Adjustable Robust Singular Value Decomposition: Design, Analysis and Application to Finance

Wang, De-Shen

doi:10.3390/data2030029

Cited by 7 publications

(13 citation statements)

References 28 publications

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“…Among many applications mentioned in Section 1.1 where the proposed rSVDdpd algorithm may substitute the usual SVD procedure for robust inference, one such interesting usecase is the stock-price modeling in the guise of factor analysis. In finance, the price of a stock is generally assumed to be composed of two components, a latent market risk specific to the economy of the whole country or the industry at an aggregate level, and an asset specific risk particular to the company at the individual level (Wang, 2017). Since the stock prices exhibit jumps and can change drastically within a short period of time, standard SVD often fails to capture this decomposition while robust SVD methods prove useful.…”

Section: Discussionmentioning

confidence: 99%

“…Financial Application: Stock Price Latent Factor Analysis. In finance, the price of a stock is generally assumed to be composed of two components, a latent market risk specific to the economy of the whole country or the industry at an aggregate level, and an asset specific risk particular to the company at the individual level (Wang, 2017).…”

Section: S4 Applications Of Rsvddpdmentioning

confidence: 99%

“…Alternatively, Zhang, Shen and Huang (2013) used the same Huber weight function in defining the loss and combined it with a squared error based penalty function for regularization to construct the minimization criterion for obtaining a robust SVD estimator. Wang (2017) used a myriad estimator derived from an α-stable distribution with the cost function ρ(x) = log(x 2 + K 2 ), where K is a tuning parameter which provides a balance between a mean type estimator and a mode type estimator, thus creating a bridge between robustness and efficiency. However, the suitable value of such tuning parameter K cannot be easily obtained unless a large amount of data are present, and hence a heuristic process has been suggested.…”

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confidence: 99%

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A New Robust Scalable Singular Value Decomposition Algorithm for Video Surveillance Background Modelling

Roy¹,

Basu²,

Ghosh³

2021

Preprint

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A basic algorithmic task in automated video surveillance is to separate background and foreground objects. Camera tampering, noisy videos, low frame rate, etc., pose difficulties in solving the problem. A general approach which classifies the tampered frames, and performs subsequent analysis on the remaining frames after discarding the tampered ones, results in loss of information. We propose a robust singular value decomposition (SVD) approach based on the density power divergence to perform background separation robustly even in the presence of tampered frames. We also provide theoretical results and perform simulations to validate the superiority of the proposed method over the few existing robust SVD methods. Finally, we indicate several other use-cases of the proposed method to show its general applicability to a large range of problems.

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Section: Discussionmentioning

confidence: 99%

Section: S4 Applications Of Rsvddpdmentioning

confidence: 99%

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confidence: 99%

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A New Robust Scalable Singular Value Decomposition Algorithm for Video Surveillance Background Modelling

Roy¹,

Basu²,

Ghosh³

2021

Preprint

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“…The TLS approach to solving an over-determined system of linear equations is based on the singular value decomposition (SVD) technique [53,54]. The resulting procedure is stated in Algorithm 1.…”

Section: Optical Flow Estimation By Total Least Squaresmentioning

confidence: 99%

First Order and Second Order Learning Algorithms on the Special Orthogonal Group to Compute the SVD of Data Matrices

et al. 2020

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The present paper deals with neural algorithms to learn the singular value decomposition (SVD) of data matrices. The neural algorithms utilized in the present research endeavor were developed by Helmke and Moore (HM) and appear under the form of two continuous-time differential equations over the special orthogonal group of matrices. The purpose of the present paper is to develop and compare different numerical schemes, under the form of two alternating learning rules, to learn the singular value decomposition of large matrices on the basis of the HM learning paradigm. The numerical schemes developed here are both first-order (Euler-like) and second-order (Runge-like). Moreover, a reduced Euler scheme is presented that consists of a single learning rule for one of the factors involved in the SVD. Numerical experiments performed to estimate the optical-flow (which is a component of modern IoT technologies) in real-world video sequences illustrate the features of the novel learning schemes.Electronics 2020, 9, 334 2 of 21 (Runge-like). Moreover, a reduced Euler scheme will be presented that consists of a single learning equation for one of the factors involved in the SVD.The developed methods to learn an SVD of a data matrix are applied to optical-flow estimation. Optical flow estimation is a well-known image-processing operation that allows estimating the motion of portions of an image over a video sequence and has found widespread applications (see, for instance, [22][23][24][25][26][27][28][29]). Optical flow is closely related to motion estimation [30]. Optical flow refers to the change of structured light in an image and captures such change through a velocity vector field. Most of the optical-flow estimation algorithms used in video encoding belong to either the class of block matching algorithms (BMAs) or to the class of pixel recursive algorithms (PRAs) [31].Optical flow estimation algorithms are essential components in a number of complex Internet of Things (IoT) technologies, as testified by several existing applications, such as intelligent fall detection [32,33], mobile robotics [34], intelligent flight monitoring [35], mobile object tracing [36], automated surveillance [37], smart healthcare [38], solar energy forecasting [39], and in IoT-based analytics in urban space, shops, and retail stores to inform policy makers, shop owners, and the general public about how they interact with the physical space [40]. See also the interesting discussion in [41].The majority of the current optical-flow estimation methods rely on a block-matching algorithm. The BMA methods are based on the concept of template-matching: it is supposed that a single block in a time-frame has moved solidly to another location in the next time-frame, so the image-block is regarded as a template to be looked for in the subsequent frame. The BMA methods try to evaluate the motion of a block by reducing the number of search locations in the search range and/or by reducing the number of computations at each search location. These algorithm...

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“…In most cases, the numerical solution of an IE with kernels of the specified type is carried out by replacing the integrals with finite sums having a sufficiently high degree of discretization of the integration surface (contour) and reducing them to systems of linear algebraic equations (SLAEs). However, it should be noted that, depending on the boundary conditions and parameters connected with the characteristics of the media, the SLAEs may be ill-conditioned-the task becomes incorrect [26], and its solution requires the application of special methods such as singular value decomposition (SVD).The effectiveness of this procedure has been repeatedly noted [27,28] (particularly in [29]), but its implementation is connected with multiple matrix transformations, the computation of which requires the creation of a sufficiently large database related to the configuration of the integration surfaces.…”

Section: Problem Statementmentioning

confidence: 99%

Geometrical Platform of Big Database Computing for Modeling of Complex Physical Phenomena in Electric Current Treatment of Liquid Metals

Zaporozhets¹,

Иванов²,

Kondratenko

2019

Data

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According to the principles of multiphysical, multiscale simulation of phenomena and processes which take place during the electric current treatment of liquid metals, the need to create an adjustable and concise geometrical platform for the big database computing of mathematical models and simulations is justified. In this article, a geometrical platform was developed based on approximation of boundary contours using arcs for application of the integral equations method and matrix transformations. This method achieves regular procedures using multidimensional scale matrices for big data transfer and computing. The efficiency of this method was verified by computer simulation and used for different model contours, which are parts of real contours. The obtained results showed that the numerical algorithm was highly accurate based on the presented geometrical platform of big database computing and that it possesses a potential ability for use in the organization of computational processes regarding the modeling and simulation of electromagnetic, thermal, hydrodynamic, wave, and mechanical fields (as a practical case in metal melts treated by electric current). The efficiency of this developed approach for big data matrices computing and equation system formation was displayed, as the number of numerical procedures, as well as the time taken to perform them, were much smaller when compared to the finite element method used for the same model contours.

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Adjustable Robust Singular Value Decomposition: Design, Analysis and Application to Finance

Cited by 7 publications

References 28 publications

A New Robust Scalable Singular Value Decomposition Algorithm for Video Surveillance Background Modelling

A New Robust Scalable Singular Value Decomposition Algorithm for Video Surveillance Background Modelling

First Order and Second Order Learning Algorithms on the Special Orthogonal Group to Compute the SVD of Data Matrices

Geometrical Platform of Big Database Computing for Modeling of Complex Physical Phenomena in Electric Current Treatment of Liquid Metals

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