Assessing regional sustainable development through an integration of nonlinear principal component analysis and Gram Schmidt orthogonalization

The regional sustainable development level (SDL), sustainability of regional development (SRD) and system coordination (SC) make up the triangular truss of regional sustainable development assessment, but it is debated how should traditional practice best weight and calculate the whole sustainable development system level. The Bohai Rim, covering three provinces and two municipalities in China, lies in a region that is sensitive to profound conflict between socioeconomic development and environment pollution in the process of sustainable development. Considering the defects of traditional models and the multidimensionality of regional sustainability issues, we proposed an integrated model of nonlinear principal component analysis and Gram Schmidt orthogonalization and presented a novel regional sustainable development assessment method and framework from three perspectives for the society-economy-environment system of the Bohai Rim region. The results show that: (a) the integration of nonlinear principal component analysis and Gram Schmidt orthogonalization can well remedy the defects of traditional methods and provide a more objective conceptual framework; (b) the sustainability of regional development and system coordination models graphically demonstrate the essence and connotation of a dynamic sustainable development system; (c) the empirical study demonstrated that the Bohai Rim region has experienced a distinct development period in which the SRD experienced a steady decline and the SDL and SC generally increased; (d) the coordination ability can be improved by a decline in the environmental sustainability, which reveals the importance of environment subsystem optimization; and (e) the weight distribution of variables demonstrates that the most significant factors affecting sustainable development are the indicators from the dimensions of people's standard of living, economic structure and environmental pollution. This study enriches the sustainable development assessment theory and methodology, and lays the foundation for further sustainable development research in the Bohai Rim region.