自适应局部稀疏线性嵌入降维算法
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摘要
针对局部线性嵌入近邻选取和权重矩阵奇异的问题,提出一种自适应局部稀疏线性嵌入降维算法。采用稀疏度自适应匹配追踪求解权重矩阵,利用匹配追踪的残差迭代出近邻点的权重,避免权重矩阵求解过程中引起的奇异问题。通过样本重构的残差大小,自适应地选取合适的近邻点个数,对邻域进行二次选择,保留更多的样本结构信息。实验结果表明,该算法的分类正确率均高于其他降维算法,同时也缩短了运行时间。
In order to improve the effectiveness of local linear embedding in dimensionality reduction(LLE), a locally and sparsely adaptive linear embedding(LSALE) algorithm is proposed. In this algorithm, weight matrixis solved by using sparsity adaptive matching pursuit(SAMP), the weight of neighboursis obtainedusing its residuals to avoid calculating the inverse of the weight matrix. In additional, through the residual size of the reconstructed sample, the appropriate number of neighbours for each sample is automatically selectedbased on the residuals of the neighbours at the time of sample reconstruction. Therefore more structural information of the sample is retained, and the anti-noise ability of the algorithm is improved. Experimental results indicate that the recognition rate of LSALE is higher than that of the locally linear embedding.
In order to improve the effectiveness of local linear embedding in dimensionality reduction(LLE), a locally and sparsely adaptive linear embedding(LSALE) algorithm is proposed. In this algorithm, weight matrixis solved by using sparsity adaptive matching pursuit(SAMP), the weight of neighboursis obtainedusing its residuals to avoid calculating the inverse of the weight matrix. In additional, through the residual size of the reconstructed sample, the appropriate number of neighbours for each sample is automatically selectedbased on the residuals of the neighbours at the time of sample reconstruction. Therefore more structural information of the sample is retained, and the anti-noise ability of the algorithm is improved. Experimental results indicate that the recognition rate of LSALE is higher than that of the locally linear embedding.
引文
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[2] 刘颖,魏丽娜,王殿伟,等.基于流形学习的车牌图像超分辨率算法 [J/OL].西安邮电大学学报,2014,19(6):22-25[2018-09-28].http://www.cnki.net/k-cms/doi/10.13682/j.issn.2095-6533.2014.06.005.html.
[3] 黄宏臣,韩振南,张倩倩,等.基于拉普拉斯特征映射的滚动轴承故障识别[J/OL].振动与冲击,2015,34(5):128-134[2018-09-28].http://www.doi.org/10.13465/j.cnki.jvs.2015.05.022.
[4] 王宪保,陈诗文,姚明海.基于正则化的半监督等距映射数据降维方法[J/OL].电子与信息学报,2016,38(1):241-245[2018-12-21].http://www.doi.org/10.11999/JEIT150694.
[5] 孙斌,刘立远,牛翀.基于局部切空间排列和K-最近邻分类器的转子故障诊断方法[J/OL].中国机械工程,2015,26(1):74-78[2018-12-22].http://www.doi.org/10.3969/j.issn.1004132X.2015.01.013.
[6] 王东,张强,严亮.一种融合聚类的监督局部线性嵌入算法研究[J/OL].半导体光电,2017(3):113-118[2018-12-22].https://www.doi.org/10.16818/j.issn1001-5868.2017.03.024.
[7] CHANG H,YEUNG D Y.Robust locally linear em-bedding[J/OL].Pattern Recognition,2006,39(6):1053-1065[2019-02-02].https://doi.org/10.1016/j.patcog.2005.07.011.
[8] 闫德勤,刘胜蓝,李燕燕.一种基于稀疏嵌入分析的降维方法[J/OL].自动化学报,2011,37(11):1306-1312[2018-09-28].http://www.doi.org/10.3724/SP.J.1004.2011.01306.
[9] 冷亦琴,张莉,杨季文.一种基于局部稀疏线性嵌入的降维方法及其应用[J/OL].南京大学学报自然科学版,2013,49(4):403-410[2018-09-28].https://www.doi.org/10.13232/j.cnki.jnju.2013.04.001.
[10] 徐立军,杨秋翔,雷海卫.一种基于压缩感知的改进全变分图像去噪方法[J/OL].微电子学与计算机,2016,33(6):100-103[2018-09-28].https://www.doi.org/10.19304/j.cnki.issn1000-7180.2016.06.023.
[11] XIE Z,MA L,LIU L.Content-Aware Compressive Sensing Recovery Using Laplacian Scale Mixture Priors and Side Information[J/OL].Mathematical Problems in Engineering,2018,2018(1):1-15 [2018-09-28].https://www.doi.org/10.1155/2018/7171352.
[12] 文方青,张弓,贲德.基于块稀疏贝叶斯学习的多任务压缩感知重构算法[J/OL].物理学报,2015,64(7):87-93[2018-11-10].https://www.doi.org/10.7498/aps.64.070201.
[13] 刘亚新,赵瑞珍,胡绍海.用于压缩感知信号重建的正则化自适应匹配追踪算法[J/OL].电子与信息学,2010,32(11):2713-2717[2018-09-28].https://dx.doi.org/10.3724/SP.J.1146.2009.01623.
[14] 周燕,曾凡智,赵慧民,等.一种基于精细化稀疏自适应匹配追踪算法的图像检索方法研究[J/OL].电子学报,2014,42(12):2457-2466[2018-09-28].https://doi.org/10.3969/j.issn.0372-2112.2014.12.018.
[15] 甘伟,许录平,罗楠,等.一种自适应压缩感知重构算法[J/OL].系统工程与电子技术,2011,33(9):1948-1953[2018-09-28].https://doi.org/10.3969/j.issn.1001-506X.2011.09.07.
[16] 杨真真,杨震,孙林慧.信号压缩重构的正交匹配追踪类算法综述[J/OL].信号处理,2013,29(4):486-496[2019-03-02].https://doi.org/10.3969/j.issn.1003-0530.2013.04.011.
[17] FORINA M.Wine Data Set[EB/OL].(1991-07-01)[2018-10-20].http://archive.ics.uci.edu/ml/datasets/Wine.
[18] YANN L C.The MNIST Databade of handwritten digits[EB/OL].[2018-10-20].http://yann.lecun.com/exdb/mnist.
[19] 张志友,周佳燕,邵海见,等.基于自适应邻域选择的局部线性嵌入算法[J/OL].南京理工大学学报,2017,41(6):748-752[2018-09-28].https://doi.org/10.1016/10.14177/j.cnki.32-1397n.2017.41.06.013.
[20] LIN C J.A Library for Support Vector Machines[EB/OL].(2008-07-05)[2018-10-20].https://www.csie.ntu.edu.tw/～cjlin/libsvm.