As an essential data processing technology, cluster analysis has been widely used in various fields. In clustering, it is necessary to select appropriate measures to evaluate the similarity in the data. In this paper, firstly, a cluster center selection method based on the grey relational degree is proposed to solve the problem of sensitivity in initial cluster center selection. Secondly, combining the advantages of Euclidean distance, DTW distance, and SPDTW distance, a weighted distance measurement based on three kinds of reach is proposed. Then, it is applied to Fuzzy C-MeDOIDS and Fuzzy C-means hybrid clustering technology. Numerical experiments are carried out with the UCI datasets. The experimental results show that the accuracy of the clustering results is significantly improved by using the clustering method proposed in this paper. Besides, the method proposed in this paper is applied to the MUSIC INTO EMOTIONS and YEAST datasets. The clustering results show that the algorithm proposed in this paper can also achieve a better clustering effect when dealing with practical problems.

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To address the imbalanced data problem in classification, the studies of the combination of AdaBoost, short for “Adaptive Boosting,” and cost-sensitive learning have shown convincing results in the literature. The cost-sensitive AdaBoost algorithms are practical since the “boosting” property in AdaBoost can iteratively enhance the small class of the cost-sensitive learning to solve the imbalanced data issue. However, the most available cost-sensitive AdaBoost algorithms are heuristic approaches, which are improved from the standard AdaBoost algorithm by cost-sensitively adjusting the voting weight parameters of weak classifiers or the sample updating weight parameters without strict theoretic proof. The algorithms are appended the cost-sensitive factors to focus on the high-cost and small-class samples, but they have no procedures to show the best place to add the cost factors and the cost factor value set. To complete the cost-sensitive AdaBoost algorithms’ framework, the present article has two main contributions. First, we summarize the popular cost-sensitive boosting algorithms in the literature and propose a generally comprehensive form. We name our specific one, the “AdaImC algorithm,” which is typically appliable to solve the imbalanced data classification problem with theoretic proof. Second, a statistical approach to prove the AdaImC algorithm is proposed to verify the inner relationship between the cost parameters. We show that our proposed algorithm in the machine learning field is identical to the Product of Experts (PoE) model in the statistics field. Besides, a way to determine the cost parameter value by the statistical analysis is introduced. Several numeric studies are listed finally to support our proposed algorithm.

The public transportation system of cities, including subway and public transportation, is becoming more and more perfect. With the rapid development of urban public transport, the path selection considering multiple factors has become a new problem. Based on the optimization model, we take urban public transport operators and travelers as the objects, and use the entroy weight TOPSIS method to comprehensively evaluate the feasible lines and paths between multiple OD pairs. Besides, the optimal path to traverse all nodes was solved by Hamilton cycle problem algorithm, which can also provide reference for both operators and travelers. According to the latest urban public transport data in 2021, we select Beijing, China as the empirical research object. This paper chooses the existing public transport network of Beijing to verify, and selects the optimal path of 5 nodes and 10 paths to traverse all nodes.

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