Related papers: Generalized Canonical Correlation Analysis for Dis…
Classical canonical correlation analysis (CCA) requires matrices to be low dimensional, i.e. the number of features cannot exceed the sample size. Recent developments in CCA have mainly focused on the high-dimensional setting, where the…
Canonical Correlation Analysis (CCA) models are powerful for studying the associations between two sets of variables. The canonically correlated representations, termed \textit{canonical variates} are widely used in unsupervised learning to…
In clinical and biomedical research, multiple high-dimensional datasets are nowadays routinely collected from omics and imaging devices. Multivariate methods, such as Canonical Correlation Analysis (CCA), integrate two (or more) datasets to…
The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling…
We introduce a novel framework for clustering a collection of tall matrices based on their column spaces, a problem we term Subspace Clustering of Subspaces (SCoS). Unlike traditional subspace clustering methods that assume vectorized data,…
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…
Random features approach has been widely used for kernel approximation in large-scale machine learning. A number of recent studies have explored data-dependent sampling of features, modifying the stochastic oracle from which random features…
We aim to analyze the relation between two random vectors that may potentially have both different number of attributes as well as realizations, and which may even not have a joint distribution. This problem arises in many practical…
Linking between two data sources is a basic building block in numerous computer vision problems. In this paper, we set to answer a fundamental cognitive question: are prior correspondences necessary for linking between different domains?…
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…
Tensor canonical correlation analysis (TCCA) has garnered significant attention due to its effectiveness in capturing high-order correlations in multi-view learning. However, existing TCCA methods often underemphasize the characterization…
Linking two data sources is a basic building block in numerous computer vision problems. Canonical Correlation Analysis (CCA) achieves this by utilizing a linear optimizer in order to maximize the correlation between the two views. Recent…
Motivation: Biomedical studies increasingly produce multi-view high-dimensional datasets (e.g., multi-omics) that demand integrative analysis. Existing canonical correlation analysis (CCA) and generalized CCA methods address at most two of…
Canonical correlation analysis (CCA) is a valuable method for interpreting cross-covariance across related datasets of different dimensionality. There are many potential applications of CCA to neuroimaging data analysis. For instance, CCA…
We propose graph canonical coherence analysis (gCChA), a novel framework that extends canonical correlation analysis to multivariate graph signals in the graph frequency domain. The proposed method addresses challenges posed by the inherent…
It is quite common for functional data arising from imaging data to assume values in infinite-dimensional manifolds. Uncovering associations between two or more such nonlinear functional data extracted from the same object across medical…
Blind source separation (BSS) is one of the most important and established research topics in signal processing and many algorithms have been proposed based on different statistical properties of the source signals. For second-order…
Extracting meaningful latent representations from high-dimensional sequential data is a crucial challenge in machine learning, with applications spanning natural science and engineering. We introduce InfoDPCCA, a dynamic probabilistic…
Various new brain-computer interface technologies or neuroscience applications require decoding stimulus-following neural responses to natural stimuli such as speech and video from, e.g., electroencephalography (EEG) signals. In this…
There are a multitude of methods to perform multi-set correlated component analysis (MCCA), including some that require iterative solutions. The methods differ on the criterion they optimize and the constraints placed on the solutions. This…