Yu Jiyang, Pan Baicheng, Yu Shanshan, Leung Man-Fai
College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China.
Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China.
Math Biosci Eng. 2023 May 24;20(7):12486-12509. doi: 10.3934/mbe.2023556.
Non-negative matrix factorization (NMF) has been widely used in machine learning and data mining fields. As an extension of NMF, non-negative matrix tri-factorization (NMTF) provides more degrees of freedom than NMF. However, standard NMTF algorithm utilizes Frobenius norm to calculate residual error, which can be dramatically affected by noise and outliers. Moreover, the hidden geometric information in feature manifold and sample manifold is rarely learned. Hence, a novel robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization (RCHNMTF) is proposed. First, a robust capped norm is adopted to handle extreme outliers. Second, dual hyper-graph regularization is considered to exploit intrinsic geometric information in feature manifold and sample manifold. Third, orthogonality constraints are added to learn unique data presentation and improve clustering performance. The experiments on seven datasets testify the robustness and superiority of RCHNMTF.
非负矩阵分解（NMF）已在机器学习和数据挖掘领域中得到广泛应用。作为NMF的扩展，非负矩阵三因子分解（NMTF）比NMF提供了更多的自由度。然而，标准的NMTF算法利用弗罗贝尼乌斯范数来计算残差误差，这可能会受到噪声和离群值的显著影响。此外，特征流形和样本流形中的隐藏几何信息很少被学习到。因此，提出了一种新颖的鲁棒 capped 范数双超图正则化非负矩阵三因子分解（RCHNMTF）。首先，采用鲁棒 capped 范数来处理极端离群值。其次，考虑双超图正则化以利用特征流形和样本流形中的内在几何信息。第三，添加正交性约束以学习唯一的数据表示并提高聚类性能。在七个数据集上的实验证明了RCHNMTF的鲁棒性和优越性。
