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Tensor computations are increasingly prevalent numerical techniques in data science, but pose unique challenges for high-performance implementation. We provide novel algorithms and systems infrastructure which enable efficient parallel…
We consider $N$-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is…
Since higher-order tensors are naturally suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become one of the emerging areas in machine learning and computer…
We propose personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global…
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…
Existing compression methods typically focus on the removal of signal-level redundancies, while the potential and versatility of decomposing visual data into compact conceptual components still lack further study. To this end, we propose a…
Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using…
Tensor decomposition methods are popular tools for analysis of multi-way datasets from social media, healthcare, spatio-temporal domains, and others. Widely adopted models such as Tucker and canonical polyadic decomposition (CPD) follow a…
We propose a nonparametric factorization approach for sparsely observed tensors. The sparsity does not mean zero-valued entries are massive or dominated. Rather, it implies the observed entries are very few, and even fewer with the growth…
Most machine learning models for structured data encode the structural knowledge of a node by leveraging simple aggregation functions (in neural models, typically a weighted sum) of the information in the node's neighbourhood. Nevertheless,…
Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic…
In this work we investigate efficient data compression for spatiotemporal Black, Azov and Marmara Seas temperature tensors that contain significant number of missing values. These tensors have a complex structure influenced by the…
Scientific applications are generating unprecedented volumes of data that overwhelm storage and transmission systems, posing significant challenges for the design of data management tools and scientific databases. Lossy compression has…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…
We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special structure and are important to various data science problems. We…
We propose a scalable tensorization framework for neural network compression based on slice-wise feature distillation. Unlike conventional tensor decomposition methods that rely on costly global finetuning, our approach decomposes the…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
Compressed file formats are the corner stone of efficient data storage and transmission, yet their potential for representation learning remains largely underexplored. We introduce TEMPEST (TransformErs froM comPressed rEpreSenTations), a…
CP decomposition is a powerful tool for data science, especially gene analysis, deep learning, and quantum computation. However, the application of tensor decomposition is largely hindered by the exponential increment of the computational…
In this paper, we demonstrate some applications of compressive sensing over networks. We make a connection between compressive sensing and traditional information theoretic techniques in source coding and channel coding. Our results provide…