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Tensors are ubiquitous in science and engineering and tensor factorization approaches have become important tools for the characterization of higher order structure. Factorizations includes the outer-product rank Canonical Polyadic…
Scale-invariance, good localization and robustness to noise and distortions are the main properties that a local feature detector should possess. Most existing local feature detectors find excessive unstable feature points that increase the…
Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
Quality-of-service (QoS) data exhibit dynamic temporal patterns that are crucial for accurately predicting missing values. These patterns arise from the evolving interactions between users and services, making it essential to capture the…
How can we find patterns and anomalies in a tensor, or multi-dimensional array, in an efficient and directly interpretable way? How can we do this in an online environment, where a new tensor arrives each time step? Finding patterns and…
Existing methods of vector autoregressive model for multivariate time series analysis make use of low-rank matrix approximation or Tucker decomposition to reduce the dimension of the over-parameterization issue. In this paper, we propose a…
In automatic target recognition (ATR) systems, sensors may fail to capture discriminative, fine-grained detail features due to environmental conditions, noise created by CMOS chips, occlusion, parallaxes, and sensor misalignment. Therefore,…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
We propose a new data-driven approach for learning the fundamental solutions (Green's functions) of various linear partial differential equations (PDEs) given sample pairs of input-output functions. Building off the theory of functional…
Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank…
Knowledge graphs are structured representations of real world facts. However, they typically contain only a small subset of all possible facts. Link prediction is a task of inferring missing facts based on existing ones. We propose TuckER,…
Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…
In numerous applications, binary reactions or event counts are observed and stored within high-order tensors. Tensor decompositions (TDs) serve as a powerful tool to handle such high-dimensional and sparse data. However, many traditional…
We propose the time-delayed transformer (TD-TF), a simplified transformer architecture for data-driven modeling of unsteady spatio-temporal dynamics. TD-TF bridges linear operator-based methods and deep sequence models by showing that a…
This paper develops the concept of the Adjacent Deviation Subspace (ADS), a novel framework for reducing infinite-dimensional functional data into finite-dimensional vector or scalar representations while preserving critical information of…
Feature Transformation (FT) crafts new features from original ones via mathematical operations to enhance dataset expressiveness for downstream models. However, existing FT methods exhibit critical limitations: discrete search struggles…
Tabular data learning has extensive applications in deep learning but its existing embedding techniques are limited in numerical and categorical features such as the inability to capture complex relationships and engineering. This paper…
Currently, the size of scientific data is growing at an unprecedented rate. Data in the form of tensors exhibit high-order, high-dimensional, and highly sparse features. Although tensor-based analysis methods are very effective, the large…