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

Abstract

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.

Abnormal State Detection of OLTC Based on Improved Fuzzy C-means Clustering

“…In this thesis, the WP-SSA [18][19] is proposed to denoise the vibration signal, where the WP transform is used for the first denoising while the SSA is used for secondary denoising. The WP overcomes the shortcoming of the wavelet transform, which cannot decompose high-frequency signals.…”

“…When WP is used to decompose the signal, it decomposes the signal layer-by-layer according to the decomposition scale from low to high, and all sub-band signals in each layer are decomposed into low-frequency and high-frequency components. This decomposition process is called the WP tree [19] . After the n-layer decomposition, a pure low-frequency component and 2…”

“…The EMD algorithm, which has been applied for signal analysis for a long time [11][12][13] , was also introduced to detect the mechanical state of the OLTC [14][15] . In addition to the aforementioned methods or algorithms, including the wavelet transform analysis, EMD, Hilbert transform, and K-means clustering, other methods such as the Fourier transform [16] , deep belief network (DBN) [17][18] , wavelet and modal analysis [19] , and expert system [20] were proposed for analyzing the vibration signals of the OLTC.…”

The Tensor Discriminant Ridge Regression Model With Extreme Learning Machine for Hyperspectral Image Classification

“…So, in this paper, we retain the component with the largest singular value. The approximate steps include build the trajectory matrix, SVD decomposition, grouping, giagonal reconstruction [5][28] [29]. On hyperspectral images, building the trajectory matrix is described as follows:…”

“…In our experiments, the classification results were compared quantitatively based on the Overall classification accuracy Fig. 1: The schematic diagram of algorithm (OA) and kappa coefficient [29]. All experiments are performed on a machine with Intel Core(TM) i7 7700 3.60 GHz and 8GB RAM using MATLAB R2020a.…”