相关论文: Visual Analytics Using Tensor Unified Linear Compa…

Tucker decomposition is one of the most popular models for analyzing and compressing large-scale tensorial data. Existing Tucker decomposition algorithms usually rely on a single solver to compute the factor matrices and core tensor, and…

Given two data matrices $X$ and $Y$, sparse canonical correlation analysis (SCCA) is to seek two sparse canonical vectors $u$ and $v$ to maximize the correlation between $Xu$ and $Yv$. However, classical and sparse CCA models consider the…

An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…

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…

Dimension reduction is an essential tool for analyzing high dimensional data. Most existing methods, including principal component analysis (PCA), as well as their extensions, provide principal components that are often linear combinations…

Vision language models (VLMs) excel in multimodal understanding but are prone to adversarial attacks. Existing defenses often demand costly retraining or significant architecture changes. We introduce a lightweight defense using tensor…

We consider moment matching techniques for estimation in Latent Dirichlet Allocation (LDA). By drawing explicit links between LDA and discrete versions of independent component analysis (ICA), we first derive a new set of cumulant-based…

Multilinear Discriminant Analysis (MDA) is a powerful dimension reduction method specifically formulated to deal with tensor data. Precisely, the goal of MDA is to find mode-specific projections that optimally separate tensor data from…

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…

In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently…

As tensors become widespread in modern data analysis, Tucker low-rank Principal Component Analysis (PCA) has become essential for dimensionality reduction and structural discovery in tensor datasets. Motivated by the common scenario where…

The rapid development of Convolutional Neural Networks (CNNs) in recent years has triggered significant breakthroughs in many machine learning (ML) applications. The ability to understand and compare various CNN models available is thus…

In response to the challenges of data mining, discriminant analysis continues to evolve as a vital branch of statistics. Our recently introduced method of vertex discriminant analysis (VDA) is ideally suited to handle multiple categories…

Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…

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…

Dimensionality reduction (DR) is frequently used for analyzing and visualizing high-dimensional data as it provides a good first glance of the data. However, to interpret the DR result for gaining useful insights from the data, it would…

We consider the problem of extracting a common structure from multiple tensor datasets. For this purpose, we propose multilinear common component analysis (MCCA) based on Kronecker products of mode-wise covariance matrices. MCCA constructs…

In probabilistic principal component analysis (PPCA), an observed vector is modeled as a linear transformation of a low-dimensional Gaussian factor plus isotropic noise. We generalize PPCA to tensors by constraining the loading operator to…

Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…