Singular value decomposition using an array of CORDIC processors

Milford, D.; Sandell, Magnus

doi:10.1016/j.sigpro.2014.03.022

Cited by 13 publications

(7 citation statements)

References 24 publications

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“…The latter is adopted in majority of the existing hardware implementations of the Jacobi SVD method. For small matrix dimensions, an efficient implementation of SVD for the use in Multiple Input Multiple Output (MIMO) precoding and real-time signal processing has been presented in [19]. The implementation is based on CORDIC processors.…”

Section: A Literature Reviewmentioning

confidence: 99%

A Shallow Neural Network for Real-Time Embedded Machine Learning for Tensorial Tactile Data Processing

Younes

Ibrahim

Rizk

et al. 2021

IEEE Trans. Circuits Syst. I

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This paper presents a novel hardware architecture of the Tensorial Support Vector Machine (TSVM) based on Shallow Neural Networks (NN) for the Single Value Decomposition (SVD) computation. The proposed NN achieves a comparable Mean Squared Error and Cosine Similarity to the widely used one-sided Jacobi algorithm. When implemented on an FPGA, the NN offers 324× faster computations than the one-sided Jacobi with reductions up to 58% and 67% in terms of hardware resources and power consumption respectively. When validated on a touch modality classification problem, the NN-based TSVM implementation has achieved a real-time operation while consuming about 88% less energy per classification than the Jacobi-based TSVM with an accuracy loss of at most 3%. Such results offer the ability to deploy intelligence on resource-limited platform for energy-constrained applications.

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Section: A Literature Reviewmentioning

confidence: 99%

A Shallow Neural Network for Real-Time Embedded Machine Learning for Tensorial Tactile Data Processing

Younes

Ibrahim

Rizk

et al. 2021

IEEE Trans. Circuits Syst. I

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“…Apart from the accuracy and stability of Jacobi algorithm, it also has high degree potential for parallelism, and hence can be implemented on FPGA [5], [6]. In [3], [5], [4], [6], [7], [8], [9], [10] this algorithm is implemented on FPGA with fixed-point arithmetic to reduce power consumption and silicon area. However, in all the works, fixed-point implementation of Jacobi algorithm uses the simulation-based approach for estimating the ranges of variables.…”

Section: Motivationmentioning

confidence: 99%

“…IWLs can be determined either using simulation [1], [11], [12] or by analytical (formal) methods [13], [14], [15], [16]. Existing works on fixed-point EVD have mainly used simulation-based approach for finding the IWLs [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [17] because of its capability to be performed on any kind of systems. In simulation-based methods, variable bounds are estimated using the extreme values obtained from the simulation of the floating-point model.…”

Section: Introductionmentioning

confidence: 99%

“…Eigenvalue decomposition (EVD) is a key building block in signal processing and control applications. The fixed-point development of eigenvalue decomposition (EVD) algorithm have been extensively studied in the past few years [1], [2], [3], [4], [5], [6], [7], [8], [9], [10] because fixed-point circuitry is significantly simpler and faster. Owing to its simplicity, fixed-point arithmetic is ubiquitous in low cost embedded platforms.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An overflow free fixed-point eigenvalue decomposition algorithm: Case study of dimensionality reduction in hyperspectral images

Kabi

Sahadevan

Pradhan

2017

2017 Conference on Design and Architectures for Signal and Image Processing (DASIP)

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Abstract-We consider the problem of enabling robust range estimation of eigenvalue decomposition (EVD) algorithm for a reliable fixed-point design. The simplicity of fixed-point circuitry has always been so tempting to implement EVD algorithms in fixed-point arithmetic. Working towards an effective fixed-point design, integer bit-width allocation is a significant step which has a crucial impact on accuracy and hardware efficiency. This paper investigates the shortcomings of the existing range estimation methods while deriving bounds for the variables of the EVD algorithm. In light of the circumstances, we introduce a range estimation approach based on vector and matrix norm properties together with a scaling procedure that maintains all the assets of an analytical method. The method could derive robust and tight bounds for the variables of EVD algorithm. The bounds derived using the proposed approach remain same for any input matrix and are also independent of the number of iterations or size of the problem. Some benchmark hyperspectral data sets have been used to evaluate the efficiency of the proposed technique. It was found that by the proposed range estimation approach, all the variables generated during the computation of Jacobi EVD is bounded within ±1.

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“…To solve singularity avoidance problem, a large amount of research work has been made. Jacobian singular value decomposition (SVD) algorithm (Okša and Vajteršic, 2006; Milford and Sandell, 2014) is a commonly used algorithm for singularity avoidance, but there exists a problem of heavy computation burden and poor real-time performance. Another commonly used algorithm is the damped least square algorithm (Nakamura and Hanafusa, 1986; Luo et al , 2013; Yang et al , 2014); the algorithm can guarantee the continuity and smoothness of joint angles in singularity region, but tracking accuracies of the end-effector in all directions are poor.…”

Section: Introductionmentioning

confidence: 99%

Singularity avoidance of 6R decoupled manipulator using improved Gaussian distribution damped reciprocal algorithm

Cui

Feng

2017

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Purpose To improve the trajectory tracking accuracy of 6R decoupled manipulator in singularity region, this paper aims to propose a singularity avoidance algorithm named “singularity separation plus improved Gaussian distribution damped reciprocal”. Design/methodology/approach The manipulator is divided into forearm and wrist, and the corresponding singularity factors are separated based on kinematics calculation. Singularity avoidance is achieved by replacing the common reciprocal with the improved Gaussian distribution damped reciprocal. Findings Compared with common damped reciprocal algorithm and classical Gaussian distribution algorithm, the continuity of the proposed algorithm is improved and the tracking error is minimized. The simulation and experiment results prove effectiveness and practicability of the proposed algorithm. Originality/value This study has an important significance to improve the efficiency and operation accuracy of 6R decoupled manipulator.

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Singular value decomposition using an array of CORDIC processors

Cited by 13 publications

References 24 publications

A Shallow Neural Network for Real-Time Embedded Machine Learning for Tensorial Tactile Data Processing

A Shallow Neural Network for Real-Time Embedded Machine Learning for Tensorial Tactile Data Processing

An overflow free fixed-point eigenvalue decomposition algorithm: Case study of dimensionality reduction in hyperspectral images

Singularity avoidance of 6R decoupled manipulator using improved Gaussian distribution damped reciprocal algorithm

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