相关论文: Tensor-Train Parameterization for Ultra Dimensiona…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…

This paper proposes a new methodology to predict and update the residual useful lifetime of a system using a sequence of degradation images. The methodology integrates tensor linear algebra with traditional location-scale regression widely…

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality…

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

Hyper spectral imaging is a remote sensing technology, providing variety of applications such as material identification, space object identification, planetary exploitation etc. It deals with capturing continuum of images of the earth…

Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…

We first show that the commonly used dimensionality reduction (DR) methods such as t-SNE and LargeVis poorly capture the global structure of the data in the low dimensional embedding. We show this via a number of tests for the DR methods…

Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the missing entries of incomplete…

The era of exascale computing opens new venues for innovations and discoveries in many scientific, engineering, and commercial fields. However, with the exaflops also come the extra-large high-dimensional data generated by high-performance…

Many recent works have shown trainability plays a central role in neural network pruning -- unattended broken trainability can lead to severe under-performance and unintentionally amplify the effect of retraining learning rate, resulting in…

Recurrent neural networks (RNN) such as long-short-term memory (LSTM) networks are essential in a multitude of daily live tasks such as speech, language, video, and multimodal learning. The shift from cloud to edge computation intensifies…

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…

Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…

Learning neural fields has been an active topic in deep learning research, focusing, among other issues, on finding more compact and easy-to-fit representations. In this paper, we introduce a novel low-rank representation termed Tensor…

Originating from condensed matter physics, tensor networks are compact representations of high-dimensional tensors. In this paper, the prowess of tensor networks is demonstrated on the particular task of one-class anomaly detection. We…

The tensor low-rank prior has attracted considerable attention in dynamic MR reconstruction. Tensor low-rank methods preserve the inherent high-dimensional structure of data, allowing for improved extraction and utilization of intrinsic…

Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…

We propose a method for learning topology-preserving data representations (dimensionality reduction). The method aims to provide topological similarity between the data manifold and its latent representation via enforcing the similarity in…