Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRobust approximation of tensor networks: application to grid-free tensor factorization of the Coulomb interaction
217
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Approximation of a tensor network by approximating (e.g., factorizing) one or more of its constituent tensors can be improved by canceling the leading-order error due to the constituents approximation. The utility of such robust approximation is demonstrated for robust canonical polyadic (CP) approximation of a (density-fitting) factorized 2-particle Coulomb interaction tensor. The resulting algebraic (grid-free) approximation for the Coulomb tensor, closely related to the factorization appearing in pseudospectral and tensor hypercontraction approaches, is efficient and accurate, with significantly reduced rank compared to the naive (non-robust) approximation. Application of the robust approximation to the particle-particle ladder term in the coupled-cluster singles and doubles reduces the size complexity from $mathcal{O}(N^6)$ to $mathcal{O}(N^5)$ with robustness ensuring negligible errors in chemically-relevant energy differences using CP ranks approximately equal to the size of the density-fitting basis.
rate research
Read More
Tensor network methods are a conceptually elegant framework for encoding complicated datasets, where high-order tensors are approximated as networks of low-order tensors. In practice, however, the numeric implementation of tensor network algorithms is often a labor-intensive and error-prone task, even for experienced researchers in this area. emph{TensorTrace} is application designed to alleviate the burden of contracting tensor networks: it provides a graphic drawing interface specifically tailored for the construction of tensor network diagrams, from which the code for their optimal contraction can then be automatically generated (in the users choice of the MATLAB, Python or Julia languages). emph{TensorTrace} is freely available at url{https://www.tensortrace.com} wi
Tensor factorization has been proved as an efficient unsupervised learning approach for health data analysis, especially for computational phenotyping, where the high-dimensional Electronic Health Records (EHRs) with patients history of medical procedures, medications, diagnosis, lab tests, etc., are converted to meaningful and interpretable medical concepts. Federated tensor factorization distributes the tensor computation to multiple workers under the coordination of a central server, which enables jointly learning the phenotypes across multiple hospitals while preserving the privacy of the patient information. However, existing federated tensor factorization algorithms encounter the single-point-failure issue with the involvement of the central server, which is not only easily exposed to external attacks, but also limits the number of clients sharing information with the server under restricted uplink bandwidth. In this paper, we propose CiderTF, a communication-efficient decentralized generalized tensor factorization, which reduces the uplink communication cost by leveraging a four-level communication reduction strategy designed for a generalized tensor factorization, which has the flexibility of modeling different tensor distribution with multiple kinds of loss functions. Experiments on two real-world EHR datasets demonstrate that CiderTF achieves comparable convergence with the communication reduction up to 99.99%.
Anomaly detection in road networks is vital for traffic management and emergency response. However, existing approaches do not directly address multiple anomaly types. We propose a tensor-based spatio-temporal model for detecting multiple types of anomalies in road networks. First, we represent network traffic data as a 3rd-order tensor. Next, we acquire spatial and multi-scale temporal patterns of traffic variations via a novel, computationally efficient tensor factorization algorithm: sliding window tensor factorization. Then, from the factorization results, we can identify different anomaly types by measuring deviations from different spatial and temporal patterns. Finally, we discover path-level anomalies by formulating anomalous path inference as a linear program that solves for the best matched paths of anomalous links. We evaluate the proposed methods via both synthetic experiments and case studies based on a real-world vehicle trajectory dataset, demonstrating advantages of our approach over baselines.
Because of the limitations of matrix factorization, such as losing spatial structure information, the concept of low-rank tensor factorization (LRTF) has been applied for the recovery of a low dimensional subspace from high dimensional visual data. The low-rank tensor recovery is generally achieved by minimizing the loss function between the observed data and the factorization representation. The loss function is designed in various forms under different noise distribution assumptions, like $L_1$ norm for Laplacian distribution and $L_2$ norm for Gaussian distribution. However, they often fail to tackle the real data which are corrupted by the noise with unknown distribution. In this paper, we propose a generalized weighted low-rank tensor factorization method (GWLRTF) integrated with the idea of noise modelling. This procedure treats the target data as high-order tensor directly and models the noise by a Mixture of Gaussians, which is called MoG GWLRTF. The parameters in the model are estimated under the EM framework and through a new developed algorithm of weighted low-rank tensor factorization. We provide t
Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over fitting and the performance decreases significantly. To address this problem, the completion method for a tensor based on a Biased Deep Tensor Factorization Network (BDTFN) is proposed. This method can not only overcome the shortcomings of traditional tensor factorization, but also deal with complex non-linear data. Firstly, the horizontal and lateral tensors corresponding to the observed values of the input tensors are used as inputs and projected to obtain their horizontal (lateral) potential feature tensors. Secondly, the horizontal (lateral) potential feature tensors are respectively constructed into a multilayer perceptron network. Finally, the horizontal and lateral output tensors are fused by constructing a bilinear pooling layer. Tensor forward-propagation is composed of those three step, and its parameters are updated by tensor back-propagation using the multivariable chain rule. In this paper, we consider the large-scale 5-minute traffic speed data set and use it to address the missing data imputation problem for large-scale spatiotemporal traffic data. In addition, we compare the numerical performance of the proposed algorithm with those for state-of-the-art approaches on video recovery and color image recovery. Numerical experimental results illustrate that our approach is not only much more accurate than those state-of-the-art methods, but it also has high speed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
