Liao Qingshui, Liu Qilong, Razak Fatimah Abdul
Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia.
School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550025, People's Republic of China.
Sci Rep. 2024 Apr 20;14(1):9098. doi: 10.1038/s41598-024-59300-3.
Tucker decomposition is widely used for image representation, data reconstruction, and machine learning tasks, but the calculation cost for updating the Tucker core is high. Bilevel form of triple decomposition (TriD) overcomes this issue by decomposing the Tucker core into three low-dimensional third-order factor tensors and plays an important role in the dimension reduction of data representation. TriD, on the other hand, is incapable of precisely encoding similarity relationships for tensor data with a complex manifold structure. To address this shortcoming, we take advantage of hypergraph learning and propose a novel hypergraph regularized nonnegative triple decomposition for multiway data analysis that employs the hypergraph to model the complex relationships among the raw data. Furthermore, we develop a multiplicative update algorithm to solve our optimization problem and theoretically prove its convergence. Finally, we perform extensive numerical tests on six real-world datasets, and the results show that our proposed algorithm outperforms some state-of-the-art methods.
塔克分解广泛应用于图像表示、数据重建和机器学习任务，但更新塔克核的计算成本很高。三层分解（TriD）的双层形式通过将塔克核分解为三个低维三阶因子张量克服了这个问题，并在数据表示的降维中发挥重要作用。另一方面，TriD无法精确编码具有复杂流形结构的张量数据的相似关系。为了解决这个缺点，我们利用超图学习并提出了一种用于多向数据分析的新型超图正则化非负三重分解，该方法采用超图对原始数据之间的复杂关系进行建模。此外，我们开发了一种乘法更新算法来解决我们的优化问题，并从理论上证明了它的收敛性。最后，我们在六个真实世界的数据集上进行了广泛的数值测试，结果表明我们提出的算法优于一些现有技术的方法。
