An Entropy Clustering Method for the Model and Its Algorithm of the Maximizing a Submodular Function Subject to a Matroid Constraint
Abstract: This paper proposes a new clustering objective function with information entropy, which is composed of entropy rate of random path based on graph theory and balance item. Entropy rate is conducive to compact and uniform clustering, the balance function encourages objects with high similarity to cluster, and punishes those objects with low similarity. First, the weighted undirected graph associated with data is constructed, and it is found that this structure induces a matroid, a combination of the structure of linear independent concept in vector space. Then, the model of which is maximizing a submodular function under the constraints of the matroid is obtained. Finally, according to the monotonicity, increment and submodular of the objective function, an efficient greedy algorithm is developed and its performance guarantee is discussed.
文章引用: 梁国宏 , 李 映 , 叶 萌 , 李炳杰 (2017) 拟阵约束下最大化子模函数的模型及其算法的一种熵聚类方法。 计算机科学与应用， 7， 994-1001. doi: 10.12677/CSA.2017.710112
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