Tucker Model Research Articles

Compression of Head-Related Transfer Function Based on Tucker and Tensor Train Decomposition

Head-related transfer function (HRTF) plays an important role in three-dimensional spatial sound system. However, the direct application of a large amount of original HRTF data would involve a great deal of computational burden, especially for high-spatial-resolution individual HRTF. To address this problem, we propose a novel compression method (called TT-Tucker) combining Tucker model with tensor train decomposition based on a 5-order HRTF tensor model developed in subspaces of an ear, subject, azimuth, elevation, and frequency. Lots of HRTF data can be decomposed into several low-parametric factors representing the key spectrum information of HRTF by capturing the hidden interactions among different subspaces. To evaluate the reconstruction performance, the numerical experiments were conducted on the CIPIC HRTF database. Under the same compression ratio of nearly 98%, the results suggest that the proposed method has a better performance in spectral distortion and signal-to-distortion ratio than that of the usual tensor method and the standard method principal component analysis (PCA). Moreover, the subjective listening test shows that the TT-Tucker method performs better in that, the compressed and reconstructed HRTF is closer to the original HRTF in the sound localization similarity.

Feature Extraction for Incomplete Data Via Low-Rank Tensor Decomposition With Feature Regularization.

Multidimensional data (i.e., tensors) with missing entries are common in practice. Extracting features from incomplete tensors is an important yet challenging problem in many fields such as machine learning, pattern recognition, and computer vision. Although the missing entries can be recovered by tensor completion techniques, these completion methods focus only on missing data estimation instead of effective feature extraction. To the best of our knowledge, the problem of feature extraction from incomplete tensors has yet to be well explored in the literature. In this paper, we therefore tackle this problem within the unsupervised learning environment. Specifically, we incorporate low-rank tensor decomposition with feature variance maximization (TDVM) in a unified framework. Based on orthogonal Tucker and CP decompositions, we design two TDVM methods, TDVM-Tucker and TDVM-CP, to learn low-dimensional features viewing the core tensors of the Tucker model as features and viewing the weight vectors of the CP model as features. TDVM explores the relationship among data samples via maximizing feature variance and simultaneously estimates the missing entries via low-rank Tucker/CP approximation, leading to informative features extracted directly from observed entries. Furthermore, we generalize the proposed methods by formulating a general model that incorporates feature regularization into low-rank tensor approximation. In addition, we develop a joint optimization scheme to solve the proposed methods by integrating the alternating direction method of multipliers with the block coordinate descent method. Finally, we evaluate our methods on six real-world image and video data sets under a newly designed multiblock missing setting. The extracted features are evaluated in face recognition, object/action classification, and face/gait clustering. Experimental results demonstrate the superior performance of the proposed methods compared with the state-of-the-art approaches.

Linear systems with a canonical polyadic decomposition constrained solution: Algorithms and applications

SummaryReal‐life data often exhibit some structure and/or sparsity, allowing one to use parsimonious models for compact representation and approximation. When considering matrix and tensor data, low‐rank models such as the (multilinear) singular value decomposition, canonical polyadic decomposition (CPD), tensor train, and hierarchical Tucker model are very common. The solution of (large‐scale) linear systems is often structured in a similar way, allowing one to use compact matrix and tensor models as well. In this paper, we focus on linear systems with a CPD‐constrained solution (LS‐CPD). Our main contribution is the development of optimization‐based and algebraic methods to solve LS‐CPDs. Furthermore, we propose a condition that guarantees generic uniqueness of the obtained solution. We also show that LS‐CPDs provide a broad framework for the analysis of multilinear systems of equations. The latter are a higher‐order generalization of linear systems, similar to tensor decompositions being a generalization of matrix decompositions. The wide applicability of LS‐CPDs in domains such as classification, multilinear algebra, and signal processing is illustrated.

Microphone array speech enhancement based on tensor filtering methods

This paper proposes a novel microphone array speech denoising scheme based on tensor filtering methods including truncated HOSVD (High-Order Singular Value Decomposition), low rank tensor approximation and multi-mode Wiener filtering. Microphone array speech signal is represented in three-order tensor space with channel, time, and spectrum modes and then tensor filtering model can be designed to process the multiway array data. As to the first method, noise can be reduced through the truncated HOSVD which is a simple scheme in tensor processing. It is more accurate to find the lower-rank approximation of the three-order tensor with Tucker model. Then MDL (Minimum Description Length) criterion is used to estimate the optimal tensor rank in the second method. Further, multimode Wiener filtering approach upon tensor analysis can be considered as the spanning of one-mode wiener filtering. How to take advantages of tensor model to obtain a set of filters is the heart of the novel scheme. The performances of the proposed three approaches are evaluated with objective indexes and listening quality test. The experimental results indicate that the proposed tenor filtering methods have potential ability of retrieving the target signal from noisy microphone array signal and the multi-mode Wiener filtering method provides the best denoising results among the three ones.

Tucker Tensor Regression and Neuroimaging Analysis.

Neuroimaging data often take the form of high dimensional arrays, also known as tensors. Addressing scientific questions arising from such data demands new regression models that take multidimensional arrays as covariates. Simply turning an image array into a vector would both cause extremely high dimensionality and destroy the inherent spatial structure of the array. In a recent work, Zhou et al. (2013) proposed a family of generalized linear tensor regression models based upon the CP (CANDECOMP/PARAFAC) decomposition of regression coefficient array. Low rank approximation brings the ultrahigh dimensionality to a manageable level and leads to efficient estimation. In this article, we propose a tensor regression model based on the more flexible Tucker decomposition. Compared to the CP model, Tucker regression model allows different number of factors along each mode. Such flexibility leads to several advantages that are particularly suited to neuroimaging analysis, including further reduction of the number of free parameters, accommodation of images with skewed dimensions, explicit modeling of interactions, and a principled way of image downsizing. We also compare the Tucker model with CP numerically on both simulated data and a real magnetic resonance imaging data, and demonstrate its effectiveness in finite sample performance.

DOES INCOME SMOOTHING IMPROVE INFORMATIVENESS OF STOCK PRICES?

The purpose of this research is to get empirical evidence from effect Income smoothing to Informativeness of Stock Prices in Indonesian Stock Exchange (IDX). Population from this research is take from companies that have been listing Index LQ 45 in IDX form 2003 until 2015. Income Smoothing is masured by Jones’s Model which have been modified by Kothari et. all (2005). Informativeness of stock price using Zarowin and Tucker Model (2006) Future Earnings Response Coeficient, and the relations to earnings persistence, which is can been seen from relation from current earnings dan future earnings. 
 The research is using data from year 2003 until 2015 period, and year 2014 used as terminal year. That found income smoothing have a negative effect to informativeness of stock price and also found the managers’ income smoothing action always decreases earnings from 2013 to 2015. Current earnings have related to future earnings.

Traffic data imputation via tensor completion based on soft thresholding of Tucker core

Technological limitations and practical difficulties cause inevitable losses of traffic data in the typical processing chain of an intelligent transportation system. This has motivated the development of imputation algorithms for mitigating the consequences of such losses. As the involved datasets are usually multidimensional and bear strong spatio-temporal correlations, we propose for traffic data imputation a tensor completion algorithm which promotes parsimony of an estimated orthogonal Tucker model by iteratively softly thresholding its core. The motivation of this strategy is discussed on the basis of characteristics typically possessed by real-world datasets. An evaluation of the proposed method using speed data from the Grenoble south ring (France) shows that our algorithm outperforms other imputation methods, including tensor completion algorithms, and delivers good results even when the loss is severely systematic, being mostly concentrated in long time windows (of up to three hours) spread along the considered time horizon.

Comprehensive Feature-Based Robust Video Fingerprinting Using Tensor Model

Content-based near-duplicate video detection (NDVD) is essential for effective search and retrieval, and robust video fingerprinting is a good solution for NDVD. Most existing video fingerprinting methods use a single feature or concatenate different features to generate video fingerprints, and show good performance under single-mode modifications such as noise addition and blurring. However, when they suffer combined modifications, the performance is degraded to a certain extent because such features cannot characterize the video content completely. By contrast, the assistance and consensus among different features can improve the performance of video fingerprinting. Therefore, in the present study, we mine the assistance and consensus among different features based on a tensor model, and we present a new comprehensive feature to fully use them in the proposed video fingerprinting framework. We also analyze what the comprehensive feature really is for representing the original video. In this framework, the video is initially set as a high-order tensor that consists of different features, and the video tensor is decomposed via the Tucker model with a solution that determines the number of components. Subsequently, the comprehensive feature is generated by the low-order tensor obtained from tensor decomposition. Finally, the video fingerprint is computed using this feature. A matching strategy used for narrowing the search is also proposed based on the core tensor. The robust video fingerprinting framework is resistant not only to single-mode modifications but also to their combination.

Robust Multilinear Tensor Rank Estimation Using Higher Order Singular Value Decomposition and Information Criteria

Model selection in tensor decomposition is important for real applications if the rank of the original data tensor is unknown and the observed tensor is noisy. In the Tucker model, the minimum description length (MDL) or Bayesian information criteria have been applied to tensors via matrix unfolding, but these methods are sensitive to noise when the tensors have a multilinear low rank structure given by the Tucker model. In this study, we propose new methods for improving the MDL so it is more robust to noise. The proposed methods are justified theoretically by analyzing the “multilinear low-rank structure” of tensors. Extensive experiments including numerical simulations and a real application to image denoising are provided to illustrate the advantages of the proposed methods.

Partial Least-Squares Method for Three-Mode Three-Way Datasets Based on Tucker Model

When analyzing two three-mode three-way datasets (object × variable × condition), the objective is to obtain common factors that show the relationships between the two datasets. The partial least-squares (PLS) method has been applied to such datasets to investigate the common factors. However, the PLS method was proposed for two-mode two-way datasets, such as multivariate datasets. Therefore, this method does not consider the condition when searching for relationships between datasets; that is, it tends to regard the same variable under different conditions as different variables. To address this problem, we extended the PLS method to three-mode three-way datasets by using the Tucker model so that the same variable under different conditions is regarded as the same. Moreover, we can apply the proposed method to three-mode three-way datasets with different dimensions for the conditions and variables, and the output is obtained in the form of three-mode three-way datasets. We show the advantage of the proposed method by applying it to a multicollinearity case as a numerical example.

A Tensor Decomposition Based Multiway Structured Sparse SAR Imaging Algorithm with Kronecker Constraint

This paper investigates a structured sparse SAR imaging algorithm for point scattering model based on tensor decomposition. Several SAR imaging schemes have been developed by researchers for improving the imaging quality. For a typical SAR target scenario, the scatterers distribution usually has the feature of structured sparsity. Without considering this feature thoroughly, the existing schemes have still certain drawbacks. The classic matching pursuit algorithms can obtain clearer imaging results, but the cost is resulting in an extreme complexity and a huge computation resource consumption. Therefore, this paper put forward a tensor-based SAR imaging algorithm by means of multiway structured sparsity which makes full use of the above geometrical feature of the scatterers distribution. The spotlight SAR observation signal is formulated as a Tucker model considering the Kronecker constraint, and then a sparse reconstruction algorithm is introduced by utilizing the structured sparsity of the scene. The proposed tensor-based SAR imaging model is able to take advantage of the Kronecker information in each mode, which ensures the robustness for the signal reconstruction. Both the algorithm complexity analysis and numerical simulations show that the proposed method requires less computation than the existing sparsity-driven SAR imaging algorithms. The imaging realizations based on the practical measured data also indicate that the proposed algorithm is superior to the reference methods even in the severe noisy environment, under the condition of multiway structured sparsity.

Analysis of the Folgar & Tucker model for concentrated fibre suspensions in unconfined and confined shear flows via direct numerical simulation

The classical Jeffery model allows for the prediction of the flow-induced orientation in dilute fibre suspensions. In most industrial applications, however, fibre suspensions are concentrated and fibre-fibre interactions cannot be ignored any longer. These interactions have been traditionally modelled at the mesoscopic and macroscopic scales by introducing a phenomenological diffusion term inducing a randomizing effect. In the so-called Folgar & Tucker (F&T) model, widely used in applications, the diffusion coefficient is assumed to scale linearly with the flow intensity, the latter being described by the second invariant of the rate of strain tensor. Modifications and alternatives to the F&T model have been proposed in view of the difficulty for the F&T model to explain an apparent orientation delay observed experimentally in injection-moulded parts. The noticed deviations were attributed to the intense fibre-fibre interactions, thus pointing to the limitations of a phenomenological diffusion term for describing them. In the present work, we revisit the F&T model and compare its predictions with those obtained bysimplified yet state-of-the-art direct numerical simulation (DNS) in unconfined and confined simple shear flows for a range of shear rates and concentrations, the latter ensuring intense fibre-fibre interactions. In unconfined flows, we find that the F&T model agrees quantitatively with the DNS results once an adequate closure relation is considered for approximating the fourth-order orientation tensor involved in the F&T model. Thus, the results seem to confirm, at least in simple shear flows, the F&T assumption for the form of the isotropic rotary diffusion function scaling linearly with the magnitude of the scalar rate of deformation. Also, a linear scalingof the diffusivity with the fibre concentration is observed. This conclusion remains unexpectedly valid under moderately-confined flow conditions as soon as an advanced fitted closure, like the IBOF, is considered within the F&T model. Other simpler closures (e.g. quadratic or hybrid), however, definitively fail to address confinement issues as also reported in our former work for the dilute regime. Obviously, these conclusions rest on the validity of the considered state-of-the-art DNS, which remains at present an open question.

Evaluating Rigid and Semiflexible Fiber Orientation Evolution Models in Simple Flows

As American vehicle fuel efficiency requirements have become more stringent due to the CAFE standards, the auto industry has turned to fiber reinforced polymer composites as replacements for metal parts to reduce weight while simultaneously maintaining established safety standards. Furthermore, these composites may be easily processed using established techniques such as injection molding and compression molding. The mechanical properties of these composites are dependent on, among other variables, the orientation of the fibers within the part. Several models have been proposed to correlate fiber orientation with the kinematics of the polymer matrix during processing, each using various strategies to account for fiber interactions and fiber flexing. However, these all require the use of empirical fitting parameters. Previous work has obtained these parameters by fitting to orientation data at a specific location in an injection-molded part. This ties the parameters to the specific mold design used. Obtaining empirical parameters is not a trivial undertaking and adds significant time to the entire mold design process. Considering that new parameters must be obtained any time some aspect of the part or mold is changed, an alternative technique that obtains model parameters independent of the mold design could be advantageous. This paper continues work looking to obtain empirical parameters from rheological tests. During processing, the fiber–polymer suspension is subjected to a complex flow with both shear and extensional behavior. Rather than use a complex flow, this study seeks to isolate and compare the effects of shear and extension on two orientation models. To this end, simple shear and planar extension are employed, and the evolution of orientation from a planar random initial condition is tracked as a function of strain. Simple shear was imparted using a sliding plate rheometer designed and fabricated in-house. A novel rheometer tool was developed and fabricated in-house to impart planar extension using a lubricated squeeze flow technique, where a low-viscosity Newtonian lubricant is applied to the solid boundaries to minimize the effect of shearing due to the no-slip boundary condition. The Folgar–Tucker model with a strain reduction factor is used as a rigid fiber model and compared against a bead–rod model (a semiflexible model) proposed by Ortman. Both models are capable of predicting the data, with the bead–rod model performing slightly better. Orientation occurs at a much faster rate under startup of planar extension and also attains a much higher degree of flow alignment when compared with startup of steady shear.

Recovering Incomplete Data using Tucker Model for Tensor with Low-n-rank

Tensor with missing or incomplete values is a ubiquitous problem in various fields such as biomedical signal processing, image processing, and social network analysis. In this paper, we considered how to reconstruct a dataset with missing values by using tensor form which is called tensor completion process. We applied Tucker factorization to solve tensor completion which was built base on optimization problem. We formulated the optimization objective function using components of Tucker model after decomposing. The weighted least square matric contained only known values of the tensor with low rank in its modes. A first order optimization method, namely Nonlinear Conjugated Gradient, was applied to solve the optimization problem. We demonstrated the effectiveness of the proposed method in EEG signals with about 70% missing entries compared to other algorithms. The relative error was proposed to compare the difference between original tensor and the process output.

Second-order capillary electrophoresis diode array detector data modeled with the Tucker3 algorithm: A novel strategy for Argentinean white wine discrimination respect to grape variety.

Data obtained by capillary electrophoresis with diode array detection (CE-DAD) were modeled with the purpose to discriminate Argentinean white wines samples produced from three grape varieties (Torrontés, Chardonnay, and Sauvignon blanc). Thirty-eight samples of commercial white wine from four wine-producing provinces of Argentina (Mendoza, San Juan, Salta, and Rio Negro) were analyzed. CE-DAD matrices with dimensions of 421 elution times (from 1.17 to 7.39 minutes) × 71 wavelengths (from 227 to 367 nm) were joined in a three way data array and decomposed by Tucker3 method under non-negativity constraint, employing 18, 18 and six factors in the modes 1, 2 and 3, respectively. Using the scores of Tucker model, it was possible to discriminate samples of Argentinean white wine by linear discriminant analysis and Kernel linear discriminant analysis. Core element analysis of the Tucker3 model allows identifying the loading profiles in spectral mode related to Argentinean white wine samples.

Orientation kinematics of short fibres in a second-order viscoelastic fluid

Most theoretical fibre suspension models currently used for predicting the flow-induced evolution of microstructure in the processing of reinforced thermoplastics are based on the Jeffery model of dilute suspensions in a Newtonian suspending fluid or phenomenological adaptations of it that account for fibre-fibre interactions. An important assumption of all these models is the Newtonian character of the fluid in which the fibres are suspended. In industrial practice, the considered fluids are in general molten thermoplastics that exhibit a viscoelastic behaviour. Even though few counterparts of the Jeffery theory exist for second-order fluids, they have been rarely considered and, to our knowledge, never taken into account at the macroscopic scale. In this paper, we address the modelling of short fibre suspensions in second-order fluids throughout the different description scales, from microscopic to macroscopic. We propose a simplified modelling framework that allows one to extend to viscoelastic suspending fluids the standard Folgar and Tucker model widely used in industrial simulation software.

Connected Categorical Canonical Covariance Analysis for Three-mode Three-way data Sets Based on Tucker Model

When we work with two three-mode three-way data sets, such as panel data, we often investigate two types of factors: common factors, which represent relationships between the two data sets, and unique factors, which show the uniqueness of each data set relative to the other. We propose a method for investigating common and unique factors simultaneously. Canonical covariance analysis is an existing method that allows the estimation of common and unique factors simultaneously; however, this method was proposed for use with two-mode two-way data, and it is limited to quantitative data. Thus, applying canonical covariance analysis to three-mode three-way data sets or to categorical data sets is not suitable. To overcome this problem, we build on the concept of the Tucker model and the concept of non-metric principal component analysis to develop and propose a method suitable the analysis of categorical three-mode three-way data sets. Moreover, we introduce connector matrices, making it easy to determine which factors are common and allowing the selection of different numbers of dimensions for the factors.

Applying the Kuhn–Tucker model to estimate the value of recreational ecosystem services in Sicily

This paper applies the Kuhn–Tucker model to estimate recreation demand of parks in Sicily. We estimate a fixed coefficient specification and a random coefficient specification to take into account heterogeneity across visitors. Estimates suggest a diversity of preferences across the population and that parks with higher level of quality attributes are more likely to be visited. We also simulate two sets of hypothetical policy scenarios to evaluate and compare the recreational value of each park and the welfare impacts of changes in a quality attribute.

Valuing hypothetical wildfire impacts with a Kuhn–Tucker model of recreation demand

This study uses a nonmarket valuation method to investigate the recreation values of the San Jacinto Wilderness in southern California. The analysis utilizes survey data from a stated-choice experiment involving backcountry visitors who responded to questions about hypothetical wildfire burn scenarios. Benefits of landscape preservation are derived using a Kuhn–Tucker (KT) demand system. Model results suggest that recreationists are attracted to sites with recent wildfires that can be viewed up-close. For example, recreational welfare estimates increased for sites that were partially affected by different types of wildfires, with the greatest gains being observed for the most recent wildfires. Per person mean seasonal willingness-to-pay varied from a low of $10 to a high of $48, for total gains ranging from $62,223 to $635,286. However, wildfires that cause trail closures create welfare losses. Seasonal losses per person for complete closure of particular sites range from $3 to $221, for total losses ranging from $29,600 to $2.9 million.

Lossy volume compression using Tucker truncation and thresholding

Tensor decompositions, in particular the Tucker model, are a powerful family of techniques for dimensionality reduction and are being increasingly used for compactly encoding large multidimensional arrays, images and other visual data sets. In interactive applications, volume data often needs to be decompressed and manipulated dynamically; when designing data reduction and reconstruction methods, several parameters must be taken into account, such as the achievable compression ratio, approximation error and reconstruction speed. Weighing these variables in an effective way is challenging, and here we present two main contributions to solve this issue for Tucker tensor decompositions. First, we provide algorithms to efficiently compute, store and retrieve good choices of tensor rank selection and decompression parameters in order to optimize memory usage, approximation quality and computational costs. Second, we propose a Tucker compression alternative based on coefficient thresholding and zigzag traversal, followed by logarithmic quantization on both the transformed tensor core and its factor matrices. In terms of approximation accuracy, this approach is theoretically and empirically better than the commonly used tensor rank truncation method.