Tutorial explains various canonical correlation methods.
problem Analyzing paired sets of variables.
method Regularized, kernel, sparse, and Bayesian CCA.
result Comprehensive overview of canonical correlation methods.
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48 results for “Canonical Correlation”
Sparse CCA improves classical CCA for high-dimensional data.
problem High-dimensional data limits classical CCA's effectiveness.
method Sparse CCA with l1 constraints and ADMM for efficient solution.
result Efficiently solved sparse CCA using ADMM and TFOCS.
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 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 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.
Towards Aligned Canonical Correlation Analysis: Preliminary Formulation and Proof-of-Concept Resultscs.LG
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…
SWCCA identifies specific subsets of samples for better correlation analysis.
problem Identify specific subsets of samples contributing to correlation between two data matrices.
method Proposes SWCCA with weights to regularize different samples, solves using alternating iterative algorithm.
result Demonstrates effectiveness and superiority over related methods on synthetic and real-world data.
Deep LSTMs learn correlated representations of time-series data.
problem Learning nonlinear transformations and correlated embeddings of variable-length sequences.
method Use LSTMs to transform multi-view time-series data, then correlate outputs to find a fixed-dimensional representation.
result Deep LSTMs can effectively learn and project correlated representations of time-series data.
Proposes -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 -regularization.
result Improves representation learning by gating nuisance variables.
MPPCCA extracts multiple causal relationships from multivariate time series.
problem Extracting multiple causal relationships from multivariate time series data.
method Mixture of probabilistic partial canonical correlation analysis (MPPCCA) combined with an expectation-maximization (EM) algorithm.
result MPPCCA accurately estimates multiple partial canonical correlations in synthetic and real datasets.
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.
Functional Generalized Canonical Correlation Analysis for studying multiple longitudinal variablesstat.ME
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.
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.
Subspace Perspective on Canonical Correlation Analysis: Dimension Reduction and Minimax Ratesmath.ST
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…
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.
New algorithms improve CCA with stochastic approximation.
problem Efficiently compute canonical correlation analysis.
method Inexact MSG and MEG algorithms for CCA.
result Achieves ε-suboptimality in poly(1/ε) iterations.
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.
Study on estimating CCA with stochastic methods and sample complexity.
problem Estimating canonical correlation and directions from samples.
method Exact and approximate solutions using stochastic optimization and power iterations.
result Achieve optimal alignment with minimal samples and passes.
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…
This paper provides an overview of CCA-based multi-view learning approaches.
problem Fusing data from different sources or subsets.
method Canonical correlation analysis (CCA) for mapping data onto a common space with maximum correlation.
result Overview of many representative CCA-based multi-view learning approaches.
CCA features from medical codes predict future surgeries.
problem Predicting future surgeries based on medical codes.
method Canonical correlation analysis applied to sequences of medical codes.
result CCA embeddings capture meaningful relationships among medical codes.
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.
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.
We introduce canonical correlation forests (CCFs), a new decision tree ensemble method for classification and regression. Individual canonical correlation trees are binary decision trees with hyperplane splits based on local canonical correlation coefficients calculated during training. Unlike axis-aligned alternatives…
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.
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.
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.
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…
Gen-Oja efficiently computes principal vectors and canonical correlations in streaming data.
problem Principal Generalized Eigenvector computation and Canonical Correlation Analysis in stochastic settings.
method Gen-Oja is a simple and efficient algorithm that leverages two-time-scale stochastic approximation and fast-mixing Markov chains.
result Gen-Oja achieves optimal convergence rates for these problems.
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.
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.
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.
Fast feature selection for SHM using canonical correlation.
problem Feature selection for structural health monitoring.
method Greedy search of sum of squared canonical correlation coefficients.
result Extremely fast feature selection with good performance.
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.
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…
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.
Algorithm aligns correlated Erdős-Rényi graphs efficiently.
problem Graph alignment in correlated Erdős-Rényi graphs.
method A canonical labeling algorithm with two steps: degree-based matching and bipartite graph alignment.
result The algorithm succeeds in aligning correlated Erdős-Rényi graphs in a specific time complexity region.
Canonical correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited by its capability of only handling data represented by two-view features, while i…
We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
problem Complex computations for block matrices, especially for covariance and correlation matrices.
method Obtained a canonical representation for block matrices, facilitating computation of various matrix operations.
result Simplified computation of matrix operations for block matrices, particularly useful for covariance and correlation matrices.
Paper presents a new framework for optimal asset and signal combination.
problem Optimal asset and signal combination problem.
method Two-stage approach: reformulate dynamic portfolio selection problem, then use Canonical Correlation Analysis.
result Improved performance of proposed method over natural benchmarks.
Sparse Generalized Canonical Correlation Analysis: Distributed Alternating Iteration based Approachcs.LG
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.
Finding the needle in high-dimensional haystack: A tutorial on canonical correlation analysisstat.ML
CCA helps find hidden connections in complex biomedical data.
problem Analyzing large, multi-variable datasets in biology and medicine.
method Canonical correlation analysis (CCA) for exploring relationships between two sets of variables.
result CCA uncovers essential hidden associations between diverse data types.
Quantum-inspired CCA improves correlation analysis for high-dimensional data.
problem High-dimensional data limits conventional CCA due to time complexity.
method Developed a quantum-inspired CCA (qiCCA) with logarithmic time complexity.
result qiCCA extracts more correlations than linear CCA and is comparable to deep and kernel CCA.
Estimates linear model from noisy covariates and instruments using spectral regularization.
problem Estimating a linear model from many noisy covariates and instruments.
method Two-stage least squares with spectral regularization of canonical correlations.
result Upper and lower bounds on estimation error, proving optimality of the method with noisy data.
DTCCA learns nonlinear transformations of multi-view data for high-order correlation.
problem Learning complex nonlinear transformations of multiple data views.
method Maximizes high-order canonical correlation by jointly learning transformations of each view using a reformulated tensor decomposition.
result DTCCA efficiently handles high-dimensional and large number of views, overcoming scalability issues.
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.