Completamento de matrizes de posto reduzido usando gradiente projetado
Resumo
O problema de completamento de matrizes (PCM) consiste em fazer estimativas numéricas para um conjunto de entradas faltantes em uma matriz de dados, de modo a satisfazer determinadas condições de regularização, em geral descritas sob a condição de posto reduzido [1, 6]. [...]
Downloads
Referências
Emmanuel J Candès e Benjamin Recht. “Exact matrix completion via convex optimization”. Em: Foundations of Computational mathematics 9.6 (2009), pp. 717–772. doi: 10 . 1007/s10208-009-9045-5.
Ivan Dokmanic et al. “Euclidean distance matrices: essential theory, algorithms, and applications”. Em: IEEE Signal Processing Magazine 32.6 (2015), pp. 12–30. doi: 10.1109/ MSP.2015.2398954.
Carl Eckart e Gale Young. “The approximation of one matrix by another of lower rank”. Em: Psychometrika 1.3 (1936), pp. 211–218. doi: 10.1007/BF02288367. [4] Prateek Jain, Ambuj Tewari e Purushottam Kar. On iterative hard thresholding methods for high-dimensional m-estimation. Vol. 27. 2014. isbn: 9781510800410.
Shiqian Ma, Donald Goldfarb e Lifeng Chen. “Fixed point and Bregman iterative methods for matrix rank minimization”. Em: Mathematical Programming 128.1 (2011), pp. 321–353. doi: 10.1007/s10107-009-0306-5.
Rahul Mazumder, Trevor Hastie e Robert Tibshirani. “Spectral regularization algorithms for learning large incomplete matrices”. Em: Journal of Machine Learning Research 11 (2010), pp. 2287–2322. issn: 1533-7928.
Nilson JM Moreira et al. “A novel low-rank matrix completion approach to estimate missing entries in Euclidean distance matrix”. Em: Computational and Applied Mathematics 37.4 (2018), pp. 4989–4999. doi: 10.1137/080716542.