Tensor Data Research Articles

On how to incorporate public sources of situational context in descriptive and predictive models of traffic data

BackgroundEuropean cities are placing a larger emphasis on urban data consolidation and analysis for optimizing public transport in response to changing urban mobility dynamics. Despite the existing efforts, traffic data analysis often disregards vital situational context, including large-scale events, weather factors, traffic generation poles, social distancing norms, or traffic interdictions. Some of these sources of context data are still private, dispersed, or unavailable for the purpose of planning or managing urban mobility. Addressing the above observation, the Lisbon city Council has already established efforts for gathering historic and prospective sources of situational context in standardized semi-structured repositories, triggering new opportunities for context-aware traffic data analysis.Research questionsThe work presented in this paper aims at tackling the following main research question: How to incorporate historical and prospective sources of situational context into descriptive and predictive models of urban traffic data?MethodologyWe propose a methodology anchored in data science methods to integrate situational context in the descriptive and predictive models of traffic data, with a focus on the three following major spatiotemporal traffic data structures: i) georeferenced time series data; ii) origin-destination tensor data; iii) raw traffic event data. Second, we introduce additional principles for the online consolidation and labelling of heterogeneous sources of situational context from public repositories. Third, we quantify the impact produced by situational context aspects on public passenger transport data gathered from smart card validations along the bus (CARRIS), subway (METRO) and bike sharing (GIRA) modes in the city of Lisbon.ResultsThe gathered results stress the importance of incorporating historical and prospective context data for a guided description and prediction of urban mobility dynamics, irrespective of the underlying data representation.Overall, the research offers the following major contributions:A novel methodology on how to acquire, consolidate and incorporate different sources of context for the context-enriched analysis of traffic data;The instantiation of the proposed methodology in the city of Lisbon, discussing the role of recent initiatives for the ongoing monitoring of relevant context data sources within semi-structured repositories, and further showing how these initiatives can be extended for the context-sensitive modelling of traffic data for descriptive and predictive ends;A roadmap of practical illustrations quantifying impact of different context factors (including weather, traffic interdictions and public events) on different transportation modes using different spatiotemporal traffic data structures; andA review of state-of-the-art contributions on context-enriched traffic data analysis.The contributions reported in this work are anchored in the empirical observations gathered along the first stage of the ILU project (see footnote 1), providing a study case of interest to be followed by other European cities.

Tensor local linear embedding with global subspace projection optimisation

In this paper, a novel tensor dimensionality reduction (TDR) approach is proposed, which maintains the local geometric structure of tensor data by tensor local linear embedding and explores the global feature by optimising global subspace projection. Firstly, we analyse the local linear feature of tensor data for learning the linear separable embedding of the tenor data. Furthermore, a global subspace projection distance minimisation strategy is introduced to extract the global characteristic of the tensor data. The aim of this strategy is to find an optimal low-dimensional subspace for TDR. In particular, two novel TDR algorithms are developed by the ensemble of tensor local feature preservation and global subspace projection distance minimisation, which express the subspace projection optimisation as an iteration optimisation problem and a Rayleigh quotient problem, respectively. The extensive experimental results on tensor data classification and clustering have demonstrated the proposed algorithms performed well.

One‐class tensor machine with randomized projection for large‐scale anomaly detection in high‐dimensional and noisy data

The modern industrial sector generates enormous amounts of high-dimensional heterogeneous data daily. However, mostly the vectored data (rank-one tensor) have been considered for anomaly detection, whereas the data in real-life is high dimensional. The expressive power of methods based on vector data is restrictive as they may destroy the structural information embedded in data and lead to the curse-of-dimensionality and overfitting. In this paper, we present a novel anomaly detection approach for large-scale tensor data. We first present novel one-class support tensor machines (OCSTM) with bounded loss function. We further extend it by leveraging the randomness to design a scalable approach that can also be used for large-scale anomaly detection. To solve the corresponding optimization of the objective function, we utilize half-quadratic optimization followed by solving it like a traditional OCSTM optimization at each iteration. We demonstrate the proposed randomized OCSTM with bounded hinge loss through experiments on 14 benchmark data sets. Experimental results demonstrate the effectiveness of the proposed approach against anomalies and a significant reduction in the computational complexity.

Guidelines to handle large-scale and complex tensor data in R

Guidelines to handle large-scale and complex tensor data in R

Generalized Tensor Decomposition With Features on Multiple Modes

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of node features and interactions thereof, together with the tensor data. Such data problems are common in neuroimaging, network analysis, and spatial-temporal modeling. Identifying the relationship between a high-dimensional tensor and side information is important yet challenging. Here, we develop a tensor decomposition method that incorporates multiple feature matrices as side information. Unlike unsupervised tensor decomposition, our supervised decomposition captures the effective dimension reduction of the data tensor confined to feature space of interest. An efficient alternating optimization algorithm with provable spectral initialization is further developed. Our proposal handles a broad range of data types, including continuous, count, and binary observations. We apply the method to diffusion tensor imaging data from human connectome project and multi-relational political network data. We identify the key global connectivity pattern and pinpoint the local regions that are associated with available features. The package and data used are available at https://CRAN.R-project.org/package=tensorregress. Supplementary materials for this article are available online.

Parallel tensor decomposition with distributed memory based on hierarchical singular value decomposition

AbstractAs an important tool of multiway/tensor data analysis tool, Tucker decomposition has been applied widely in various fields. But traditional sequential Tucker algorithms have been outdated because tensor data is growing rapidly in term of size. To address this problem, in this article, we focus on parallel Tucker decomposition of dense tensors on distributed‐memory systems. The proposed method uses hierarchical SVD to accelerate the SVD step in traditional sequential algorithms, which usually takes up most computation time. The data distribution strategy is designed to follow the implementation of hierarchical SVD. We also find that compared with the state‐of‐the‐art method, the proposed method has lower communication cost in large‐scale parallel cases under the assumption of the α–β model.

Sparse nonnegative tensor decomposition using proximal algorithm and inexact block coordinate descent scheme

Nonnegative tensor decomposition is a versatile tool for multiway data analysis, by which the extracted components are nonnegative and usually sparse. Nevertheless, the sparsity is only a side effect and cannot be explicitly controlled without additional regularization. In this paper, we investigated the nonnegative CANDECOMP/PARAFAC (NCP) decomposition with the sparse regularization item using l_1-norm (sparse NCP). When high sparsity is imposed, the factor matrices will contain more zero components and will not be of full column rank. Thus, the sparse NCP is prone to rank deficiency, and the algorithms of sparse NCP may not converge. In this paper, we proposed a novel model of sparse NCP with the proximal algorithm. The subproblems in the new model are strongly convex in the block coordinate descent (BCD) framework. Therefore, the new sparse NCP provides a full column rank condition and guarantees to converge to a stationary point. In addition, we proposed an inexact BCD scheme for sparse NCP, where each subproblem is updated multiple times to speed up the computation. In order to prove the effectiveness and efficiency of the sparse NCP with the proximal algorithm, we employed two optimization algorithms to solve the model, including inexact alternating nonnegative quadratic programming and inexact hierarchical alternating least squares. We evaluated the proposed sparse NCP methods by experiments on synthetic, real-world, small-scale, and large-scale tensor data. The experimental results demonstrate that our proposed algorithms can efficiently impose sparsity on factor matrices, extract meaningful sparse components, and outperform state-of-the-art methods.

TensorClus: A python library for tensor (Co)-clustering

Tensor data analysis is the evolutionary step of data analysis to more than two dimensions. Dealing with tensor data is often based on tensor decomposition methods. The present paper focuses on unsupervised learning and provides a python package referred to as TensorClus including novel co-clustering algorithms of three-way data. All proposed algorithms are based on the latent block models and suitable to different types of data, sparse or not. They are successfully evaluated on challenges in text mining, recommender systems, and hyperspectral image clustering. TensorClus is an open-source Python package that allows easy interaction with other python packages such as NumPy and TensorFlow; it also offers an interface with some tensor decomposition packages namely Tensorly and TensorD on the one hand, and on the other, the co-clustering package Coclust. Finally, it provides CPU and GPU compatibility. The TensorClus library is available at https://pypi.org/project/TensorClus/.

Tensor decision trees for continual learning from drifting data streams

Data stream classification is one of the most vital areas of contemporary machine learning, as many real-life problems generate data continuously and in large volumes. However, most of research in this area focuses on vector-based representations, which are unsuitable for capturing properties of more complex multi-dimensional structures, such as images and video sequences. In this paper, we propose a novel methodology for learning adaptive decision trees from data streams of tensors. We introduce Chordal Kernel Decision Tree for continual learning from tensor data streams. In order to maintain the tensor characteristics, we propose to train and update classifiers in the kernel space designed to work with tensor representation. We use chordal distance to compute similarities between tensors and then apply it as a new feature space in which decision trees are trained. This allows for a direct decision tree induction on tensors. In order to accommodate the streaming and drifting nature of data, we propose a concept drift detection scheme based on tensor representation. It allows us to reconstruct the kernel feature space every time when change is detected. The proposed approach allows for fast and efficient induction of decision trees on streaming data with tensor representation. Experimental study, conducted on 4 real-world and 52 artificial large-scale tensor data streams, shows that using the native tensor feature space leads to more accurate classification than outperforms the vectorized representations.

Kernelized support tensor train machines

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 propose a tensor train (TT)-based kernel technique for the first time, and apply it to the conventional support vector machine (SVM) for high-dimensional image classification with very small number of training samples. Specifically, we propose a kernelized support tensor train machine that accepts tensorial input and preserves the intrinsic kernel property. The main contributions are threefold. First, we propose a TT-based feature mapping procedure that maintains the TT structure in the feature space. Second, we demonstrate two ways to construct the TT-based kernel function while considering consistency with the TT inner product and preservation of information. Third, we show that it is possible to apply different kernel functions on different data modes. In principle, our method tensorizes the standard SVM on its input structure and kernel mapping scheme. This reduces the storage and computation complexity of kernel matrix construction from exponential to polynomial. The validity proof and computation complexity of the proposed TT-based kernel functions are provided elaborately. Extensive experiments are performed on high-dimensional fMRI and color images datasets, which demonstrates the superiority of the proposed scheme compared with the state-of-the-art techniques.

Multilinear Common Component Analysis via Kronecker Product Representation.

We consider the problem of extracting a common structure from multiple tensor data sets. For this purpose, we propose multilinear common component analysis (MCCA) based on Kronecker products of mode-wise covariance matrices. MCCA constructs a common basis represented by linear combinations of the original variables that lose little information of the multiple tensor data sets. We also develop an estimation algorithm for MCCA that guarantees mode-wise global convergence. Numerical studies are conducted to show the effectiveness of MCCA.

Dimensionality reduction of tensor data based on local linear embedding and mode product

There are three contributions in this paper. (1) A tensor version of LLE (short for Local Linear Embedding algorithm) is deduced and presented. LLE is the most famous manifold learning algorithm. Since its proposal, various improvements to LLE have kept emerging without interruption. However, all these achievements are only suitable for vector data, not tensor data. The proposed tensor LLE can also be used a bridge for various improvements to LLE to transfer from vector data to tensor data. (2) A framework of tensor dimensionality reduction based on tensor mode product is proposed, in which the mode matrices can be determined according to specific criteria. (3) A novel dimensionality reduction algorithm for tensor data based on LLE and mode product (LLEMP-TDR) is proposed, in which LLE is used as a criterion to determine the mode matrices. Benefiting from local LLE and global mode product, the proposed LLEMP-TDR can preserve both local and global features of high-dimensional tenser data during dimensionality reduction. The experimental results on data clustering and classification tasks demonstrate that our method performs better than 5 other related algorithms published recently in top academic journals.

Column-Wise Element Selection for Computationally Efficient Nonnegative Coupled Matrix Tensor Factorization

Coupled Matrix Tensor Factorization (CMTF) facilitates the integration and analysis of multiple data sources and helps discover meaningful information. Nonnegative CMTF (N-CMTF) has been employed in many applications for identifying latent patterns, prediction, and recommendation. However, due to the added complexity with coupling between tensor and matrix data, existing N-CMTF algorithms exhibit poor computation efficiency. In this paper, a computationally efficient N-CMTF factorization algorithm is presented based on the column-wise element selection, preventing frequent gradient updates. Theoretical and empirical analyses show that the proposed N-CMTF factorization algorithm is not only more accurate but also more computationally efficient than existing algorithms in approximating the tensor as well as in identifying the underlying nature of factors.

Joint nuclear- and [formula omitted]-norm regularized heterogeneous tensor decomposition for robust classification

Traditional approaches that represent observations in vector or matrix notation easily lead to structure information losses and dependency destruction between elements. Tensors are the generalizations of matrices, providing a natural representation of rich structure in real-world multiway arrays. Although tensor decomposition has been verified and used in classification tasks, the heterogeneity gap among different orders is often neglected. In this paper, we exploited tensor decomposition framework and presented a heterogeneous tensor decomposition for robust classification (HTDRC) approach, which integrates nuclear and ℓ2,1-norm for intrinsic representation learning. Specifically, to obtain the lowest-rank intrinsic representations of tensorial data from an underlying low-dimensional subspace, HTDRC simultaneously learns a set of orthogonality constrained factor matrices and a low-rank constrained representation matrix. To better guide the decomposition process, a robust discriminant feature selection scheme is utilized by imposing ℓ2,1-norm penalty on the constructed classification loss and the regularized terms simultaneously. Experiments on four datasets demonstrated the superior performance of our proposed approach.

An Efficient 2.5D Shadow Detection Algorithm for Urban Planning and Design Using a Tensor Based Approach

Urbanization is leading us to a more chaotic state where healthy living becomes a prime concern. The high-rise buildings influence the urban setting with a high shadow rate on surroundings that can have no positive impact on the general neighborhood. Nevertheless, shadows are the main factor of defeatist virtual settings, they are expensive to render in real-time. This paper investigates how the amount of sunlight varies by season and how seasons can indicate the time of year to understand how shadows vary in length at different times of the day and how they change over the seasons. We propose a novel efficient (fast and scalable) algorithm to calculate a 2.5D cast-shadow map from a given LiDAR-derived Digital Surface Model (DSM). We present a proof-of-concept demonstration to examine the technical practicability of the introduced algorithm. Tensor-based techniques such as singular value decomposition, tensor unfolding are examined and deployed to represent the multidimensional data. The proposed method exploits horizon mapping ideas and extends the method to a modern graphics algorithm (Bresenham’s line drawing algorithm) to account for the DSM’s underlying surface geometry. A proof-of-concept is developed utilizing Python’s TensorFlow library, exploring data flow graphs and the tensor data structure. The heavy computer graphics algorithm used in this paper is parallelized using PySpark. Results explicate significant enhancements in overall performance while preserving accuracy at negligible variations.

SWCNTs Interaction with Dopamine and Serotonin Anticancer Through QM/MM Methods: A Drug Delivery Approaches

Objetive: Dopamine and Serotonin are the two important biological transmitters that have hormonal activities and responsible for happiness and felling well. The aim of this article was to study theoretically the structure features of Dopamine and Serotonin in the complex of single-walled carbon nanotube as a neurotransmitter. Material and Methods: The structure of Dopamine and Serotonin binding with SWCNT with four different diameters (7.0,7.5,7.7,10.0 nm) was studied by using molecular mechanic (MM) and quantum mechanic (QM). The remarkable energies including potential energy, total energy and kinetic energy in time of simulation 10 ns steps in two temperatures (298, 310 kelvin degree) were investigated by Monte Carlo method with opls force filed. NMR shielding tensor data by B3LYP level of theory with 6-31 G(d) as a basis set and semi empirical method have been also fulfilled. Results: Theoretical computations were performed to study NMR chemical shift data including magnetic shielding tensor (σ, ppm), shielding asymmetry (η), magnetic shielding anisotropy (σaniso), magnetic shielding isotropy (σiso) , skew of a tensor (Κ) and chemical shift anisotropy (Δσ) and span (Ω) at various rotation angles around a specific rotation, physical and chemical properties of atomic nuclei. Semi empirical calculations such as total energy, binding energy, isolated atomic energy, electronic energy, core–core interaction and heat of formation in AM1 were revealed. Conclusion: It is figured out in Monte Carlo method our two specific drug and its nanotube with small diameter are the most stable one than the others. The larger diameter leads the combination stability into lower value.

RETRACTED ARTICLE: The application of twin network target tracking and support tensor machine in the evaluation of orienteering teaching

Siamese network target tracking task is one of the more difficult research topics in the field of computer vision. A large number of methods based on deep neural networks have been proposed, which are dedicated to solving some of the current problems in computer vision. And experts in various fields have expressed their opinions. More twin network target tracking algorithms have gradually appeared. The SiamFC target tracking algorithm is widely used, which is based on twin neural networks and has the advantage of fast tracking speed. Today’s era is an era covered by big data. There are many ways to classify tensor data. Among them, supporting tensor machine algorithm is a better method, and it is also a current hot research direction. This article mainly studies the relationship between supporting tensor machine analysis method and orientation sports teaching quality evaluation system, analyzes and explores related factors that affect and determines teaching quality, so that the evaluation can be more accurate and reliable, and gradually realize the improvement of leisure sports teaching quality. Through research, it is concluded that the teaching evaluation system contains a total of two indicators, namely 3 first-level indicators and 13 second-level indicators. A main content that can evaluate the quality of teaching is route design. At present, there are certain problems in the evaluation of the teaching practice of orienteering used by many schools. Among them are the obstacles caused by traditional teaching, and the professional ability of some teachers is not strong enough. In order to better solve these problems, this article proposes a more efficient school orienteering teaching practice strategy: improving the traditional teaching mode, and continuously improving the overall teaching ability of teachers.

Exploiting Spatial Information to Enhance DTI Segmentations via Spatial Fuzzy c-Means with Covariance Matrix Data and Non-Euclidean Metrics

A diffusion tensor models the covariance of the Brownian motion of water at a voxel and is required to be symmetric and positive semi-definite. Therefore, image processing approaches, designed for linear entities, are not effective for diffusion tensor data manipulation, and the existence of artefacts in diffusion tensor imaging acquisition makes diffusion tensor data segmentation even more challenging. In this study, we develop a spatial fuzzy c-means clustering method for diffusion tensor data that effectively segments diffusion tensor images by accounting for the noise, partial voluming, magnetic field inhomogeneity, and other imaging artefacts. To retain the symmetry and positive semi-definiteness of diffusion tensors, the log and root Euclidean metrics are used to estimate the mean diffusion tensor for each cluster. The method exploits spatial contextual information and provides uncertainty information in segmentation decisions by calculating the membership values for assigning a diffusion tensor at one voxel to different clusters. A regularisation model that allows the user to integrate their prior knowledge into the segmentation scheme or to highlight and segment local structures is also proposed. Experiments on simulated images and real brain datasets from healthy and Spinocerebellar ataxia 2 subjects showed that the new method was more effective than conventional segmentation methods.

Semi-supervised non-negative Tucker decomposition for tensor data representation

Semi-supervised non-negative Tucker decomposition for tensor data representation

Geodesic fiber tracking in white matter using activation function

Background and objective:The geodesic ray-tracing method has shown its effectiveness for the reconstruction of fibers in white matter structure. Based on reasonable metrics on the spaces of the diffusion tensors, it can provide multiple solutions and get robust to noise and curvatures of fibers. The choice of the metric on the spaces of diffusion tensors has a significant impact on the outcome of this method. Our objective is to suggest metrics and modifications of the algorithms leading to more satisfactory results in the construction of white matter tracts as geodesics.Methods:Starting with the DTI modality, we propose to rescale the initially chosen metric on the space of diffusion tensors to increase the geodetic cost in the isotropic regions. This change should be conformal in order to preserve the angles between crossing fibers. We also suggest to enhance the methods to be more robust to noise and to employ the fourth order tensor data in order to handle the fiber crossings properly.Results: We propose a way to choose the appropriate conformal class of metrics where the metric gets scaled according to tensor anisotropy. We use the logistic functions, which are commonly used in statistics as cumulative distribution functions. To prevent deviation of geodesics from the actual paths, we propose a hybrid ray-tracing approach. Furthermore, we suggest how to employ diagonal projections of 4th order tensors to perform fiber tracking in crossing regions.Conclusions: The algorithms based on the newly suggested methods were succesfuly implemented, their performance was tested on both synthetic and real data, and compared to some of the previously known approaches.