Unsupervised feature selection via graph regularized nonnegative CP decomposition

Bilian Chen, Jiewen Guan, Zhening Li

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Unsupervised feature selection has attracted remarkable attention recently. With the development of data acquisition technology, multi-dimensional tensor data has been appeared in enormous real-world applications. However, most existing unsupervised feature selection methods are non-tensor-based which results the vectorization of tensor data as a preprocessing step. This seemingly ordinary operation has led to an unnecessary loss of the multi-dimensional structural information and eventually restricted the quality of the selected features. To overcome the limitation, in this paper, we propose a novel unsupervised feature selection model: Nonnegative tensor CP (CANDECOMP/PARAFAC) decomposition based Unsupervised Feature Selection, CPUFS for short. In specific, we devise new tensor-oriented linear classifier and feature selection matrix for CPUFS. In addition, CPUFS simultaneously conducts graph regularized nonnegative CP decomposition and newly-designed tensor-oriented pseudo label regression and feature selection to fully preserve the multi-dimensional data structure. To solve the CPUFS model, we propose an efficient iterative optimization algorithm with theoretically guaranteed convergence, whose computational complexity scales linearly in the number of features. A variation of the CPUFS model by incorporating nonnegativity into the linear classifier, namely CPUFSnn, is also proposed and studied. Experimental results on ten real-world benchmark datasets demonstrate the effectiveness of both CPUFS and CPUFSnn over the state-of-the-arts.
Original languageEnglish
Pages (from-to)2582-2594
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number2
Early online date17 Mar 2022
Publication statusPublished - 1 Feb 2023


  • unsupervised feature selection
  • nonnegative CP decomposition
  • optimization algorithm
  • classification


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