Related papers: Sparse Weighted Canonical Correlation Analysis

Canonical Correlation Analysis (CCA) is widely used for multimodal data analysis and, more recently, for discriminative tasks such as multi-view learning; however, it makes no use of class labels. Recent CCA methods have started to address…

Classic and deep generalized canonical correlation analysis (GCCA) algorithms seek low-dimensional common representations of data entities from multiple ``views'' (e.g., audio and image) using linear transformations and neural networks,…

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,…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

This paper considers canonical correlation analysis for two longitudinal variables that are possibly sampled at different time resolutions with irregular grids. We modeled trajectories of the multivariate variables using random effects and…

Sparse estimation for Gaussian graphical models is a crucial technique for making the relationships among numerous observed variables more interpretable and quantifiable. Various methods have been proposed, including graphical lasso, which…

In this paper, we consider stochastic dual coordinate (SDCA) {\em without} strongly convex assumption or convex assumption. We show that SDCA converges linearly under mild conditions termed restricted strong convexity. This covers a wide…

Sparse attention as a efficient method can significantly decrease the computation cost, but current sparse attention tend to rely on window self attention which block the global information flow. For this problem, we present Shifted Cross…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…

In this paper, we compared the general forms of CCA and PLS on three simulated and two empirical datasets, all having large sample sizes. We took successively smaller subsamples of these data to evaluate sensitivity, reliability, and…

Comparing tensors and identifying their (dis)similar structures is fundamental in understanding the underlying phenomena for complex data. Tensor decomposition methods help analysts extract tensors' essential characteristics and aid in…

It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…

Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical…

Dimension reduction algorithms aim to discover latent variables which describe underlying structures in high-dimensional data. Methods such as factor analysis and principal component analysis have the downside of not offering much…

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…

While distributed training is often viewed as a solution to optimizing linear models on increasingly large datasets, inter-machine communication costs of popular distributed approaches can dominate as data dimensionality increases. Recent…

Integration of multi-omics data provides opportunities for revealing biological mechanisms related to certain phenotypes. We propose a novel method of multi-omics integration called supervised deep generalized canonical correlation analysis…

We give oracle inequalities on procedures which combines quantization and variable selection via a weighted Lasso $k$-means type algorithm. The results are derived for a general family of weights, which can be tuned to size the influence of…

Sparse regression is frequently employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data that hampers both feature selection and estimation is the presence of strong correlations between…

Principal component analysis (PCA) is one of the most widely used dimensionality reduction methods in scientific data analysis. In many applications, for additional interpretability, it is desirable for the factor loadings to be sparse,…