Coordinate System Transformation Method for Comparing Different Types of Data in Different Dataset Using Singular Value Decomposition

In the current era of AI technology, where systems increasingly rely on big data to process vast amounts of societal information, efficient methods for integrating and utilizing diverse datasets are essential. This article presents a novel approach for transforming the feature space of different datasets through singular value decomposition (SVD) to extract common and hidden features as using the prior domain knowledge. Specifically, we apply this method to two datasets: 1) one related to physical and cognitive frailty in the elderly; and 2) another focusing on identifying IKIGAI (happiness, self-efficacy, and sense of contribution) in volunteer staff of a civic health promotion activity. Both datasets consist of multiple sub-datasets measured using different modalities, such as facial expressions, sound, activity, and heart rates. By defining feature extraction methods for each subdataset, we compare and integrate the overlapping data. The results demonstrated that our method could effectively preserve common characteristics across different data types, offering a more interpretable solution than traditional dimensionality reduction methods based on linear and nonlinear transformation. This approach has significant implications for data integration in multidisciplinary fields and opens the door for future applications to a wide range of datasets.