面向多维分类的监督式降维  

Supervised dimensionality reduction for multi-dimensional classification

作　　者：贾彬彬 张敏灵[1,3] Bin-Bin JIA;Min-Ling ZHANG(School of Computer Science and Engineering,Southeast University,Nanjing 210096,China;College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 730050,China;Key Laboratory of Computer Network and Information Integration(Southeast University),Ministry of Education,Nanjing 210096,China)

机构地区：[1]东南大学计算机科学与工程学院,南京210096 [2]兰州理工大学电气工程与信息工程学院,兰州730050 [3]计算机网络和信息集成教育部重点实验室(东南大学),南京210096

出　　处：《中国科学：信息科学》2023年第12期2325-2340,共16页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:62225602,62306131)资助项目。

摘　　要：与传统多类分类相比,多维分类中每个对象仍由一个示例(特征向量)表示,但同时与多个类别变量相关联,各类别变量基于异构类别空间刻画对象的语义.降维可以有效地缓解维度灾难并加速模型训练,已有多维分类研究均关注于设计性能更好的学习算法,尚未出现面向多维分类数据降维方面的工作.本文基于特征空间和语义空间的相关性,首次面向多维分类数据设计了一种名为SDeM的监督式线性降维方法.该方法使用Hilbert-Schmidt独立判据衡量两个空间的相关性,通过最大化投影特征空间与语义空间在该度量下的相关性确定投影矩阵.实验结果表明,相比于无监督式降维方法,SDeM所得降维特征更有利于多维分类方法取得更好的泛化性能.Compared to traditional multi-class classification,each object in multi-dimensional classification is also represented by a single instance while associated with multiple class variables.Here,each class variable corresponds to one heterogeneous class space characterizing an object’s semantics from one dimension.Dimensionality reduction effectively alleviates the curse of dimensionality and expedites model training.Existing multi-dimensional classification studies aim at designing learning algorithms with better performance,while the problem of dimensionality reduction for multi-dimensional classification has not been investigated.According to the correlation between feature space and semantic space,this paper makes a first attempt at designing a supervised linear dimensionality reduction method called SDeM for multi-dimensional classification.SDeM measures the correlation between two spaces with the Hilbert-Schmidt independence criterion and determines the projection matrix by maximizing the correlation between the projected feature space and the semantic space under this metric.Experimental results show that the reduced features obtained by SDeM are more conducive than those obtained by unsupervised dimensionality reduction methods to achieve better generalization performance for multi-dimensional classification methods.

关 键 词：机器学习 多维分类 降维 空间相关性 Hilbert-Schmidt独立准则 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]