arXiv research

Proposes PSCCA for estimating correlations and canonical correlations in sparse count data.

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…

Proposes $\ell_0$-CCA for sparse CCA with improved representation learning.

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…

Proposes GCCA for detecting latent relations in multiview data with sparse structures.

New method estimates sparse canonical vectors efficiently.

We consider the scenario where one observes an outcome variable and sets of features from multiple assays, all measured on the same set of samples. One approach that has been proposed for dealing with this type of data is ``sparse multiple canonical correlation analysis'' (sparse mCCA). All of the current sparse mCCA t…

We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view…

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…

We introduce Block Sparse Canonical Correlation Analysis which estimates multiple pairs of canonical directions (together a "block") at once, resulting in significantly improved orthogonality of the sparse directions which, we demonstrate, translates to more interpretable solutions. Our approach builds on the sparse CC…

Paper proposes ASCCA for sparse CCA with trace Lasso regularization.

A new approach to the sparse Canonical Correlation Analysis (sCCA)is proposed with the aim of discovering interpretable associations in very high-dimensional multi-view, i.e.observations of multiple sets of variables on the same subjects, problems. Inspired by the sparse PCA approach of Journee et al. (2010), we also s…

Canonical correlation analysis (CCA) is a multivariate statistical technique for finding the linear relationship between two sets of variables. The kernel generalization of CCA named kernel CCA has been proposed to find nonlinear relations between datasets. Despite their wide usage, they have one common limitation that…

New method for analyzing multiple longitudinal data processes.

Given two sets of variables, derived from a common set of samples, sparse Canonical Correlation Analysis (CCA) seeks linear combinations of a small number of variables in each set, such that the induced canonical variables are maximally correlated. Sparse CCA is NP-hard. We propose a novel combinatorial algorithm for s…

Sparse GCA finds linear relationships in multiple datasets, using gradient descent.

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 methods integrate nonlinear, sparse, and multi-view aspects for high-dimensional data analysis.

Canonical Correlation Analysis (CCA) is a classical tool for finding correlations among the components of two random vectors. In recent years, CCA has been widely applied to the analysis of genomic data, where it is common for researchers to perform multiple assays on a single set of patient samples. Recent work has pr…

Sparse Canonical Correlation Analysis (CCA) has received considerable attention in high-dimensional data analysis to study the relationship between two sets of random variables. However, there has been remarkably little theoretical statistical foundation on sparse CCA in high-dimensional settings despite active methodo…

Reducing the number of false discoveries is presently one of the most pressing issues in the life sciences. It is of especially great importance for many applications in neuroimaging and genomics, where datasets are typically high-dimensional, which means that the number of explanatory variables exceeds the sample size…

Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow since it involves implementing QR decomposition or singular value decomposition of h…

Bayesian method improves sparse CCA for multi-view data.

Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as an optimization problem with nonsmooth objective and nonconvex constraints. Sinc…

New method finds linear relationships across multiple data blocks using proximal gradient descent with $\ell_1$ constraint.

Graph Canonical Correlation Analysis improves CCA for multiomics datasets.

A new method estimates conditional canonical correlations using random forests.

Proposes ACCA for better alignment 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…

Paper develops IFTRR to solve sparse generalized eigenvalue problems efficiently.

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…

Approximate inference via information projection has been recently introduced as a general-purpose approach for efficient probabilistic inference given sparse variables. This manuscript goes beyond classical sparsity by proposing efficient algorithms for approximate inference via information projection that are applica…

A new method scales CCA parameters by input to learn more correlated representations.

A new method for real-time CCA on streaming data.

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…

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…

In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue problem and obtain sparse principal component analysis (PCA), sparse canonical cor…

This work discusses the problem of sparse signal recovery when there is correlation among the values of non-zero entries. We examine intra-vector correlation in the context of the block sparse model and inter-vector correlation in the context of the multiple measurement vector model, as well as their combination. Algor…

Regularised canonical correlation analysis was recently extended to more than two sets of variables by the multiblock method Regularised generalised canonical correlation analysis (RGCCA). Further, Sparse GCCA (SGCCA) was proposed to address the issue of variable selection. However, for technical reasons, the variable …

D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.

Two new methods for analyzing repeated measures data using embeddings into Reproducing Kernel Hilbert Spaces.

SAEs struggle with feature consistency across runs, hindering MI reliability.

Algorithm improves online canonical correlation analysis.

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…

Sparse generalized eigenvalue problem (GEP) plays a pivotal role in a large family of high-dimensional statistical models, including sparse Fisher's discriminant analysis, canonical correlation analysis, and sufficient dimension reduction. Sparse GEP involves solving a non-convex optimization problem. Most existing met…

Paper tackles fairness in CCA by minimizing correlation disparity error.

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.