De-Hankelization of Singular Spectrum Analysis Matrices via L1 Norm Criterion

Abstract

For the de-Hankelization process in the singular spectrum analysis (SSA), the elements in the one dimensional SSA vectors are obtained via the conventional diagonal averaging method. That is, the average value of each off-diagonal of each two dimensional SSA matrix is computed. However, there are many large valued elements in the error vectors defining as the absolute differences between the off-diagonal vectors and the vectors with all the elements being the represented values. In other words, many elements in the off-diagonal vectors are different from the represented values. To address this issue, this paper proposes to find the represented values using the L 1 norm criterion subject to the exact perfect reconstruction condition. Compared to the conventional diagonal averaging method, the computer numerical simulation results show that our proposed method could yield a smaller total number of the large valued elements in the error vectors.