CAJ | 학술논문

在目前复杂网络聚类算法中，基于 Laplace 特征值的谱聚类方法具有严密的数学理论和较高的精度，但受限于该方法对簇结构数量、规模等先验知识的依赖，难以实际应用。针对这一问题，基于Laplace矩阵的Jordan型变换，提出了一种先验知识的自动获取方法，实现了基于Jordan矩阵特征向量的初始划分。基于Jordan型特征值定义了簇结构的模块化密度函数，并使用该函数和初始划分结果完成了高精度聚类算法。该算法在多个数据集中的实验结果表明，与目前主流的Fast-Newman算法、Girvan-Newman算法相比，基于Laplace矩阵Jordan型聚类算法在不依赖先验知识的情况下，实现了更高的聚类精度，验证了先验知识获取方法的有效性和合理性。
재목전복잡망락취류산법중，기우 Laplace 특정치적보취류방법구유엄밀적수학이론화교고적정도，단수한우해방법대족결구수량、규모등선험지식적의뢰，난이실제응용。침대저일문제，기우Laplace구진적Jordan형변환，제출료일충선험지식적자동획취방법，실현료기우Jordan구진특정향량적초시화분。기우Jordan형특정치정의료족결구적모괴화밀도함수，병사용해함수화초시화분결과완성료고정도취류산법。해산법재다개수거집중적실험결과표명，여목전주류적Fast-Newman산법、Girvan-Newman산법상비，기우Laplace구진Jordan형취류산법재불의뢰선험지식적정황하，실현료경고적취류정도，험증료선험지식획취방법적유효성화합이성。
Among existing clustering algorithms, the graph-Laplacian-based spectrum clustering algorithm has rigorous theoretical basis and high accuracy. However, the application of this algorithm is limited by its dependence on the prior knowledge, such as the number and the size of clusters. Based on the Jordan form of graph Laplacian, an algorithm was proposed which can obtain the prior knowledge, and perform the primary clustering based on the eigenvalues of the Jor-dan form. The modularity density function of clusters was defined, and an improved spectrum clustering algorithm with the help of the function and the primary clustering was proposed. The experiments were conducted on diverse datasets showing that, compared with the classic algorithms such as Fast-Newman and Girvan-Newman, the algorithm can reach a high clustering accuracy and a fast convergence rate.