25 papers · ranked by Valyu relevance
Kevin De Azevedo, Florian Buettner
In recent years, the exponential growth of high-dimensional, multi-modal molecular data has created both opportunities and challenges in personalized medicine. While existing approaches like matrix decomposition and neural network-based embeddings have been used to analyze such data, they have limitations in…
Lili Guo, Huiwen Yu, Yuan Li, Chenxi Zhang + 1 more
Plant metabolomics is an important research area in plant science. Chemometrics is a useful tool for plant metabolomic data analysis and processing. Among them, high-order chemometrics represented by tensor modeling provides a new and promising technical method for the analysis of complex multi-way plant metabolomics…
Saritha Kodikara, Brendan Lu, Shuhe Wang, Kim-Anh Lê Cao
Multi-omics studies capture comprehensive molecular profiles across biological layers to understand complex biological processes. A central challenge is integrating information across heterogeneous data types to identify coordinated molecular responses, particularly when measurements are collected longitudinally.…
Fen Liu, Jianfeng Chen, Weijie Tan, Chang Cai + 1 more
'Amelia Carolina Sparavigna'] Multi-modal fusion can achieve better predictions through the amalgamation of information from different modalities. To improve the performance of accuracy, a method based on Higher-order Orthogonal Iteration Decomposition and Projection (HOIDP) is proposed, in the fusion process…
Manal Helal
The burgeoning growth of public domain data and the increasing complexity of deep learning model architectures have underscored the need for more efficient data representation and analysis techniques. This paper is motivated by the work of (Helal, 2023) and aims to present a comprehensive overview of tensorization.…
Ilya Kisil, Giuseppe G. Calvi, Bruno Scalzo Dees, Danilo P. Mandic
HOTTBOX is a Python library for exploratory analysis and visualisation of multi-dimensional arrays of data, also known as tensors. The library includes methods ranging from standard multi-way operations and data manipulation through to multi-linear algebra based tensor decompositions. HOTTBOX also comprises…
Fernando Hermosillo-Reynoso, Deni Torres-Roman, George Yannis
Since multi-view learning leverages complementary information from multiple feature sets to improve model performance, a tensor-based data fusion layer for neural networks, called Multi-View Data Tensor Fusion (MV-DTF), is used. It fuses M feature spaces $X_{1},\cdots,X_{M}$, referred to as views, in a new latent…
Roberto Casarin, Radu V. Craiu, Qīng Wáng
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of information about the responses. The method is flexible, allowing for…
Jiani Liu, Qinghua Tao, Ce Zhu, Yipeng Liu + 1 more
Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. Highorder tensors are capable of providing efficient representations for such tasks, while preserving structural task-relations. In…
Takashi Sasagawa, Masato Tanaka
We present a construction method for reduced-order models (ROMs) to explore alternatives to numerical simulations. The proposed method can efficiently construct ROMs for non-linear problems with contact and impact behaviors by using tensor decomposition for factorizing multidimensional data and Akima-spline…
Maolin Wang, Pan Yu, Xiangli Yang, Guangxi Li + 1 more
—Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial complexity. As a result, they have attracted significant attention in the fields…
Panqi Chen, Lei Cheng, Jianlong Li, Weichang Li + 3 more
'Jiang Bian' 'Shikai Fang'] Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning lowrank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by incorporating continuous timestamps in latent factors, they…
Fen Liu, Jianfeng Chen, Kemeng Li, Weijie Tan + 4 more
'Muhammad Saad Ayub' 'Lianmeng Jiao' 'Hang Geng'] Multi-modal fusion can exploit complementary information from various modalities and improve the accuracy of prediction or classification tasks. In this paper, we propose a parallel, multi-modal, factorized, bilinear pooling method based on a semi-tensor product (STP)…
Beichen Wang, Jiazhang Cai, Luyang Fang, Ping Ma + 1 more
Contemporary neurobehavior research often collects multi-dimensional tensor (MDT) data, consisting of time-series measurements for multiple features from multiple animals subjected to various perturbations. Proper analysis of the MDT data can facilitate the dissection of the underlying neural circuitry driving the…
Christos Chatzis, David Horner, Rasmus Bro, Ann-Marie Malby Schoos + 2 more
Temporal multivariate data is ubiquitous in many domains, for instance, being collected over time at planned visits (every few months/years) in longitudinal cohorts, or every few minutes/hours in challenge tests. The analysis of such data often focuses on revealing the underlying temporal patterns common across…
Authors not listed
Improving the performance of thermoelectric (TE) materials is essential for their wider adoption in sustainable energy and cooling applications. Impurity doping is a common strategy for enhancing transport properties, yet synthesizing every possible TE composition is infeasible, and high-fidelity ab initio simulations…
Dionysia Kaziki, Andreas K. Engel, Guido Nolte
Cross-bispectral measures provide a rich description of interactions in EEG signals, but their third-order tensor structure poses substantial challenges for interpretation and dimensionality reduction. We introduce a low-rank tensor decomposition framework specifically designed for cross-bispectral EEG data. The model…
Angela F Harper, Simone S Köcher, Karsten Reuter, Christoph Scheurer
Machine learning (ML) surrogate modeling is a powerful approach to reduce the computational cost of first-principles calculations. While well established for the prediction of scalar observables like energetics or band gaps, performance metrics for the learning of tensor-based observables have not yet been formalized.…
Authors not listed
Elucidating Collective Variables (CVs) for biomolecular dynamics is crucial for understanding numerous biological processes. By leveraging the tensor-train data structure, a multilinear version of the AMUSE (Algorithm for Multiple Unknown Signals) algorithm for Koopman approximation (AMUSEt) was recently developed to…
Maxwell Venetos, Mingjian Wen, Kristin Persson
The nuclear magnetic resonance (NMR) chemical shift tensor is a highly sensitive probe of the electronic structure of an atom and furthermore its local structure. Re- cently, machine learning has been applied to NMR in the prediction of isotropic chemi- cal shifts from a structure. Current machine learning models…
Siqi Liu, Xiaoyu Shi, Qifeng Liao, Yanlin Geng + 2 more
Tensor completion is a fundamental tool to estimate unknown information from observed data, which is widely used in many areas, including image and video recovery, traffic data completion and the multi-input multi-output problems in information theory. Based on Tucker decomposition, this paper proposes a new algorithm…
W. Jeffrey Johnston, Stefano Fusi
Humans and other animals demonstrate a remarkable ability to generalize knowledge across distinct contexts and objects during natural behavior. We posit that this ability to generalize arises from a specific representational geometry, that we call abstract and that is referred to as disentangled in machine learning.…
Cheng, Zhengyun, Wang, Changhao + 8 more
Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these can be viewed as using Dirac delta distributions to model the relationships…
Authors not listed
Real-world datasets in chemical engineering and bioengineering processes--such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials--can often be unlabelled or disorganized, rendering the training of existing supervised learning models ineffective at learning the…
Yajushi Khurana, Keisuke Ishihara
Three-dimensional biological morphologies encode functional and physiological state, yet the directional, orientational, and topological properties of these shapes are rarely captured by morphometric tools available for bioimage analysis. Minkowski tensors are mathematically rigorous tensor-valued measures that encode…