Metrics for Inter-Dataset Similarity with Example Applications in Synthetic Data and Feature Selection Evaluation -- Extended Version

Measuring inter-dataset similarity is an important task in machine learning and data mining with various use cases and applications. Existing methods for measuring inter-dataset similarity are computationally expensive, limited, or sensitive to different entities and non-trivial choices for parameters. They also lack a holistic perspective on the entire dataset. In this paper, we propose two novel metrics for measuring inter-dataset similarity. We discuss the mathematical foundation and the theoretical basis of our proposed metrics. We demonstrate the effectiveness of the proposed metrics by investigating two applications in the evaluation of synthetic data and in the evaluation of feature selection methods. The theoretical and empirical studies conducted in this paper illustrate the effectiveness of the proposed metrics.