Related papers: Streaming Tensor Train Approximation
In this work, we present the tree tensor network Nystr\"om (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker and tensor-train formats, to the more general tree tensor network format,…
This paper describes a new algorithm for computing a low-Tucker-rank approximation of a tensor. The method applies a randomized linear map to the tensor to obtain a sketch that captures the important directions within each mode, as well as…
Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…
Low-tubal-rank tensor approximation has been proposed to analyze large-scale and multi-dimensional data. However, finding such an accurate approximation is challenging in the streaming setting, due to the limited computational resources. To…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
In this paper, we focus on the fixed TT-rank and precision problems of finding an approximation of the tensor train (TT) decomposition of a tensor. Note that the TT-SVD and TT-cross are two well-known algorithms for these two problems.…
This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…
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…
We present a sequential version of the multilinear Nystr\"om algorithm which is suitable for the low-rank Tucker approximation of tensors given in a streaming format. Accessing the tensor $\mathcal{A}$ exclusively through random sketches of…
We present a tensor train (TT) based algorithm designed for sampling from a target distribution and employ TT approximation to capture the high-dimensional probability density evolution of overdamped Langevin dynamics. This involves…
Nearest-neighbor search in large vector databases is crucial for various machine learning applications. This paper introduces a novel method using tensor-train (TT) low-rank tensor decomposition to efficiently represent point clouds and…
This work proposes a novel tensor train random projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically constructed through a tensor train (TT) representation with…
The ability to learn compact, high-quality, and easy-to-optimize representations for visual data is paramount to many applications such as novel view synthesis and 3D reconstruction. Recent work has shown substantial success in using tensor…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional function approximations arising from computational and data sciences. Various sequential and parallel TT decomposition algorithms have…
Dynamic behaviors are becoming prevalent in tensor applications, like machine learning, where many widely used models contain data-dependent tensor shapes and control flow. However, the limited expressiveness of prior programming…
Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some…
This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank…