拉普拉斯矩阵在聚类中的应用
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摘要
高维数据受冗余数据和噪声数据的影响,聚类效率和准确率低,基于拉普拉斯矩阵的特征值和特征向量的特点,介绍了一种适用于高维数据的新的聚类中心选择算法,算法将拉普拉斯矩阵用于候选聚类中心选择前的数据降维处理,经过对数据进行降维处理,提高了候选聚类中心的准确性,增大了聚类准确率,扩大了聚类数据的种类范围.在10个包含不同数量样本、维度、类别数的数据集上进行了聚类分析,实验结果表明了基于拉普拉斯降维的新聚类中心选择方法的有效性.
High-dimensional data is affected by redundant data and noise data,and the clustering efficiency and accuracy are low.Based on the characteristics of eigenvalues and eigenvectors of Laplacian matrix,a new algorithm for cluster center selection is introduced.The algorithm is suitable for high-dimensional data set.Laplacian matrix is used for data set dimension reduction before the selection of the candidate cluster center.After the dimensionality reduction of the data set,the accuracy of the candidate cluster center is improved,and the clustering accuracy is increased.The types of clustering data has been enriched.Cluster analysis was carried out on ten data sets containing different numbers of samples,dimensions and categories.The experimental results have justified the effectiveness of the new cluster center selection algorithm based on Laplacian matrix dimension reduction.
High-dimensional data is affected by redundant data and noise data,and the clustering efficiency and accuracy are low.Based on the characteristics of eigenvalues and eigenvectors of Laplacian matrix,a new algorithm for cluster center selection is introduced.The algorithm is suitable for high-dimensional data set.Laplacian matrix is used for data set dimension reduction before the selection of the candidate cluster center.After the dimensionality reduction of the data set,the accuracy of the candidate cluster center is improved,and the clustering accuracy is increased.The types of clustering data has been enriched.Cluster analysis was carried out on ten data sets containing different numbers of samples,dimensions and categories.The experimental results have justified the effectiveness of the new cluster center selection algorithm based on Laplacian matrix dimension reduction.
引文
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[2]杜辉,王宇平,董晓盼.采用万有引力定律自动确定类数的K均值算法[J].西安交通大学学报,2014,48(10):115-119.
[3]王伟文.拉普拉斯特征映射新增样本点问题及正则化降维研究[D].广州:暨南大学,2017.
[4]谢德喜.拉普拉斯变换在工程方程中的应用[J].天津轻工业学院学报,1990(1):103-110.
[5]汪玉美,陈代梅,赵根保.基于目标提取与拉普拉斯变换的红外和可见光图像融合算法[J].激光与光电子学进展,2017,54(1):98-106.
[6]Hagen L,Kahng A B.New spectral methods for ratio cut partitioning and clustering[J].IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,1992,11(9):1074-1085.
[7]胡乾坤,丁世飞.局部相似性优化的p-谱聚类算法[J].计算机科学与探索,2018,12(3):462-471.
[8]郭磊,杨静,宋乃庆.谱聚类算法在不同属性层级结构诊断评估中的应用[J].心理科学,2018,41(3):735-742.
[9]朱晓欣.拉普拉斯矩阵特征值的图论意义[J].江苏教育学院:自然科学版,2006,23(1):19-20.
[10]郭继明.图的拉普拉斯特征值[D].上海:同济大学,2006.
[11]侯臣平,吴翊,易东云.新的流形学习方法统一框架及改进的拉普拉斯特征映射方法[J].计算机研究与发展,2009,46(4):676-682.
[12]Rodriguez A,Laio A.Machine learning.Clustering by fast search and find of density peaks[J].Science,2014,344(6191):1492-1496.