scholarly journals Three-Way Tensor Decompositions: A Generalized Minimum Noise Subspace Based Approach

2018 ◽  
Author(s):  
Le Trung Thanh ◽  
Viet-Dung Nguyen ◽  
Nguyen Linh-Trung ◽  
Karim Abed-Meraim
Keyword(s):  
Computational Complexity ◽  
State Of The Art ◽  
Tensor Decomposition ◽  
Decomposition Algorithms ◽  
Subspace Analysis ◽  
Tensor Decompositions ◽  
Noise Subspace ◽  
Parallel Factor ◽  
Value Decomposition ◽  
Minimum Noise

Tensor decomposition has recently become a popular method of multi-dimensional data analysis in various applications. The main interest in tensor decomposition is for dimensionality reduction, approximation or subspace purposes. However, the emergence of “big data” now gives rise to increased computational complexity for performing tensor decomposition. In this paper, motivated by the advantages of the generalized minimum noise subspace (GMNS) method, recently proposed for array processing, we proposed two algorithms for principal subspace analysis (PSA) and two algorithms for tensor decomposition using parallel factor analysis (PARAFAC) and higher-order singular value decomposition (HOSVD). The proposed decomposition algorithms can preserve several desired properties of PARAFAC and HOSVD while substantially reducing the computational complexity. Performance comparisons of PSA and tensor decomposition of our proposed algorithms against the state-of-the-art ones were studied via numerical experiments. Experimental results indicated that the proposed algorithms are of practical values.

scholarly journals Image Completion with Hybrid Interpolation in Tensor Representation

2020 ◽  
Vol 10 (3) ◽  
pp. 797 ◽  
Author(s):  
Rafał Zdunek ◽  
Tomasz Sadowski
Keyword(s):  
Polynomial Interpolation ◽  
State Of The Art ◽  
Tensor Decomposition ◽  
Good Alternative ◽  
Low Rank ◽  
Decomposition Algorithms ◽  
Image Completion ◽  
The Matrix ◽  
Low Rank Approximations ◽  
Incomplete Images

The issue of image completion has been developed considerably over the last two decades, and many computational strategies have been proposed to fill-in missing regions in an incomplete image. When the incomplete image contains many small-sized irregular missing areas, a good alternative seems to be the matrix or tensor decomposition algorithms that yield low-rank approximations. However, this approach uses heuristic rank adaptation techniques, especially for images with many details. To tackle the obstacles of low-rank completion methods, we propose to model the incomplete images with overlapping blocks of Tucker decomposition representations where the factor matrices are determined by a hybrid version of the Gaussian radial basis function and polynomial interpolation. The experiments, carried out for various image completion and resolution up-scaling problems, demonstrate that our approach considerably outperforms the baseline and state-of-the-art low-rank completion methods.

scholarly journals Multiple particle filtering for tracking wireless agents via Monte Carlo likelihood approximation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Stephan Schlupkothen ◽  
Gerd Ascheid
Keyword(s):  
Monte Carlo ◽  
Computational Complexity ◽  
Particle Filtering ◽  
Gaussian Approximation ◽  
State Of The Art ◽  
Approximation Techniques ◽  
Accurate Localization ◽  
Likelihood Approximation ◽  
Current State ◽  
Multiple Particle

Abstract The localization of multiple wireless agents via, for example, distance and/or bearing measurements is challenging, particularly if relying on beacon-to-agent measurements alone is insufficient to guarantee accurate localization. In these cases, agent-to-agent measurements also need to be considered to improve the localization quality. In the context of particle filtering, the computational complexity of tracking many wireless agents is high when relying on conventional schemes. This is because in such schemes, all agents’ states are estimated simultaneously using a single filter. To overcome this problem, the concept of multiple particle filtering (MPF), in which an individual filter is used for each agent, has been proposed in the literature. However, due to the necessity of considering agent-to-agent measurements, additional effort is required to derive information on each individual filter from the available likelihoods. This is necessary because the distance and bearing measurements naturally depend on the states of two agents, which, in MPF, are estimated by two separate filters. Because the required likelihood cannot be analytically derived in general, an approximation is needed. To this end, this work extends current state-of-the-art likelihood approximation techniques based on Gaussian approximation under the assumption that the number of agents to be tracked is fixed and known. Moreover, a novel likelihood approximation method is proposed that enables efficient and accurate tracking. The simulations show that the proposed method achieves up to 22% higher accuracy with the same computational complexity as that of existing methods. Thus, efficient and accurate tracking of wireless agents is achieved.

scholarly journals ShadingNet: Image Intrinsics by Fine-Grained Shading Decomposition

2021 ◽  
Author(s):  
Anil S. Baslamisli ◽  
Partha Das ◽  
Hoang-An Le ◽  
Sezer Karaoglu ◽  
Theo Gevers
Keyword(s):  
Neural Network ◽  
Large Scale ◽  
State Of The Art ◽  
Image Decomposition ◽  
Natural Environments ◽  
Decomposition Algorithms ◽  
Ambient Light ◽  
Fine Grained ◽  
Large Scale Dataset ◽  
Direct Illumination

AbstractIn general, intrinsic image decomposition algorithms interpret shading as one unified component including all photometric effects. As shading transitions are generally smoother than reflectance (albedo) changes, these methods may fail in distinguishing strong photometric effects from reflectance variations. Therefore, in this paper, we propose to decompose the shading component into direct (illumination) and indirect shading (ambient light and shadows) subcomponents. The aim is to distinguish strong photometric effects from reflectance variations. An end-to-end deep convolutional neural network (ShadingNet) is proposed that operates in a fine-to-coarse manner with a specialized fusion and refinement unit exploiting the fine-grained shading model. It is designed to learn specific reflectance cues separated from specific photometric effects to analyze the disentanglement capability. A large-scale dataset of scene-level synthetic images of outdoor natural environments is provided with fine-grained intrinsic image ground-truths. Large scale experiments show that our approach using fine-grained shading decompositions outperforms state-of-the-art algorithms utilizing unified shading on NED, MPI Sintel, GTA V, IIW, MIT Intrinsic Images, 3DRMS and SRD datasets.

scholarly journals Two-Step Root-MUSIC for Direction of Arrival Estimation without EVD/SVD Computation

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Feng-Gang Yan ◽  
Shuai Liu ◽  
Jun Wang ◽  
Ming Jin
Keyword(s):  
Super Resolution ◽  
Direction Of Arrival ◽  
Doa Estimation ◽  
Low Complexity ◽  
Music Algorithm ◽  
Correlation Matrices ◽  
Noise Subspace ◽  
Using Data ◽  
Eigen Decomposition ◽  
Value Decomposition

Most popular techniques for super-resolution direction of arrival (DOA) estimation rely on an eigen-decomposition (EVD) or a singular value decomposition (SVD) computation to determine the signal/noise subspace, which is computationally expensive for real-time applications. A two-step root multiple signal classification (TS-root-MUSIC) algorithm is proposed to avoid the complex EVD/SVD computation using a uniform linear array (ULA) based on a mild assumption that the number of signals is less than half that of sensors. The ULA is divided into two subarrays, and three noise-free cross-correlation matrices are constructed using data collected by the two subarrays. A low-complexity linear operation is derived to obtain a rough noise subspace for a first-step DOA estimate. The performance is further enhanced in the second step by using the first-step result to renew the previous estimated noise subspace with a slightly increased complexity. The new technique can provide close root mean square error (RMSE) performance to root-MUSIC with reduced computational burden, which are verified by numerical simulations.

scholarly journals User-independent accelerometer-based gesture recognition for mobile devices

2013 ◽  
Vol 1 (3) ◽  
pp. 11-25 ◽  
Author(s):  
Xian Wang ◽  
Paula Tarrío ◽  
Ana María Bernardos ◽  
Eduardo Metola ◽  
José Ramón Casar
Keyword(s):  
Computational Complexity ◽  
Mobile Devices ◽  
Gesture Recognition ◽  
Inertial Sensors ◽  
Recognition Accuracy ◽  
State Of The Art ◽  
Smart Phone ◽  
Recognition System ◽  
Independent Manner ◽  
Wheeled Robot

Many mobile devices embed nowadays inertial sensors. This enables new forms of human-computer interaction through the use of gestures (movements performed with the mobile device) as a way of communication. This paper presents an accelerometer-based gesture recognition system for mobile devices which is able to recognize a collection of 10 different hand gestures. The system was conceived to be light and to operate in a user-independent manner in real time. The recognition system was implemented in a smart phone and evaluated through a collection of user tests, which showed a recognition accuracy similar to other state-of-the art techniques and a lower computational complexity. The system was also used to build a human-robot interface that enables controlling a wheeled robot with the gestures made with the mobile phone

scholarly journals Multi-Aspect Incremental Tensor Decomposition Based on Distributed In-Memory Big Data Systems

2020 ◽  
Vol 5 (2) ◽  
pp. 13-32
Author(s):  
Hye-Kyung Yang ◽  
Hwan-Seung Yong
Keyword(s):  
Execution Time ◽  
Three Dimensional ◽  
Large Data ◽  
Tensor Decomposition ◽  
Decomposition Methods ◽  
Apache Spark ◽  
Decomposition Algorithms ◽  
Data Systems ◽  
Big Data Systems ◽  
Spark Framework

AbstractPurposeWe propose InParTen2, a multi-aspect parallel factor analysis three-dimensional tensor decomposition algorithm based on the Apache Spark framework. The proposed method reduces re-decomposition cost and can handle large tensors.Design/methodology/approachConsidering that tensor addition increases the size of a given tensor along all axes, the proposed method decomposes incoming tensors using existing decomposition results without generating sub-tensors. Additionally, InParTen2 avoids the calculation of Khari–Rao products and minimizes shuffling by using the Apache Spark platform.FindingsThe performance of InParTen2 is evaluated by comparing its execution time and accuracy with those of existing distributed tensor decomposition methods on various datasets. The results confirm that InParTen2 can process large tensors and reduce the re-calculation cost of tensor decomposition. Consequently, the proposed method is faster than existing tensor decomposition algorithms and can significantly reduce re-decomposition cost.Research limitationsThere are several Hadoop-based distributed tensor decomposition algorithms as well as MATLAB-based decomposition methods. However, the former require longer iteration time, and therefore their execution time cannot be compared with that of Spark-based algorithms, whereas the latter run on a single machine, thus limiting their ability to handle large data.Practical implicationsThe proposed algorithm can reduce re-decomposition cost when tensors are added to a given tensor by decomposing them based on existing decomposition results without re-decomposing the entire tensor.Originality/valueThe proposed method can handle large tensors and is fast within the limited-memory framework of Apache Spark. Moreover, InParTen2 can handle static as well as incremental tensor decomposition.

scholarly journals Numerical methods for kinetic equations

Acta Numerica ◽  
2014 ◽  
Vol 23 ◽  
pp. 369-520 ◽  
Author(s):  
G. Dimarco ◽  
L. Pareschi
Keyword(s):  
Computational Complexity ◽  
Numerical Methods ◽  
State Of The Art ◽  
Kinetic Equations ◽  
Numerical Techniques ◽  
Asymptotic Preserving ◽  
Hybrid Schemes ◽  
Velocity Models ◽  
Current State ◽  
Number Of Particles

In this survey we consider the development and mathematical analysis of numerical methods for kinetic partial differential equations. Kinetic equations represent a way of describing the time evolution of a system consisting of a large number of particles. Due to the high number of dimensions and their intrinsic physical properties, the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity. Here we review the basic numerical techniques for dealing with such equations, including the case of semi-Lagrangian methods, discrete-velocity models and spectral methods. In addition we give an overview of the current state of the art of numerical methods for kinetic equations. This covers the derivation of fast algorithms, the notion of asymptotic-preserving methods and the construction of hybrid schemes.

Retrieving the leaked signals from noise using a fast dictionary learning method

Geophysics ◽  
2021 ◽  
pp. 1-86
Author(s):  
Wei Chen ◽  
Omar M. Saad ◽  
Yapo Abolé Serge Innocent Oboué ◽  
Liuqing Yang ◽  
Yangkang Chen
Keyword(s):  
Dictionary Learning ◽  
Seismic Data ◽  
State Of The Art ◽  
Computational Cost ◽  
Learning Method ◽  
Global Parameter ◽  
Radius Parameter ◽  
Orthogonalization Method ◽  
Value Decomposition ◽  
Learned Features

Most traditional seismic denoising algorithms will cause damages to useful signals, which are visible from the removed noise profiles and are known as signal leakage. The local signal-and-noise orthogonalization method is an effective method for retrieving the leaked signals from the removed noise. Retrieving leaked signals while rejecting the noise is compromised by the smoothing radius parameter in the local orthogonalization method. It is not convenient to adjust the smoothing radius because it is a global parameter while the seismic data is highly variable locally. To retrieve the leaked signals adaptively, we propose a new dictionary learning method. Because of the patch-based nature of the dictionary learning method, it can adapt to the local feature of seismic data. We train a dictionary of atoms that represent the features of the useful signals from the initially denoised data. Based on the learned features, we retrieve the weak leaked signals from the noise via a sparse co ding step. Considering the large computational cost when training a dictionary from high-dimensional seismic data, we leverage a fast dictionary up dating algorithm, where the singular value decomposition (SVD) is replaced via the algebraic mean to update the dictionary atom. We test the performance of the proposed method on several synthetic and field data examples, and compare it with that from the state-of-the-art local orthogonalization method.

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