基于稀疏字典的李群机器学习算法  

Lie Group Machine Learning Based on Sparse Dictionary

作　　者：熊啸东 李凡长[1] 王邦军[1] 梁合兰[1] XIONG Xiaodong;LI Fanzhang;WANG Bangjun;LIANG Helan(School of Computer Science and Technology,Soochow University,Suzhou 215006)

机构地区：[1]苏州大学计算机科学与技术学院,苏州215006

出　　处：《模式识别与人工智能》2020年第5期449-457,共9页Pattern Recognition and Artificial Intelligence

基　　金：国家重点研发计划项目(No.2018YFA07070,2018YFA0701701);国家自然科学基金项目(No.61373093,61402310,61672364,61672365)资助。

摘　　要：李群机器学习理论被广泛应用于图像集分类中的数据表示和处理,并获得较优结果.由此,文中提出基于稀疏字典的李群机器学习算法.首先使用协方差矩阵对图像集建模,分析协方差矩阵构成的李群结构,应用对数映射将数据映射到线性空间中,得到数据的距离矩阵.再使用路标多维缩放对数据进行降维处理,降低运算成本.最后,使用带费舍尔判别字典学习进行分类.在YTC数据集上的实验证明文中算法具有良好的鲁棒性和准确率.Lie group machine learning(LML)theory is widely applied to data representation and processing in image set classification,and satisfactory results are obtained.Therefore,a method of Lie group dictionary learning based on sparse dictionary is proposed.Firstly,the covariance matrix is employed to model the image set,and the Lie group structure composed of covariance matrix is analyzed.Logarithmic map is applied to map the data into the linear space to obtain the distance matrix of the data.Then,landmark multi-dimensional scaling is employed to realize dimension reduction of data and reduce the computational cost.Finally,Fisher discriminant dictionary learning is applied for classification.The experiments on YTC dataset indicate the good performance of the proposed algorithm in robustness and accuracy.

关 键 词：李群机器学习 稀疏表示 路标多维度缩放 李群字典学习 图像集分类 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]