Related papers: Eigenvector-based sparse canonical correlation ana…
Regularized Generalized Canonical Correlation Analysis (RGCCA) is a general statistical framework for multi-block data analysis. RGCCA enables deciphering relationships between several sets of variables and subsumes many well-known…
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…
Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance $\Sigma$, whose top eigenvector $v \in R^d$ is $s$-sparse. Existing sparse PCA…
Canonical correlation analysis (CCA) is a state-of-the-art method for frequency recognition in steady-state visual evoked potential (SSVEP)-based brain-computer interface (BCI) systems. Various extended methods have been developed, and…
Canonical correlation analysis is a technique to extract common features from a pair of multivariate data. In complex situations, however, it does not extract useful features because of its linearity. On the other hand, kernel method used…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…
The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…
Multi-view learning (MVL) is a strategy for fusing data from different sources or subsets. Canonical correlation analysis (CCA) is very important in MVL, whose main idea is to map data from different views onto a common space with maximum…
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…
Recently the widely used multi-view learning model, Canonical Correlation Analysis (CCA) has been generalised to the non-linear setting via deep neural networks. Existing deep CCA models typically first decorrelate the feature dimensions of…
We consider estimation in a high-dimensional linear model with strongly correlated variables. We propose to cluster the variables first and do subsequent sparse estimation such as the Lasso for cluster-representatives or the group Lasso…
Canonical Correlation Analysis (CCA) is a classic technique for multi-view data analysis. To overcome the deficiency of linear correlation in practical multi-view learning tasks, various CCA variants were proposed to capture nonlinear…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…
Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…
We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of…
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…
Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…
Canonical correlation analysis (CCA) is a technique for finding correlations between different data modalities and learning low-dimensional representations. As fairness becomes crucial in machine learning, fair CCA has gained attention.…
Feature selection refers to the process of selecting useful features for machine learning tasks, and it is also a key step for structural health monitoring (SHM). This paper proposes a fast feature selection algorithm by efficiently…
We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish lower bounds on the rates of convergence of the estimators of the…