Related papers: TTHRESH: Tensor Compression for Multidimensional V…

In the era of big data, effectively compressing large datasets while performing complex mathematical operations is crucial. Tensor-based decomposition methods have shown superior compression capabilities with minimal loss of accuracy…

We introduce NeuralVDB, which improves on an existing industry standard for efficient storage of sparse volumetric data, denoted VDB [Museth 2013], by leveraging recent advancements in machine learning. Our novel hybrid data structure can…

In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…

A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major…

We study the tensor renormalization group (TRG) in the dimension larger than two as the Higher-order TRG (HOTRG) with the randomized SVD method. The randomized SVD and the detailed discussion on the low order tensor representation, we can…

The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…

The recently proposed fully-connected tensor network (FCTN) decomposition has demonstrated significant advantages in correlation characterization and transpositional invariance, and has achieved notable achievements in multi-dimensional…

Classical data analysis requires computational efforts that become intractable in the age of Big Data. An essential task in time series analysis is the extraction of physically meaningful information from a noisy time series. One algorithm…

Three dimensional convolutional neural networks (3DCNNs) have been applied in many tasks, e.g., video and 3D point cloud recognition. However, due to the higher dimension of convolutional kernels, the space complexity of 3DCNNs is generally…

Lossy compression has become an important technique to reduce data size in many domains. This type of compression is especially valuable for large-scale scientific data, whose size ranges up to several petabytes. Although Autoencoder-based…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

Low-rank tensor compression has been proposed as a promising approach to reduce the memory and compute requirements of neural networks for their deployment on edge devices. Tensor compression reduces the number of parameters required to…

In this paper, we define a semi-tensor product for third-order tensors. Based on this definition, we present a new type of tensor decomposition strategy and give the specific algorithm. This decomposition strategy actually generalizes the…

The hierarchical SVD provides a quasi-best low rank approximation of high dimensional data in the hierarchical Tucker framework. Similar to the SVD for matrices, it provides a fundamental but expensive tool for tensor computations. In the…

High-dimensional vector similarity search (HVSS) is critical for many data processing and AI applications. However, traditional HVSS methods often require extensive data access for distance calculations, leading to inefficiencies.…

Most existing 3D Gaussian Splatting (3DGS) compression schemes focus on producing compact 3DGS representation via implicit data embedding. They have long coding times and highly customized data format, making it difficult for widespread…

In this paper, we propose an efficient approach for the compression and representation of volumetric data utilizing coordinate-based networks and multi-resolution hash encoding. Efficient compression of volumetric data is crucial for…

From linear classifiers to neural networks, image classification has been a widely explored topic in mathematics, and many algorithms have proven to be effective classifiers. However, the most accurate classifiers typically have…

Various tensor decomposition methods have been proposed for data compression. In real world applications of the tensor decomposition, selecting the tensor shape for the given data poses a challenge and the shape of the tensor may affect the…