# A Predictive Method for Temperature Based on Ensemble EMD with Linear Regression
## 2 Ensemble EMD with LR Related Works
### Emd  
EMD is the abbreviation for empirical mode decomposition. It is a signal processing approach introduced by [PERSON] et al. in 1998 [PERSON] et al. (2019). It addresses the challenges posed by traditional decomposition methods when dealing with non-stationary and nonlinear signals. Instead of relying on predefined assumptions, EMD adaptively breaks down signals into components known as IMFs (intrinsic mode functions), with each capturing specific frequency and amplitude characteristics. This technique stands out for its ability to capture local signal nuances. The EMD algorithm follows a straightforward \"sifting and extraction\" process. Initially, it constructs lower and upper boundaries using local extrema points, then iteratively computes IMFs by subtracting the mean of these envelopes. The process continues until certain IMF criteria are met, which results in a set of IMFs and a residue term. These IMFs represent the signal's oscillatory behavior across different time scales. EMD's strength lies in its data-driven approach, which eliminates the need for predefined assumptions about the signal. This versatility makes it suitable for diverse signal types, including nonlinear and non-stationary ones. Moreover, EMD excels in capturing local signal details, which leads to higher fidelity decomposition outcomes. In practical applications, EMD finds utility in various signal processing tasks. It can effectively denoise signals by selectively filtering high-frequency IMFs while preserving critical signal features. Additionally, EMD facilitates signal analysis by revealing the main characteristics of the signal through the examination of IMFs at different frequencies. Its versatility and effectiveness make it a valuable tool in signal processing contexts. When dealing with specific types of signals, the traditional EMD method may face challenges such as mode mixing and over-decomposition. In such cases, multiple intrinsic mode functions (IMFs) with similar characteristic frequencies can lead to confusion, which can make it challenging to interpret and analyze the signal characteristics. This situation is referred to as mode mixing. Additionally, traditional EMD's tendency to extract numerous IMFs from a signal can lead to over-decomposition and result in an excessive number of IMFs, some of which may contain noise or irrelevant components and thereby complicate the process of signal analysis. In 2009, [PERSON] and colleagues introduced an adaptive empirical mode decomposition technique (EEMD) [32]. It leverages the statistical properties of white noise signals. EEMD tackles these challenges by incorporating random noise. More specifically, it integrates different random noises with the initial signal. It reconstructs the signal repeatedly, using a distinct random noise profile each time. This iterative process results in the generation of subtly varying intrinsic mode functions (IMFs) with each reconstruction, which enhances the model's diversity in capturing the signal's structural characteristics. Subsequently, the outcomes of multiple reconstructions are averaged to yield the final IMF. This holistic approach aids in mitigating mode mixing by exploiting the slight deviations in the IMFs produced during each reconstruction, and allows for more comprehensive capturing of the signal's attributes. Furthermore, averaging the outcomes of multiple reconstructions can mitigate over-decomposition by potentially nullifying irrelevant IMFs in the averaging process. Based on recent studies, EEMD has demonstrated significant advancements in processing non-stationary signals across diverse domains:  
1. Biomedical signal denoising: EEMD combined with modified sigmoid thresholding effectively reduces noise in ECG signals while preserving QRS complexes and enhancing feature extraction for clinical diagnosis [33]. Novel approaches like EEMD-MD (Mahalanobis distance) further improve the noise separation in finger-based ECG by quantifying the probability density functions of IMFs [34];
2.