Dynamic Identification of Relative Poverty Among Chinese Households Using the Multiway Mahalanobis–Taguchi System: A Sustainable Livelihoods Perspective

To promote global sustainable development, this paper focuses on the identification of relative poverty. On the one hand, based on the sustainable livelihoods framework, a multi-dimensional relative poverty identification index system is constructed, covering six dimensions—human capital, financial capital, natural capital, physical capital, social capital, and livelihood environment—with a total of 18 indexes. On the other hand, addressing the limitations of traditional relative poverty identification methods in handling dynamic three-dimensional data, the multiway Mahalanobis–Taguchi system (MMTS) is proposed to identify dynamic relative poverty. This method first unfolds dynamic three-dimensional data into two-dimensional data along the sample direction through multiway statistical analysis techniques, then constructs multiway Mahalanobis distances to measure sample differences, and finally uses a Taguchi orthogonal experimental design for dimensionality reduction and noise reduction to optimize the model. Experiments using tracking survey data from 2020 to 2024 in three poverty-stricken counties in China’s Dabie Mountain area show that MMTS performs better than the Two-Way Fixed Effects (Two-way FE) model and Dynamic LSTM. MMTS shows a higher specificity, stronger noise resistance, smaller result fluctuations, better G-means performance, and a better balance between sensitivity and specificity. This proves its scientific validity and practical applicability.