## 1 Introduction
In general, an innovative approach to the effective management of railway maintenance activities involves establishing a relationship between different track properties. This perspective allows engineers to rapidly assess track health conditions without extensive record-keeping. Based on the literature review conducted above, there is limited knowledge regarding the correlation between the geometric parameters and structural characteristics of railway tracks. Among the track properties, ballast stiffness and track geometry are two significant parameters that play a crucial role in maintenance, yet a comprehensive correlation study between them has not been conducted. Therefore, the current study aims to survey the relationship between vertical track stiffness and track geometry, with a specific focus on two crucial representatives: vertical ballast stiffness and the longitudinal level. To achieve this, track geometric data and vertical track deflection measurements were collected along the Tehran-Mashhad railway line in Iran. Various correlation analyses were then conducted using both frequency-based methods and machine learning techniques. First, the relationship between vertical rail deflection and longitudinal level was examined by calculating the power spectrum density (PSD) of the collected data. This analysis aims to investigate the correlation between the data obtained from the track recording car and stiffness recording car. By analyzing the PSD, this study seeks to identify patterns and relationships that can provide insights into the impact of vertical rail deflection on track longitudinal levels and ballast stiffness, contributing to improved track maintenance and performance evaluation. Next, this study evaluated and compared the effectiveness of frequency analysis with three machine learning algorithms--linear regression, decision tree, and random forest--in analyzing the relationship between vertical track stiffness and track geometry. These correlation analyses provide insights into how variations in ballast stiffness impact the vertical longitudinal level of the track, contributing to a deeper understanding of track performance and maintenance needs. The insights mentioned above can reveal the potential of advanced analytical techniques in understanding and optimizing railway track maintenance strategies. By leveraging machine learning algorithms, railway maintenance teams can more accurately predict and address issues related to track conditions. The remainder of this paper is organized as follows: Section 2 presents the data acquisition process, detailing the methods and equipment used to gather the necessary data for track longitudinal level and vertical track deflection measurements along the Tehran-Mashhad railway line. Section 3 discusses the algorithms employed in correlation mining analyses, including both frequency-based techniques and machine learning algorithms such as linear regression, decision tree, and random forest algorithms. Section 4 provides a comprehensive analysis and discussion of the results, highlighting key findings and their implications. Finally, Section 5 concludes this paper, summarizing the main contributions and suggesting potential areas for future research.