA is for dimensionality reduction. CCA can be regarded as a linear subspace approach for one view of an object set (e.g. X) which is directed by another view of the object set (e.g. Y). However, if the correlations between X and Y are nonlinear, CCA may fail to reveal the latent structures of X. In this paper, we propose a new nonlinear dimensionality reduction algorithm, called local canonical correlation analysis alignment (LCCA). In LCCA, CCA is implemented on patches of an object set to get the local low-dimensional coordinates of Xp (Xp is a patch of X), then the local coordinates are aligned to obtain the global low-dimensional embeddings of X. Furthermore, in order to solve out-of-sample problems, a linear version of LCCA (LLCCA) algorithm is also developed. Different from LCCA, LLCCA is not only suitable for training samples but also for testing samples. Experiments for data visualization and pose estimation show that LCCA and LLCCA are superior to the related algorithms.

A gene-based test of association using canonical correlation analysis

Canonical correlation analysis (CCA) measures the association between two sets of multidimensional variables. We reasoned that CCA could provide an efficient and powerful approach for both univariate and multivariate gene-based tests of association without the need for permutation testing. Compared with a commonly used permutation-based approach, CCA (i) is faster; (ii) has appropriate type-I error rate for normally distributed quantitative traits; (iii) provides comparable power for small to medium-sized genes (<100 kb); (iv) provides greater power when the causal variants are uncommon; (v) provides considerably less power for larger genes (≥100 kb) when the causal variants have a broad minor allele frequency (MAF) spectrum. Application to a GWAS of leukocyte levels identified SAFB and a histone gene cluster as novel putative loci harboring multiple independent variants regulating lymphocyte and neutrophil counts.

Canonical Correlation Analysis for Multilabel Classification: A Least-Squares Formulation, Extensions, and Analysis

Canonical Correlation Analysis (CCA) is a well-known technique for finding the correlations between two sets of multidimensional variables. It projects both sets of variables onto a lower-dimensional space in which they are maximally correlated. CCA is commonly applied for supervised dimensionality reduction in which the two sets of variables are derived from the data and the class labels, respectively. It is well-known that CCA can be formulated as a least-squares problem in the binary class case. However, the extension to the more general setting remains unclear. In this paper, we show that under a mild condition which tends to hold for high-dimensional data, CCA in the multilabel case can be formulated as a least-squares problem. Based on this equivalence relationship, efficient algorithms for solving least-squares problems can be applied to scale CCA to very large data sets. In addition, we propose several CCA extensions, including the sparse CCA formulation based on the 1-norm regularization. We further extend the least-squares formulation to partial least squares. In addition, we show that the CCA projection for one set of variables is independent of the regularization on the other set of multidimensional variables, providing new insights on the effect of regularization on CCA. We have conducted experiments using benchmark data sets. Experiments on multilabel data sets confirm the established equivalence relationships. Results also demonstrate the effectiveness and efficiency of the proposed CCA extensions.