Analysis of Carbon Emissions Embodied in the Provincial Trade of China Based on an Input–Output Model and k-Means Algorithm

National or regional carbon emissions are generally accounted for by the principle of “producer responsibility”, which ignores the embodied carbon emissions implied in product consumption via inter-regional trade. Therefore, it is necessary to include the embodied carbon emissions into the product consumption regions for overall calculation. As an example, this paper analyzes the characteristics of China’s domestic regional carbon flow network based on a multiregional input–output table and carbon emission data, identifying three clusters of carbon emission characteristic regions by k-means—the clustering algorithm of machine learning. The research results show that some provinces—such as Beijing, Zhejiang, and Guangdong—are the net input areas of embodied carbon emissions (“consumers”), consuming products and services produced by “producers” such as Hebei, Shanxi, and Inner Mongolia through trade, implicitly transferring the responsibility for carbon emissions. Accounting for carbon emissions worldwide/countrywide should consider both production responsibility and trade income. Our findings provide a novel national or regional classification approach based on embodied carbon emissions, which calls for an equitable regional distribution system of carbon emission rights. Meantime, inter-regional cooperation is of great significance in achieving carbon neutrality. In particular, the economically developed regions need to offer assistance to improve the energy efficiency or optimize the energy structure in less developed regions, by means of capital investment and technology transformation.