# A Correction for the Paper "Symplectic geometry mode decomposition and its application to rotating machinery compound fault diagnosis"

## TL;DR

This paper identifies and corrects limitations in the symplectic geometry mode decomposition (SGMD) method by fixing bugs related to the diagonal averaging principle, enhancing its accuracy for time series analysis.

## Contribution

The authors provide a correction to SGMD by applying the pulling back theorem, improving the method's reliability for decomposing time series data.

## Key findings

- Corrected the SGMD method with the pulling back theorem
- Enhanced accuracy in time series decomposition
- Identified limitations in the original SGMD approach

## Abstract

The symplectic geometry mode decomposition (SGMD) is a powerful method for decomposing time series, which is based on the diagonal averaging principle (DAP) inherited from the singular spectrum analysis (SSA). Although the authors of SGMD method generalized the form of the trajectory matrix in SSA, the DAP is not updated simultaneously. In this work, we pointed out the limitations of the SGMD method and fixed the bugs with the pulling back theorem for computing the given component of time series from the corresponding component of trajectory matrix.