De-Hankelization of singular spectrum analysis matrices via L1 norm criterion

Huang, Ziyin; Ling, Bingo Wing‐Kuen

doi:10.1007/s11760-019-01430-7

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…The product of an eigenvalue, the corresponding column in the left unitary trajectory and the transpose of the corresponding column in the right unitary matrix forms the two dimensional SSA component. By performing the diagonal averaging operation, the one dimensional SSA components are obtained [15]. It is a remarkable fact that the original input sequence can be expressed as the sum of these one dimensional SSA components [14].…”

Section: Introductionmentioning

confidence: 99%

Performing fractional delay via fractional singular spectrum analysis

Zhou

Ling

Huang

et al. 2021

SIViP

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This paper proposes a fractional singular spectrum analysis (SSA) based method for performing the fractional delay. First, the input sequence is divided into two overlapping sequences with the first sequence being the input sequence without its last point and the second sequence being the input sequence without its first point. Then, the singular value decompositions (SVD) are performed on the trajectory matrices constructed based on these two sequences. Next, the designs of both the right unitary matrix and the left unitary matrix for generating the new trajectory matrix are formulated as the quadratically constrained quadratic programing problems. The analytical solutions of these quadratically constrained quadratic programing problems are derived via the SVD approach. Finally, the fractional SSA components are obtained by performing the diagonal averaging operation and the fractional delay sequence is obtained by summing up all the fractional SSA components together. Since the fractional SSA operations are nonlinear and adaptive, our proposed method is a kind of nonlinear and adaptive approach for performing the fractional delay. Besides, by discarding some fractional SSA components, the joint fractional delay operation and the denoising operation can be performed simultaneously.

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Section: Introductionmentioning

confidence: 99%

Performing fractional delay via fractional singular spectrum analysis

Zhou

Ling

Huang

et al. 2021

SIViP

Self Cite

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Length Reduction of Singular Spectrum Analysis With Guarantee Exact Perfect Reconstruction via Block Sliding Approach

Wang

Ling

2020

IEEE Access

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The conventional singular spectrum analysis is to divide a signal into segments where there is only one non-overlapping point between two consecutive segments. By putting these segments into the columns of a matrix and performing the singular value decomposition on the matrix, various one dimensional singular spectrum analysis vectors are obtained. Since different one dimensional singular spectrum analysis vectors represent different parts of the signal such as the trend part, the oscillation part and the noise part of the signal, the singular spectrum analysis plays a very important role in the nonlinear and adaptive signal analysis. However, as the length of each one dimensional singular spectrum analysis vector is the same as that of the original signal, there is a redundancy among these one dimensional singular spectrum analysis vectors. In order to reduce the required computational power and the required units for the memory storage for performing the singular spectrum analysis, this paper proposes a method to reduce the total number of the elements of all the one dimensional singular spectrum analysis vectors. In particular, the length of the shift block for generating the trajectory matrix is increased from one to a positive integer greater than one under a certain criterion. In this case, the total number of the columns of the trajectory matrix is reduced. As a result, the total number of the off-diagonals of all the two dimensional singular spectrum analysis matrices is reduced. Hence, the total number of the elements of all the one dimensional singular spectrum analysis vectors is reduced. In order to guarantee exact perfect reconstruction, this paper reformulates the de-Hankelization process. In particular, the first element of the off-diagonals of all the two dimensional singular spectrum analysis matrices is taken as the elements of the one dimensional singular spectrum analysis vectors. Exact perfect reconstruction condition is derived. Simulations show that exact perfect reconstruction can be achieved while the total number of the elements of all the one dimensional singular spectrum analysis vectors is significantly reduced.

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Uzun-Kısa Süreli Bellek Ağlarının Nehir Akım Tahmininde Farklı Optimizasyonlarla Karşılaştırılması Ve Tekil Spektrum Analizinin Etkisi

Kilinç¹

2021

European Journal of Science and Technology

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ÖzSu kaynaklarının sürdürülebilir olması için periyodik nehir akım ölçümlerinin yapılması gerekmektedir. Bunun için farklı tahmin yöntemlerine gereksinim duyulmaktadır. Bu çalışmada, Yapay Zeka yöntemlerinden Derin Öğrenme (DL) ile Aksu Nehri akımlarının LSTM (Uzun-Kısa Süreli Bellek) sinir ağı ile tahmini yapılmıştır. Çalışmada, Aksu Nehri üzerindeki D20A002 No'lu Başpınar Akım Gözlem İstasyonuna (AGİ) ait 2000-2019 yılları arasını kapsayan veriler analiz için girdi olarak kullanılmıştır. Ayrıca, Tekil Spektrum Analizi'nin (TSA) LSTM'ye olan perfonmans etkisi irdelenmiştir. TSA-LSTM modeline iyileştirici olarak Adam, Adamax ve AdaGrad algoritmaları uygulanmıştır. Tahmin ve gerçek değerler karşılaştırılarak en doğru tahmin modeli belirlenmiştir. Akım tahmininde iyi performansı Adamax iyileştiricisinin sağladığı görülmüştür. TSA-LSTM modeli katsayısı (R 2 ) tayini test aşamasında 0,9851 bulunmuştur. Elde edilen sonuçlar incelendiğinde TSA-LSTM modelinin akım çalışmaları tahmininde daha iyi sonuçlar verdiği görülmüştür.

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De-Hankelization of singular spectrum analysis matrices via L1 norm criterion

Cited by 3 publications

References 13 publications

Performing fractional delay via fractional singular spectrum analysis

Performing fractional delay via fractional singular spectrum analysis

Length Reduction of Singular Spectrum Analysis With Guarantee Exact Perfect Reconstruction via Block Sliding Approach

Uzun-Kısa Süreli Bellek Ağlarının Nehir Akım Tahmininde Farklı Optimizasyonlarla Karşılaştırılması Ve Tekil Spektrum Analizinin Etkisi

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