This paper offers a new algebraic perspective of GCCA using subspace intersection.
problem Finding common variables across multiple feature representations.
method Subspace intersection approach based on a (bi-)linear generative model.
result GCCA is equivalent to subspace intersection, with conditions for identifiable common subspace.
D-GCCA improves multi-view data analysis by separating common and distinctive components.
problem Analyzing multi-view high-dimensional data with latent factors.
method Decomposes each view's data matrix into common and distinctive sources with orthogonality constraints.
result Consistent estimators with good performance and efficient computation.
A scalable algorithm for MAX-VAR GCCA with improved performance and structure-promoting regularization.
problem Scalability issues and lack of structural constraints in MAX-VAR GCCA.
method Proposed an alternating optimization (AO) algorithm to handle non-convex MAX-VAR GCCA.
result The algorithm globally converges to a critical point at a sublinear rate and approaches a global optimal solution at a linear rate.
Graph Canonical Correlation Analysis improves CCA for multiomics datasets.
problem Limited ability of conventional CCA methods to incorporate structured patterns in cross-correlation matrices.
method Graph Canonical Correlation Analysis (gCCA) calculates canonical correlations based on the graph structure of cross-correlation matrices.
result gCCA outperforms competing CCA methods in simulations and multiomics dataset analysis.
New framework for large-scale SUMCOR GCCA with structural regularization.
problem Handling large-scale multiview data with structural regularization.
method Structured SUMCOR Multiview GCCA framework with scalable algorithms.
result Proposed algorithm converges to KKT point of regularized SUMCOR problem.
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 disparate data sources. In this paper we focus on a method called Canonical Correla…
Proposes GCCA for detecting latent relations in multiview data with sparse structures.
problem Sparse CCA limitations for multiple datasets.
method Developed a GCCA algorithm based on distributed alternating iteration approach.
result Demonstrated effectiveness on synthetic and real-world datasets.
For multiple multivariate data sets, we derive conditions under which Generalized Canonical Correlation Analysis (GCCA) improves classification performance of the projected datasets, compared to standard Canonical Correlation Analysis (CCA) using only two data sets. We illustrate our theoretical results with simulation…
A novel graph-regularized CCA approach for datasets with a common source graph.
problem Discovering hidden sources in datasets with common geometry.
method Graph regularizer to encode common sources' geometry in CCA.
result Improved classification performance over competing methods.
TGCCA analyzes higher-order tensors using orthogonal rank-R CP decomposition.
problem Handling higher-order structures in multi-block data analysis.
method Tensor Generalized Canonical Correlation Analysis (TGCCA) with orthogonal rank-R CP decomposition.
result TGCCA outperforms state-of-the-art methods on simulated and real data.
A new method for structured variable selection in multiblock analysis.
problem Addressing variable selection issues in multiblock analysis.
method Proposes an extension of Sparse Generalized Canonical Correlation Analysis (SGCCA) to include structural relationships and full RGCCA model.
result Illustrates the method's ability to reconstruct true underlying weight vectors on simulated data.