- Estimating Neighborhood Processes by Blind Identification of Numerous Graph Filters(arXiv)
Creator : Yu Zhu, Fernando J. Iglesias, Antonio G. Marques, Santiago Segarra
Abstract : This paper analysis the difficulty of collectively estimating plenty of neighborhood processes pushed by a typical unknown enter, thus efficiently generalizing the classical blind multi-channel identification downside to graphs. Additional precisely, we model neighborhood processes as graph filters and ponder the commentary of plenty of graph indicators just like outputs of varied filters outlined on a typical graph and pushed by the an identical enter. Assuming that the underlying graph is known and the enter is unknown, our goal is to get higher the specs of the neighborhood processes, particularly the coefficients of the graph filters, solely relying on the commentary of the outputs. Being generated by the an identical enter, these outputs are intimately related and we leverage this relationship for our estimation capabilities. Two settings are considered, one the place the orders of the filters are recognized and one different one the place they don’t seem to be recognized. For the earlier setting, we present a least-squares methodology and provide circumstances for restoration. For the latter state of affairs, we propose a sparse restoration algorithm with theoretical effectivity ensures. Numerical experiments illustrate the effectiveness of the proposed algorithms, the have an effect on of varied parameter settings on the estimation effectivity, and the validity of our theoretical claims.
