## 1 Introduction  
Rapid urbanization enhances the importance of subway systems in managing city traffic and improving commuter experiences. Accurate subway passenger flow forecasting is crucial for distributing transportation resources efficiently, reducing congestion, and planning future traffic networks. Subway passenger flow predictions utilize three main approaches: mathematical statistics, machine learning, and deep learning [1]. Our method enhances prediction accuracy by integrating elements from these established techniques. Although diverse prediction techniques aim to improve the accuracy of subway passenger flow forecasts, the complex and dynamic nature of these data presents significant challenges. These techniques struggle to capture deep-level data, impacting the precision and reliability of forecasts. Conventional mathematical statistical approaches like the Autoregressive Integrated Moving Average (ARIMA) [2] are popular in subway passenger flow forecasting due to their simplicity and ease of use. However, their effectiveness is limited when dealing with complex, non-smooth traffic flow data, often leading to poor outcomes. In response, researchers have turned to machine learning methods such as SVM, decision trees, and random forests [3; 4; 5], which offer improved data processing and pattern recognition capabilities, enhancing prediction accuracy and leading to advancements in predictive models. Despite their advancements, these machine learning models require extensive feature engineering and struggle with long-term dependencies and seasonal variations in time series data [6], limiting their effectiveness. Concurrently, more sophisticated deep learning techniques like Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) [7; 8; 9; 10] have been broadly utilized for forecasting subway passenger flow. Recent advancements in subway passenger flow prediction have utilized a range of methods, from traditional ARIMA/SARIMA models to more complex deep learning approaches such as LSTM and Transformer-based architectures. These models have shown varying degrees of success in addressing the nonlinear and time-varying nature of passenger flow data. However, many face challenges such as scalability, interpretability, and computational cost [11; 12]. To enhance the effective extraction of various types of information from raw traffic data, various methods for transforming time series data into frequency domain components have been widely applied to passenger flow data, road traffic flow data, and other types of time series data. Fourier transform is one such method, and empirical mode decomposition (EMD) proposed by [PERSON] and others can decompose time series data into a few Intrinsic Mode Functions (IMFs) and a residue term [13]. Analyzing these components enables the extraction of the deep features of the sequence data at different time scales. [PERSON] et al. employed the empirical mode decomposition and reinforcement learning techniques to predict short-term passenger flow in urban rail transit systems [14]. The model effectively enhanced the accuracy of the predictions. However, the process of EMD suffers from issues such as end effects and mode mixing, which can lead to the omission of valuable information and affect the decomposition accuracy. EEMD, CEEMDAN, and ICEEMDAN have addressed some of the limitations of the original EMD by reducing mode mixing and improving signal decomposition stability [15; 16; 17]. [PERSON] et al. used a wavelet model to decompose subway passenger flow data into low-frequency and high-frequency components to provide more accurate information extraction, but the type of wavelet limits its accuracy. Classical frequency models, such as Fourier transforms, struggle to capture non-stationary data characteristics. Wavelet transforms, while effective in decomposing non-stationary data, have limitations in selecting an appropriate wavelet basis and in capturing complex nonlinear relationships [18].