分数阶嵌入的广义多重集典型相关分析

Fractional-order embedding generalized multiset canonical correlation analysis

随着数据处理方式以及描述角度的不同,同一模式总是能够获得多种不同的特征表示.由于这些特征表示总是反映了同一模式的不同特性或视角,因此,对其进行有效地抽取与融合后,不仅可以保留参与抽取的多组特征的有效鉴别信息,还可以在一定程度上消除特征间的冗余信息,降低识别算法的复杂度,对模式分类来说无疑具有重要的实际意义.由于传统的维数约减方法,如主成分分析(PCA)与线性鉴别分析(LDA),主要针对模式的一组特征进行处理,并不适合对多表示数据进行融合与特征抽取,因此,本文以多表示数据为研究对象,深入研究了多重集典型相关分析的相关理论与算法,采用分数阶思想对组内与组间样本协方差的特征值和奇异值进行重新估计,然后建立分数阶组内与组间散布矩阵,同时引入监督信息,构建了分数阶嵌入的多重集典型相关分析(FEGMCCA)理论框架.

Due to different data processing and descriptions,the same objects usually have multiple representations from different spaces（views）.These multiple representations could be not only from different feature vector spaces,but also from different graph spaces.Since multiple feature representations always reflect different characteristics or views of the same patterns,extracting features from them can not only obtain the effectively discriminative information,but also eliminate the redundant information to a certain extent in each feature representation.Furthermore,the complexity of classifiers can be reduced much by using these extracted features.Therefore,the feature extraction of multi-representation data is undoubtablely a very necessary and fundamental problem for recognition tasks.Since traditional feature extraction or dimensionality reduction methods,e.g.,principle component analysis（PCA）and linear discriminant analysis（LDA）,etc.,are mainly based on single representation data,they are not suitable to be applied to the feature extraction of multi-representation data.In this dissertation,we focus on studying this problem basedmultiset canonical correlation analysis（MCCA）.We use the idea of fractional order to respectively correct the eigenvalues and singular values in the corresponding sample covariance matrices,and then construct fractional-order within-set and between-set scatter matrices which can obviously alleviate the problem of the deviation.On this basis,we introduce supervision information and a new approach is proposed called fractional-order embedding generalized multiset canonical correlation analysis（FEGMCCA）.