Optimal low-rank approximation to a correlation matrix

Zhang, Zhenyue; Wu, Lixin

doi:10.1016/s0024-3795(02)00551-7

Cited by 35 publications

(46 citation statements)

References 5 publications

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“…Following the errors analysis in [11], it is straightforward to show that in finite precision arithmetic, (2) become…”

Section: Lanczos Tridiagonalization Processmentioning

confidence: 99%

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A Fast Start Base on Lanczos Algorithm for Symmetric Nonnegative Positive Definition Matrix Factorization

Guo¹,

Huang²

2017

dtetr

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Abstract. Symmetric nonnegative matrix factorization(SNMF) has widely employed in many areas of applications. Symmetric nonnegative positive definition matrix factorization(SNPDMF) is a sub problem of SNMF. Authors proposed a Lanczos-based initialization method for SNPDMF, which can be combined with existing SNPDMF algorithms and achieve higher efficiency. Experiments shows that the SNPDMF algorithm which combined the proposed initialization method can converges to a better solution.

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“…Following the errors analysis in [11], it is straightforward to show that in finite precision arithmetic, (2) become…”

Section: Lanczos Tridiagonalization Processmentioning

confidence: 99%

“…The experiment data is taken from Zhang and Wu [11] and the correlation matrix A is given as follows: A correlation matrix is a symmetric symmetric semi positive definition matrix. So, it is readily can be decomposed as A = WW .…”

Section: Numerical Experimentsmentioning

confidence: 99%

A Fast Start Base on Lanczos Algorithm for Symmetric Nonnegative Positive Definition Matrix Factorization

Guo¹,

Huang²

2017

dtetr

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“…The following lemma provides the basis for the connection of the normal vector at Y versus the Lagrange multipliers of the algorithm of Zhang & Wu (2003) and Wu (2003). The result is novel since previously only an expression was known for the matrix Y given the Lagrange multipliers.…”

Section: Connection Normal With Lagrange Multipliersmentioning

confidence: 99%

“…(Characterization of the global minimum of Problem (1.1), see Zhang & Wu (2003) and Wu (2003)) Let C be a symmetric matrix. Let λ * be such that there exists Proof: Apply Lemma 6.1 and Theorem 6.2.…”

Section: Where D * Can Be Obtained By Selecting At Most D Nonnegativementioning

confidence: 99%

Efficient Rank Reduction of Correlation Matrices

Grubišić

Pietersz²

2005

SSRN Journal

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Abstract. Geometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature. The connection with the Lagrange multiplier method is established, along with an identification of whether a local minimum is a global minimum. An additional benefit of the geometric approach is that any weighted norm can be applied. The problem of finding the nearest low-rank correlation matrix occurs as part of the calibration of multi-factor interest rate market models to correlation.

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“…Brigo (2002) extended their work, specifically examining the same problem as this paper. Zhang and Wu (2003) use Lagrange multiplier techniques, and Grubisic and Pietersz (2003) use geometric optimization.…”

Section: Introductionmentioning

confidence: 99%

An EZI Method to Reduce the Rank of a Correlation Matrix in Financial Modelling

Morini

Webber

2006

Applied Mathematical Finance

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Reducing the number of factors in a model by reducing the rank of a correlation matrix is a problem that often arises in finance, for instance in pricing interest rate derivatives with Libor market models. A simple iterative algorithm for correlation rank reduction is introduced, the eigenvalue zeroing by iteration, EZI, algorithm. Its convergence is investigated and extension presented with particular optimality properties. The performance of EZI is compared with those of other common methods. Different data sets are considered including empirical data from the interest rate market, different possible market cases and criteria, and a calibration case. The EZI algorithm is extremely fast even in computationally complex situations, and achieves a very high level of precision. From these results, the EZI algorithm for financial application has superior performance to the main methods in current use.Correlation matrix, rank reduction, market models,

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Optimal low-rank approximation to a correlation matrix

Cited by 35 publications

References 5 publications

A Fast Start Base on Lanczos Algorithm for Symmetric Nonnegative Positive Definition Matrix Factorization

A Fast Start Base on Lanczos Algorithm for Symmetric Nonnegative Positive Definition Matrix Factorization

Efficient Rank Reduction of Correlation Matrices

An EZI Method to Reduce the Rank of a Correlation Matrix in Financial Modelling

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