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.
Efficient algorithm for orthogonal canonical correlation analysis (OCCA).
problem Solving the OCCA problem with orthogonality constraints.
method Sub-maximization problem with self-consistent-field (SCF) iteration for trace-fractional structure and orthogonal linear projections.
result Proposed algorithm converges globally to a KKT point and is more efficient.
BLOCCS improves sparse CCA for better interpretation of multi-omics data.
problem Improving interpretation of multi-omics data.
method Block Sparse Canonical Correlation Analysis (BLOCCS) using a bi-convex objective and gradient descent.
result BLOCCS provides more interpretable solutions with improved orthogonality of sparse directions.
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.
New method speeds up solving orthogonality constrained problems.
problem Solving orthogonality constrained problems efficiently.
method Riemannian optimization and Riemannian preconditioning.
result Preconditioning improves computational costs and convergence.
Canonical correlation analysis was proposed by Hotelling [6] and it measures linear relationship between two multidimensional variables. In high dimensional setting, the classical canonical correlation analysis breaks down. We propose a sparse canonical correlation analysis by adding l1 constraints on the canonical vec…
Canonical correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, canonical correlation analysis has for instance been extended to extract relations between two sets of variables when the sample size is insufficient in relation to the dat…
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.
Proposes ACCA for better alignment of multiple data perspectives.
problem Unclear alignment between multiple data perspectives.
method Iteratively solves alignment and multi-view embedding.
result Improved alignment and embedding of multiple data perspectives.
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…
We introduce three novel semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees. We consider moment matching techniques for estimation in these models. For that, by drawing explicit links between the new models and a discrete version of independent component analysis …
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, inp…
New method for analyzing multiple longitudinal data processes.
problem Exploring associations between multiple random processes observed jointly.
method Functional Generalized Canonical Correlation Analysis (FGCCA) based on multiblock Regularized Generalized Canonical Correlation Analysis (RGCCA).
result FGCCA framework is robust to sparsely and irregularly observed data.
Proposes PSCCA for estimating correlations and canonical correlations in sparse count data.
problem Estimating correlations and canonical correlations in sparse count data from next-generation sequencing.
method Probabilistic approach for sparse count data sets (PSCCA).
result PSCCA outperforms other methods in estimating true correlations and canonical correlations at the natural parameter level.
A new method for real-time CCA on streaming data.
problem Finding correlated features in online data streams.
method Sliding Window Informative Canonical Correlation Analysis (SWICCA) using streaming PCA.
result SWICCA provides real-time CCA components in high dimensions with theoretical guarantees.
A new method estimates conditional canonical correlations using random forests.
problem Estimating relationships between two sets of variables given covariates.
method Random Forest with Canonical Correlation Analysis (RFCCA)
result RFCCA provides accurate canonical correlation estimations and well-controlled Type-1 error.
D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.
Proposes ℓ0-CCA for sparse CCA with improved representation learning.
problem CCA models break with too many variables, and sparsity is beneficial.
method Sparse CCA with stochastic gates and ℓ0-regularization. result Improves representation learning by gating nuisance variables.
Algorithm improves online canonical correlation analysis.
problem Online canonical correlation analysis.
method Stochastic Scaled-Gradient Descent (SSGD) for minimizing expectation over Riemannian manifolds.
result Achieved optimal one-time-scale algorithm with explicit rate of local asymptotic convergence.
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…
A new method scales CCA parameters by input to learn more correlated representations.
problem Limitation of conventional CCA models in learning highly correlated representations.
method Introduces a dynamic scaling method for training input-dependent canonical correlation models.
result Learned representations are more correlated and retrieval results are preferable.
New method relaxes PCA orthogonality constraints using explained variance of correlated components.
problem Difficulty in using PCA for sparse design due to orthogonality constraints and non-differentiable penalty.
method Introduce expvar(Y) to measure variance explained by correlated components, relax orthogonality constraints.
result Two expvar(Y) definitions suitable for block PCA formulations without orthogonality constraints.
New measures link neural representation geometry to decoding ability.
problem Understanding how neural representations relate to decoding ability.
method Showed that popular similarity measures can be interpreted from a decoding perspective.
result Proved that measures like CKA and CCA quantify alignment between optimal linear readouts.
A new model for multiview data analysis using graph autoencoders.
problem Nonlinear multiview canonical correlation analysis for large datasets.
method Variational approach with graph convolutional neural networks.
result Competitive performance on classification, clustering, and recommendation tasks.
Paper proposes ICCN to learn correlations between text, audio, and video for multimodal sentiment analysis.
problem Improving multimodal sentiment analysis by learning hidden correlations between text and audio/video features.
method Interaction Canonical Correlation Network (ICCN) using deep canonical correlation analysis (DCCA).
result Empirical results confirm the effectiveness of ICCN in capturing useful information from all three views.
Given two data matrices X and Y, sparse canonical correlation analysis (SCCA) is to seek two sparse canonical vectors u and v to maximize the correlation between Xu and Yv. However, classical and sparse CCA models consider the contribution of all the samples of data matrices and thus cannot identify an unde…
Two new methods for analyzing repeated measures data using embeddings into Reproducing Kernel Hilbert Spaces.
problem Analyzing complex data structures with multiple features over time.
method Two generalizations of canonical correlation analysis for repeated measures data using embeddings into Reproducing Kernel Hilbert Spaces.
result Consistency rates for transformation and correlation estimators, relaxing common assumptions.
In this paper, we propose a mixture of probabilistic partial canonical correlation analysis (MPPCCA) that extracts the Causal Patterns from two multivariate time series. Causal patterns refer to the signal patterns within interactions of two elements having multiple types of mutually causal relationships, rather than a…
We examine Deep Canonically Correlated LSTMs as a way to learn nonlinear transformations of variable length sequences and embed them into a correlated, fixed dimensional space. We use LSTMs to transform multi-view time-series data non-linearly while learning temporal relationships within the data. We then perform corre…
ORCCA improves CCA performance with randomized features.
problem Improving CCA performance with randomized features.
method Proposes a task-specific scoring rule for selecting random features in CCA.
result ORCCA outperforms Kernel CCA in expectation.
In this paper, we formulate the Canonical Correlation Analysis (CCA) problem on matrix manifolds. This framework provides a natural way for dealing with matrix constraints and tools for building efficient algorithms even in an adaptive setting. Finally, an adaptive CCA algorithm is proposed and applied to a change dete…
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose to quantify the estimation loss…
Paper tackles fairness in CCA by minimizing correlation disparity error.
problem Fairness issues in CCA.
method Framework to minimize correlation disparity error in CCA.
result Reduces correlation disparity error without sacrificing CCA accuracy.
PROD method improves high-dimensional regression by handling strong correlations.
problem Violation of Irrepresentable Condition in LASSO for high-dimensional data.
method PROD procedure based on orthogonal decomposition of design matrix.
result PROD enhances performance of high-dimensional penalized regression.
We propose novel first-order stochastic approximation algorithms for canonical correlation analysis (CCA). Algorithms presented are instances of inexact matrix stochastic gradient (MSG) and inexact matrix exponentiated gradient (MEG), and achieve ε-suboptimality in the population objective in $\operatorname{poly}(\fr…
DICCA maps multi-view data into a shared latent space with interpretable components.
problem Learning from multiple related but distinct data views.
method DICCA extends CCA to deep generative networks and uses sparsity-inducing priors for interpretability.
result DICCA effectively disentangles shared and view-specific variations in multi-view data.
We present an extension of sparse Canonical Correlation Analysis (CCA) designed for finding multiple-to-multiple linear correlations within a single set of variables. Unlike CCA, which finds correlations between two sets of data where the rows are matched exactly but the columns represent separate sets of variables, th…
Paper extends CCA for multiview learning, improving performance.
problem Learning representations across multiple data views.
method Extends CCA to a multiview mixture model with heuristics.
result Improves performance on downstream tasks compared to standard CCA.
A fast feature selection method using OLS and SOCC for classification.
problem Feature selection for linear classification.
method Orthogonal Least Squares (OLS) with Squared Orthogonal Correlation Coefficient (SOCC).
result The proposed method outperforms other feature selection methods in speed and accuracy.
New method for accurate permutation inference in CCA.
problem Inaccurate permutation inference in CCA.
method Proposed solutions for permutation inference in CCA, including transforming residuals and stepwise estimation.
result Valid permutation tests for CCA with and without nuisance variables.
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 correlation. Traditional CCA can only be used to calculate the linear correlation…
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.
We study the sample complexity of canonical correlation analysis (CCA), \ie, the number of samples needed to estimate the population canonical correlation and directions up to arbitrarily small error. With mild assumptions on the data distribution, we show that in order to achieve ε-suboptimality in a properly define…
We propose using canonical correlation analysis (CCA) to generate features from sequences of medical billing codes. Applying this novel use of CCA to a database of medical billing codes for patients with diverticulitis, we first demonstrate that the CCA embeddings capture meaningful relationships among the codes. We th…
Study geodesics on flat tori, focusing on orthogonal lengths and their distribution.
problem Properties of geodesics on flat tori and their lengths.
method Fine study of dynamical correlation function and anisotropic Sobolev spaces.
result Properties of the length distribution and singularities of its Fourier transform.
Efficient algorithm for CCA on Riemannian manifolds with fast convergence.
problem Efficiently computing canonical correlation components on Riemannian manifolds.
method Reparametrization of projection matrices for stochastic optimization on Riemannian manifolds.
result Achieves $O( rac{1}{t})$ convergence rate for top k components with O(d2k) runtime complexity. 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.
New method estimates sparse canonical vectors efficiently.
problem Sparse canonical vectors estimation in CCA.
method Quasi-Bayesian estimation via Rayleigh quotient function.
result Achieves minimax rate with low computational cost.