相关论文: JADE for Tensor-Valued Observations

This paper is devoted to the problem of designing functional observers for linear time-invariant (LTI) descriptor systems. The observers are realized by using state-space systems governed by ordinary differential equations (ODEs). Available…

This study advances the Variational Autoencoder (VAE) framework by addressing challenges in Independent Component Analysis (ICA) under both determined and underdetermined conditions, focusing on enhancing the independence and…

The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to…

In this work, we study the problem of common and unique feature extraction from noisy data. When we have N observation matrices from N different and associated sources corrupted by sparse and potentially gross noise, can we recover the…

Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are…

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…

Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof.…

We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…

This paper uses Factored Latent Analysis (FLA) to learn a factorized, segmental representation for observations of tracked objects over time. Factored Latent Analysis is latent class analysis in which the observation space is subdivided and…

The current methods for learning representations with auto-encoders almost exclusively employ vectors as the latent representations. In this work, we propose to employ a tensor product structure for this purpose. This way, the obtained…

This paper studies the reduced-order or full-order, dead-beat observer problem for a class of nonlinear systems, linear in the unmeasured states. A novel hybrid observer design strategy is proposed, with the help of the notion of strong…

In this paper a novel efficient method for representation of facial action units by encoding an image sequence as a fourth-order tensor is presented. The multilinear tensor-based extension of the biased discriminant analysis (BDA)…

This paper considers fault estimation in nonlinear fractional order systems in observer form. For this aim, a step by step second order sliding mode observer is used. By means of a fractional inequality, the stability of the observer…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…

This paper presents a novel density estimation method for anomaly detection using density matrices (a powerful mathematical formalism from quantum mechanics) and Fourier features. The method can be seen as an efficient approximation of…

Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data. \emph{Tensor power method} (TPM) is one of the widely-used techniques in the decomposition of tensors. This paper presents a novel tensor…

Most linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss (2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo and Li…

Kjolstad et. al. proposed a tensor algebra compiler. It takes expressions that define a tensor element-wise, such as $f_{ij}(a,b,c,d) = \exp\left[-\sum_{k=0}^4 \left((a_{ik}+b_{jk})^2\, c_{ii} + d_{i+k}^3 \right) \right]$, and generates the…

Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under…

To improve the generalization of detectors, for domain adaptive object detection (DAOD), recent advances mainly explore aligning feature-level distributions between the source and single-target domain, which may neglect the impact of…