چكيده به لاتين
Matrix completion problem has gathered a lot of attention in recent years. Exact recovery of a low rank matrix from a few subsets of its entries is the main challenge in matrix completion. The graph matrix completion has been introduced based on the fact that the relation between rows (or columns) of a matrix can be modeled by a graph structure. The graph matrix completion problem may be formulated by minimizing the nuclear norm in addition to the graph total variation.
In this thesis, we apply the graph total variation base on directed Laplacian and introduce a new method for graph matrix completion. We introduce the GMCM-DL and GMCR-DL algorithms for the absent and presence noise, respectively and the GMCO-DL algorithm in presence of noise and outliers in observations. Also, we present an iterative solution for the proposed methods based on proximal algorithms.
Simulation results indicate that the proposed methods outperform the other methods when the percentage of observed entries collapses. Furthermore, using our methods, we are able to recover a row of a matrix with observing none of its entries. We refer to this matrix completion approach as the row observation technique. Moreover, we compare the proposed methods with other matrix completion methods for uniform and row observations.
Keywords: Matrix completion, Signal processing on graphs, Directed graph, Total variation, Proximal Algorithms.
