Hasan Erbay

A modified Gram-Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems

The ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD). The ULVD can be updated and downdated much faster than the SVD, hence its utility in the solution of recursive total least squares (TLS) problems. However, the robust implementation of ULVD after the addition and deletion of rows (called updating and downdating, respectively) is not altogether straightforward. When updating or downdating the ULVD, the accurate computation of the subspaces necessary to solve the TLS problem is of great importance. In this paper, algorithms are given to compute simple parameters that can often show when good subspaces have been computed.

An Alternative Algorithm for the Refinement of ULV Decompositions

The ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD). It is useful in applications of the SVD such as principal components where we are interested in approximating a matrix by one of lower rank. It can be updated and downdated much more quickly than an SVD. In many instances, the ULVD must be refined to improve the approximation it gives for the important right singular subspaces or to improve the matrix approximation. Present algorithms to perform this refinement require O(mn) operations if the rank of the matrix is k, where k is very close to 0 or n, but these algorithms require O(m n2) operations otherwise. Presented here is an alternative refinement algorithm that requires O(mn) operations no matter what the rank is. Our tests show that this new refinement algorithm produces similar improvement in matrix approximation and in the subspaces. We also propose slight improvements on the error bounds on subspaces and singular values computed by the ULVD.

Recursive ULV decomposition

The ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD). The ULVD can be modified much faster than the SVD. The accurate computation of the subspaces is required in applications in signal processing. In this paper we introduce a recursive ULVD algorithm which is faster than all available stable SVD algorithms. Moreover, we present an alternative refinement algorithm.

An efficient algorithm for rank and subspace tracking

Traditionally, the singular value decomposition (SVD) has been used in rank and subspace tracking methods. However, the SVD is computationally costly, especially when the problem is recursive in nature and the size of the matrix is large. The truncated ULV decomposition (TULV) is an alternative to the SVD. It provides a good approximation to subspaces for the data matrix and can be modified quickly to reflect changes in the data. It also reveals the rank of the matrix. This paper presents a TULV updating algorithm. The algorithm is most efficient when the matrix is of low rank. Numerical results are presented that illustrate the accuracy of the algorithm.

An Alternative Algorithm for a Sliding Window ULV Decomposition

The ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD). The ULVD can be modified much faster than the SVD. When modifiying the ULVD, the accurate computation of the subspaces is required in certain time varying applications in signal processing. In this paper, we present an updating algorithm which is suitable for large scaled matrices of low rank and as effective as alternatives. The algorithm runs in O(n2) time.

Modified Gram-Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems

The ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD). The ULVD can be updated and downdated much faster than the SVD, hence its utility in the solution of recursive total least squares (TLS) problems. However, the robust implementation of ULVD after the addition and deletion of rows (called updating and downdating respectively) is not altogether straightforward. When updating or downdating the ULVD, the accurate computation of the subspaces necessary to solve the TLS problem is of great importance. In this paper, algorithms are given to compute simple parameters that can often show when good subspaces have been computed.

Block classical Gram–Schmidt-based block updating in low-rank matrix approximation

Low-rank matrix approximations have recently gained broad popularity in scientific computing areas. They are used to extract correlations and remove noise from matrix-structured data with limited loss of information. Truncated singular value decomposition (SVD) is the main tool for computing low-rank approximation. However, in applications such as latent semantic indexing where document collections are dynamic over time, i.e. the term document matrix is subject to repeated updates, SVD becomes prohibitive due to the high computational expense. Alternative decompositions have been proposed for these applications such as low-rank ULV/URV decompositions and truncated ULV decomposition. Herein, we propose a BLAS-3 compatible block updating truncated ULV decomposition algorithm based on the block classical Gram–Schmidt process. The simulation results presented show that the block update algorithm is promising.

Yaşam Boyu Öğrenme Ölçeği Türkçe Uyarlama Çalışması

Bu calismanin amaci, orijinali Wielkiewicz ve Meuwissen (2014) tarafindan gelistirilen yasam boyu ogrenme olceginin Turkiye kosullarinda gecerlik ve guvenirlik calismasini yapmaktir. Olcegin Turkceye cevirisi dil uzmanlarinca ve arastirmacilar tarafindan yapilmistir. Daha sonra Turkceye uygunluk, icerik ve olcme degerlendirme acilarindan da uzmanlar tarafindan degerlendirilmistir. Alinan gorusler dogrultusunda duzenlemelerin yapildigi olcek, gecerlik ve guvenirliginin saptanmasi amaciyla 727 universite ogrencisine uygulanmistir. Olcegin yapi gecerligine iliskin bulgular acimlayici ve dogrulayici faktor analizi yontemi ile saglanmistir. Olcek maddeleri tek faktor altinda toplanmistir. Olcege uygulanan faktor analizi sonucu bir soru cikarilmistir, son durumda olcek toplamda 15 madde icermektedir. Olcegin geneli icin Cronbach Alpha guvenirlik katsayisi 0,93 olarak bulunmustur. Elde edilen sonuclar olcegin Turkiye’de de kullanilabilecegini gostermistir. Anahtar Kelimeler: Yasam boyu ogrenme, olcme, olcek

Open source slurm computer cluster system design and a sample application

Cluster computing combines the resources of multiple computers as they act like a single high-performance computer. In this study, a computer cluster consisting of Lustre distributed file system with one cluster server based on Slurm resource management system and thirteen calculation nodes were built by using available and inert computers that have different processors. Different bioinformatics algorithms were run using different data sets in the cluster, and the performance of the clusters was evaluated with the amount of time the computing cluster spent to finish the jobs.

Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor

Abstract In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable. The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.