一种邻域自适应半监督局部Fisher判别分析算法
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摘要
针对利用局部化思想解决多模数据的判别分析问题时,根据经验对局部邻域大小进行全局统一设定,无法体现局部几何结构差异性的不足,提出一种邻域自适应半监督局部Fisher判别分析(neighborhood adaptive semi-supervised local Fisher discriminant analysis,NA-SELF)算法。该算法在半监督局部Fisher判别分析算法的基础上,结合马氏距离和余弦相似度确定初始近邻数,并根据样本空间概率密度估计调整近邻数。通过人工数据集和五组UCI标准数据集对该算法的特征降维性能进行验证,并与典型的维数约简算法和采用传统K近邻方法的判别分析算法进行比较,实验结果表明该算法具备更高的有效性。
For the discriminant analysis of multimodal data,the idea of localization can hardly reflect the difference of local geometric structure according to the global setting of local neighborhood by experience. Aiming at this problem,this paper proposed a neighborhood adaptive semi-supervised local Fisher discriminant analysis( NA-SELF) algorithm. The new algorithm based on the semi-supervised local Fisher discriminant analysis algorithm,obtained the initial neighborhood by combining the Mahalanobis distance and cosine similarity,and adjusted the number of neighbors according to the probability density estimation of sample space. It verified the performance of feature dimensionality reduction using the algorithm by the synthetic datasets and five UCI standard datasets. Compared with several typical dimensionality reduction algorithms and the discriminant analysis algorithm using the traditional K-nearest neighbor method,the experimental results show that the proposed algorithm has higher effectiveness.
For the discriminant analysis of multimodal data,the idea of localization can hardly reflect the difference of local geometric structure according to the global setting of local neighborhood by experience. Aiming at this problem,this paper proposed a neighborhood adaptive semi-supervised local Fisher discriminant analysis( NA-SELF) algorithm. The new algorithm based on the semi-supervised local Fisher discriminant analysis algorithm,obtained the initial neighborhood by combining the Mahalanobis distance and cosine similarity,and adjusted the number of neighbors according to the probability density estimation of sample space. It verified the performance of feature dimensionality reduction using the algorithm by the synthetic datasets and five UCI standard datasets. Compared with several typical dimensionality reduction algorithms and the discriminant analysis algorithm using the traditional K-nearest neighbor method,the experimental results show that the proposed algorithm has higher effectiveness.
引文
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[15]刘晗,张庆,孟理华,等.基于Parzen窗估计的设备状态综合报警方法[J].振动与冲击,2013,32(3):110-114.(Liu Han,Zhang Qing,Meng Lihua,et al. Comprehensive alarm method for equipment conditions based on Parzen window estimation[J]. Journal of Vibration and Shock,2013,32(3):110-114.)
[2] Zhai Lidong,Ding Zhaoyun,Jia Yan,et al. A word position-related LDA model[J]. International Journal of Pattern Recognition and Artificial Intelligence,2011,25(6):909-925.
[3] Nguyen V H,Golinval J C. Fault detection based on kernel principal component analysis[J]. Engineering Structures,2010,32(11):3683-3691.
[4] Yang Wuyi,Liang Wei,Xin Le,et al. Subspace semi-supervised Fisher discriminant analysis[J]. Acta Automatica Sinica,2009,35(12):1513-1519.
[5]苏祖强,汤宝平,刘自然,等.基于正交半监督局部Fisher判别分析的故障诊断[J].机械工程学报,2014,50(18):7-13.(Su Zuqiang,Tang Baoping,Liu Ziran,et al. Fault diagnosis method based on orthogonal semi-supervised local fisher discriminant analysis[J]. Journal of Mechanical Engineering,2014,50(18):7-13.)
[6]杨昔阳,邓朝阳,李志伟.半监督模糊Fisher降维分析[J].厦门大学学报:自然科学版,2015,54(6):869-875.(Yang Xiyang,Deng Chaoyang,Li Zhiwei. A semi-supervised fuzzy dimension reduction method[J]. Journal of Xiamen University:Natural Science,2015,54(6):869-875.)
[7] Yu Jianbo. Bearing performance degradation assessment using locality preserving projections[J]. Expert Systems with Applications,2011,38(6):7440-7450.
[8] Sugiyama M. Dimensionality reduction of multimodal labeled data by local fisher discriminant analysis[J]. Journal of Machine Learning Research,2007,8:1027-1061.
[9] Yan Shuicheng,Xu Dong,Zhang Benyu,et al. Graph embedding and extension:a general framework for dimensionality reduction[J].IEEE Trans on Pattern Analysis&Machine Intelligence,2006,29(1):40-51.
[10]张晓涛,唐力伟,王平,等.自适应邻域构造流形学习算法及故障降维诊断[J].振动、测试与诊断,2016,36(6):1210-1215.(Zhang Xiaotao,Tang Liwei,Wang Ping,et al. Adaptive neighborhood selection manifold learning algorithm and its application in fault diagnosis with dimensionality reduction[J]. Journal of Vibration,Measurement&Diagnosis,2016,36(6):1210-1215.)
[11]Sugiyama M,IdéT,Nakajima S,et al. Semi-supervised local Fisher discriminant analysis for dimensionality reduction[J]. Machine Learning,2010,78:35-61.
[12]刘志勇,袁媛.基于测地距离的半监督增强[J].计算机工程与应用,2011,47(21):202-204.(Liu Zhiyong,Yuan Yuan. Semisupervised boosting based on geodesic distance[J]. Computer Engineering and Applications,2011,47(21):202-204.)
[13]李文博,王大轶,刘成瑞.一类非线性系统的故障可诊断性量化评价方法[J].宇航学报,2015,36(4):455-462.(Li Wenbo,Wang Dayi,Liu Chengrui. An approach to fault diagnosability quantitative evaluation for a class of nonlinear systems[J]. Journal of Astronautics,2015,36(4):455-462.)
[14]杨望灿,张培林,吴定海,等.基于改进半监督局部保持投影算法的故障诊断[J].中南大学学报:自然科学版,2015,46(6):2059-2064.(Yang Wangcan,Zhang Peilin,Wu Dinghai,et al.Fault diagnosis based on improved semi-supervised locality preserving projections[J]. Journal of Central South University:Science and Technology,2015,46(6):2059-2064.)
[15]刘晗,张庆,孟理华,等.基于Parzen窗估计的设备状态综合报警方法[J].振动与冲击,2013,32(3):110-114.(Liu Han,Zhang Qing,Meng Lihua,et al. Comprehensive alarm method for equipment conditions based on Parzen window estimation[J]. Journal of Vibration and Shock,2013,32(3):110-114.)
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