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The density peak clustering algorithm (DP) is proposed to identify cluster centers by two parameters, i.e. ρ value (local density) and δ value (the distance between a point and another point with a higher ρ value). According to the center-identifying principle of the DP, the potential cluster centers should have a higher ρ value and a higher δ value than other points. However, this principle may limit the DP from identifying some categories with multi-centers or the centers in lower-density regions. In addition, the improper assignment strategy of the DP could cause a wrong assignment result for the non-center points. This paper aims to address the aforementioned issues and improve the clustering performance of the DP.

First, to identify as many potential cluster centers as possible, the authors construct a point-domain by introducing the pinhole imaging strategy to extend the searching range of the potential cluster centers. Second, they design different novel calculation methods for calculating the domain distance, point-domain density and domain similarity. Third, they adopt domain similarity to achieve the domain merging process and optimize the final clustering results.

The experimental results on analyzing 12 synthetic data sets and 12 real-world data sets show that two-stage density peak clustering based on multi-strategy optimization (TMsDP) outperforms the DP and other state-of-the-art algorithms.

The authors propose a novel DP-based clustering method, i.e. TMsDP, and transform the relationship between points into that between domains to ultimately further optimize the clustering performance of the DP.

Expanding the research on traditional history of economic ideology into the research on the history of economics composed of three elements – history of ideology, history of policies and events – is a new idea for researching the history of socialist political economy with Chinese characteristics. The start of the history of socialist political economy with Chinese characteristics is consistent with that of the Sinicization of Marxist political economy and can be dated from at least 1917.

The key point of the research on the history of ideologies of the socialist political economy with Chinese characteristics is to treat the relationship between theory and people properly, i.e. we should not neglect the effect brought out by the economists on theory construction while we attach importance to the theoretical contribution of the leaders and leading group of the Communist Party of China (CPC).

For the research on the history of economic policies of socialist political economy with Chinese characteristics, on the one hand, we should clarify the relationship among ideologies, strategies and policies; on the other hand, we should not evade the summarization of lessons from history.

Besides presenting the development route of socialist political economy with Chinese characteristics under competition, the research on the events in the history of socialist political economy with Chinese characteristics should also help develop the socialist political economy with Chinese characteristics.