This paper addresses the challenge of identifying the paths for vessels with operating routes of repetitive paths, partially repetitive paths, and new paths. We propose a spatial clustering approach for labeling the vessel paths by using only position information. We develop a path clustering framework employing two methods: a distance-based path modeling and a likelihood estimation method. The former enhances the accuracy of path clustering through the integration of unsupervised machine learning techniques, while the latter focuses on likelihood-based path modeling and introduces segmentation for a more detailed analysis. The result findings highlight the superior performance and efficiency of the developed approach, as both methods for clustering vessel paths into five classes achieve a perfect F1-score. The approach aims to offer valuable insights for route planning, ultimately contributing to improving safety and efficiency in maritime transportation.