## 2 Materials and Methods
### Acoustic Stability Method  
According to the regression analysis of a large number of samples, it is confirmed that there is a linear relationship between the sea surface parameters and the EOF projection coefficients [13]. The regression relationship between the sea level anomaly (SLA), sea surface temperature anomaly (SSTA), and the EOF projection coefficients can be expressed as [13]  
\[a_{n}=A_{i,0}+A_{i,1}\times SLA+A_{i,2}\times SSTA+A_{i,3}\times SLA\times SSTA,\ \ \ i=0,1,2\ldots n, \tag{4}\]  
where \(a_{0}(t)\) is a constant value and \(A_{i}\) are the coefficients that need to be obtained through regression analysis of a large data set. After obtaining \(A_{i}\), SLA and SSTA data are input into Equation (4) to calculate the EOF projection coefficients of the corresponding orders. Finally, the SSP is inversed through Equation (1). The inversion accuracy of Equation (1) is related to the consistency of the profile disturbance law. When the profile disturbance laws are consistent, the obtained fitting coefficients are similar, and the final inversion result can achieve high accuracy. The above method demonstrates the importance of acoustic stability factors in SSP inversion. For the acoustic stability factors, air-sea interactions play a key role. Material and energy exchange in the ocean have a key impact on several important indicators in the sound speed empirical formula. For example, dynamic characteristics of the ocean affect the exchange of salt and energy, thereby directly changing the salt and temperature indicators in the corresponding sea areas. This impact does not have an accurate analytical expression, meaning the specific seawater dynamic characteristics of a certain area cannot be fully described. Therefore, the method of introducing physical constraints to analyze acoustic stability to improve the accuracy of SSP inversion is not applicable. Moreover, there are a large number of random factors in seawater that affect SSP stability. As these dynamic characteristics cannot be calculated using analytical equations, it is necessary to introduce a machine learning algorithm with a high randomness mechanism and a feature selection scheme into the analysis. Empirical Orthogonal Function Consistency Analysis of Sound Speed Profiles in the South China Sea Based on K-Means Clustering Analysis  
SSPs are widely used in the field of marine acoustics and are the basic support data for various studies. However, due to political, economic, and sampling difficulties, the distribution of Argo floats in the South China Sea is relatively sparse, making it difficult to support machine learning-based studies that require a large amount of data. Current Argo data have great time coverage, but lack spatial coverage, resulting in the overall data being more easily analyzed from the perspective of time, as they cannot meet the needs of regression analysis from the perspective of space. From the perspective of Argo float distribution density, in a \(1^{\circ}\times 1^{\circ}\) geographic grid spanning \(18^{\circ}\) N to \(19^{\circ}\) N and \(118^{\circ}\) E to \(119^{\circ}\) E from 2008 to 2018, only 147 SSPs can be queried, and the measurement time period is relatively concentrated. From a statistical point of view, the lack of samples and uneven distribution will increase the instability of the results. Facing the problem of a lack of samples, the primary solution is to expand the SSP inversion area. The EOF is a completely statistical method, and the physical meaning of each mode order needs to be combined with a relevant dynamic analysis to avoid overfitting the results. Simply expanding the inversion area to which the EOF is fit will be accompanied by a decrease in EOF consistency. The pre-clustering method can effectively divide regions with unique dynamic characteristics.