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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…

Modern biomedical studies often collect multi-view data, that is, multiple types of data measured on the same set of objects. A popular model in high-dimensional multi-view data analysis is to decompose each view's data matrix into a…

Canonical correlation analysis investigates linear relationships between two sets of variables, but often works poorly on modern data sets due to high-dimensionality and mixed data types such as continuous, binary and zero-inflated. To…

When working with large biological data sets, exploratory analysis is an important first step for understanding the latent structure and for generating hypotheses to be tested in subsequent analyses. However, when the number of variables is…

In high-dimensional settings, Canonical Correlation Analysis (CCA) often fails, and existing sparse methods force an untenable choice between computational speed and statistical rigor. This work introduces a fast and provably consistent…

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)…

Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements,…

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…

We present Deep Generalized Canonical Correlation Analysis (DGCCA) -- a method for learning nonlinear transformations of arbitrarily many views of data, such that the resulting transformations are maximally informative of each other. While…

We propose a new technique, Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and…

Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…

Sparse Canonical Correlation Analysis (SCCA) is a fundamental statistical tool for identifying linear relationships in high-dimensional, multi-view data. While minimax theory establishes an optimal sample complexity scaling additively with…

Since the introduction of the lasso in regression, various sparse methods have been developed in an unsupervised context like sparse principal component analysis (s-PCA), sparse canonical correlation analysis (s-CCA) and sparse singular…

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…

We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently…

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…

Effective understanding of a disease such as cancer requires fusing multiple sources of information captured across physical scales by multimodal data. In this work, we propose a novel feature embedding module that derives from canonical…

Correspondence analysis, multiple correspondence analysis and their discriminant counterparts (i.e., discriminant simple correspondence analysis and discriminant multiple correspondence analysis) are methods of choice for analyzing…

Canonical correlation analysis is a statistical technique that is used to find relations between two sets of variables. An important extension in pattern analysis is to consider more than two sets of variables. This problem can be expressed…

Radiogenomics is an emerging field in cancer research that combines medical imaging data with genomic data to predict patients clinical outcomes. In this paper, we propose a multivariate sparse group lasso joint model to integrate imaging…