Related papers: Canonical correlation analysis of high-dimensional…
Recent developments in regularized Canonical Correlation Analysis (CCA) promise powerful methods for high-dimensional, multiview data analysis. However, justifying the structural assumptions behind many popular approaches remains a…
Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…
We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently…
Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA…
Canonical correlation analysis (CCA) has become a key tool for population neuroimaging, allowing investigation of associations between many imaging and non-imaging measurements. As other variables are often a source of variability not of…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Many analyses of multivariate data focus on evaluating the dependence between two sets of variables, rather than the dependence among individual variables within each set. Canonical correlation analysis (CCA) is a classical data analysis…
Investigating the relationships between two sets of variables helps to understand their interactions and can be done with canonical correlation analysis (CCA). However, the correlation between the two sets can sometimes depend on a third…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
Canonical correlation analysis (CCA) is a technique for finding correlations between different data modalities and learning low-dimensional representations. As fairness becomes crucial in machine learning, fair CCA has gained attention.…
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…
Massive data analysis calls for distributed algorithms and theories. We design a multi-round distributed algorithm for canonical correlation analysis. We construct principal directions through the convex formulation of canonical correlation…
Principal Component Analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the…
Multi-view learning (MVL) is a strategy for fusing data from different sources or subsets. Canonical correlation analysis (CCA) is very important in MVL, whose main idea is to map data from different views onto a common space with maximum…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small…
Manifold matching works to identify embeddings of multiple disparate data spaces into the same low-dimensional space, where joint inference can be pursued. It is an enabling methodology for fusion and inference from multiple and massive…
Principal component analysis (PCA) is often used to analyze multivariate data together with cluster analysis, which depends on the number of principal components used. It is therefore important to determine the number of significant…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…
Canonical correlation analysis is a classic well-known multivariate statistical method focusing on the relationships between two sets of variables. The visualisation of those relationships can be achieved by means of a biplot of the…