Related papers: Tensor Generalized Canonical Correlation Analysis
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…
We introduce a technique based on the singular vector canonical correlation analysis (SVCCA) for measuring the generality of neural network layers across a continuously-parametrized set of tasks. We illustrate this method by studying…
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…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…
Comparing different neural network representations and determining how representations evolve over time remain challenging open questions in our understanding of the function of neural networks. Comparing representations in neural networks…
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…
Spatiotemporal traffic data (e.g., link speed/flow) collected from sensor networks can be organized as multivariate time series with additional spatial attributes. A crucial task in analyzing such data is to identify and detect anomalous…
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
A new framework for many multiblock component methods (including consensus and hierarchical PCA) is proposed. It is based on the consensus PCA model: a scheme connecting each block of variables to a superblock obtained by concatenation of…
Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields.…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
This paper investigates fairness and bias in Canonical Correlation Analysis (CCA), a widely used statistical technique for examining the relationship between two sets of variables. We present a framework that alleviates unfairness by…
Graph contrastive learning (GCL) has become a hot topic in the field of graph representation learning. In contrast to traditional supervised learning relying on a large number of labels, GCL exploits augmentation strategies to generate…
Multi-block CCA constructs linear relationships explaining coherent variations across multiple blocks of data. We view the multi-block CCA problem as finding leading generalized eigenvectors and propose to solve it via a proximal gradient…
Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…
How does one find dimensions in multivariate data that are reliably expressed across repetitions? For example, in a brain imaging study one may want to identify combinations of neural signals that are reliably expressed across multiple…
Tensor Robust Principal Component Analysis (TRPCA), which aims to recover a low-rank tensor corrupted by sparse noise, has attracted much attention in many real applications. This paper develops a new Global Weighted TRPCA method (GWTRPCA),…
In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product…
This paper presents an extension of Correspondence Analysis (CA) to tensors through High Order Singular Value Decomposition (HOSVD) from a geometric viewpoint. Correspondence analysis is a well-known tool, developed from principal component…