CAJ | 학술논문

针对K平均( K-means)、期望最大化( EM)等传统聚类算法在网络社团挖掘中存在的聚类结果不合理、容易陷入局部最小值等问题，以最小化社团间的连接权值为优化目标，基于节点间交互次数归一化结果建立节点间的相似矩阵，求出此矩阵对应的拉普拉斯矩阵，以拉普拉斯矩阵的前k个最小特征值对应的特征向量为基建立新的特征空间，将相似矩阵向新的特征空间做投影，在投影后的特征空间中运用K-means算法进行社团挖掘，实现目标函数的最小化。通过仿真实验对比，说明了该基于拉普拉斯矩阵的聚类方法( LMBC)比传统聚类方法更有效地解决聚类节点分布不均衡的问题，及非凸、高维数据集在保持原有几何结构的同时有效降维的问题。 LMBC从数据集相似矩阵的角度进行聚类分析，进一步丰富了流形学习的理论与方法，可广泛应用于社交网络分析及图像识别等领域。
침대K평균( K-means)、기망최대화( EM)등전통취류산법재망락사단알굴중존재적취류결과불합리、용역함입국부최소치등문제，이최소화사단간적련접권치위우화목표，기우절점간교호차수귀일화결과건립절점간적상사구진，구출차구진대응적랍보랍사구진，이랍보랍사구진적전k개최소특정치대응적특정향량위기건립신적특정공간，장상사구진향신적특정공간주투영，재투영후적특정공간중운용K-means산법진행사단알굴，실현목표함수적최소화。통과방진실험대비，설명료해기우랍보랍사구진적취류방법( LMBC)비전통취류방법경유효지해결취류절점분포불균형적문제，급비철、고유수거집재보지원유궤하결구적동시유효강유적문제。 LMBC종수거집상사구진적각도진행취류분석，진일보봉부료류형학습적이론여방법，가엄범응용우사교망락분석급도상식별등영역。
In view of problems on unreasonable clustering result and easy to fall into local minimum of traditional clustering algorithms, i. e. K-means, Expectation Maximitation ( EM) when they are applied to communities detection, in this study an different approach was proposed. It set minimizing the link weights between different communities as the optimization objective, built a similarity matrix based on normalization result of interaction times between network nodes, inferred the corresponding Laplacian matrix of this similarity matrix, established a new eigenspace based on the corresponding eigenvectors of the first k smallest eigenvalues, made a projection of the similarity matrix on the new eigenspace, did clustering on the projection eigenspace by K-means, finally, accomplished the minimization of objective function. Simulation experiment was done to illustrate that Laplacian Matrix Based Clustering ( LMBC ) can effectively resolve the problems of unbalancing distribution of network nodes and dimensionality reduction of non-convex high dimensional dataset while keeping the geometric structure. LMBC enriches the manifold learning theory and methodology by doing clustering on the dataset similarity matrix, and it can be widely used in social network analysis and image recognition areas.