Abstract: Due to different data processing and descriptions, the same objects usually have multiple representations from different spaces (views). These multiple representations could be from different feature vector spaces, but also be 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 based multiset 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).