摘要
High-dimensional,higher-order tensor data are gaining prominence in a variety of fields,including but not limited to computer vision and network analysis.Tensor factor models,induced from noisy versions of tensor decompositions or factorizations,are natural potent instruments to study a collection of tensor-variate objects that may be dependent or independent.However,it is still in the early stage of developing statistical inferential theories for the estimation of various low-rank structures,which are customary to play the role of signals of tensor factor models.In this paper,we attempt to“decode”the estimation of a higher-order tensor factor model by leveraging tensor matricization.Specifically,we recast it into mode-wise traditional highdimensional vector/fiber factor models,enabling the deployment of conventional principal components analysis(PCA)for estimation.Demonstrated by the Tucker tensor factor model(TuTFaM),which is induced from the noisy version of the widely-used Tucker decomposition,we summarize that estimations on signal components are essentially mode-wise PCA techniques,and the involvement of projection and iteration will enhance the signal-to-noise ratio to various extents.We establish the inferential theory of the proposed estimators,conduct rich simulation experiments and illustrate how the proposed estimations can work in tensor reconstruction and clustering for independent video and dependent economic datasets,respectively.
基金
supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.12301338)
the Postdoc Fellowship of Chinese Academy of Sciences Academy of Mathematics and Systems Science and the Hong Kong Polytechnic University Joint Laboratory of Applied Mathematics
supported by General Research Fund(Grant No.17306121)
supported by General Research Fund(Grant No.15301519)
Research Grants Council,Hong Kong Special Administrative Region,the Key Program of National Natural Science Foundation of China(Grant No.72033002)
Research Grants Council,Hong Kong Special Administrative Region,Hong Kong Polytechnic University Research Grant(Grant No.P0045497)
the General Program of National Natural Science Foundation of China(Grant No.12271060)
supported by the National Key Research and Development Program of China(Grant No.2020YFA0714100)
the Key Program of National Natural Science Foundation of China(Grant No.12431009)。
