  This paper generalizes the proportionate-type adaptive algorithm to the graph
signal processing and proposes two proportionate-type adaptive graph signal
recovery algorithms. The gain matrix of the proportionate algorithm leads to
faster convergence than least mean squares (LMS) algorithm. In this paper, the
gain matrix is obtained in a closed-form by minimizing the gradient of the
mean-square deviation (GMSD). The first algorithm is the Proportionate-type
Graph LMS (Pt-GLMS) algorithm which simply uses a gain matrix in the recursion
process of the LMS algorithm and accelerates the convergence of the Pt-GLMS
algorithm compared to the LMS algorithm. The second algorithm is the
Proportionate-type Graph Extended LMS (Pt-GELMS) algorithm, which uses the
previous signal vectors alongside the signal of the current iteration. The
Pt-GELMS algorithm utilizes two gain matrices to control the effect of the
signal of the previous iterations. The stability analyses of the algorithms are
also provided. Simulation results demonstrate the efficacy of the two proposed
proportionate-type LMS algorithms.
