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A new submodule clustering method via sparse and low-rank representation for multi-way data is proposed in this paper. Instead of reshaping multi-way data into vectors, this method maintains their natural orders to preserve data intrinsic…
Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
This work presents generalized low-rank signal decompositions with the aid of switching techniques and adaptive algorithms, which do not require eigen-decompositions, for space-time adaptive processing. A generalized scheme is proposed to…
Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…
Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…
Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have…
In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…
High-dimensional token embeddings underpin Large Language Models (LLMs), as they can capture subtle semantic information and significantly enhance the modelling of complex language patterns. However, this high dimensionality also introduces…
We consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in…
In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a…
The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…
Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…
Large-scale simulations of time-dependent problems generate a massive amount of data and with the explosive increase in computational resources the size of the data generated by these simulations has increased significantly. This has…
Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…
Tensor decomposition is an important tool for multiway data analysis. In practice, the data is often sparse yet associated with rich temporal information. Existing methods, however, often under-use the time information and ignore the…
Coarse-grained modeling in molecular simulations serves not only to extend accessible time and length scales beyond atomistic limits, but also to reduce high-dimensional chemical data to low-dimensional representations that expose the…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…