- Estimating Community Processes through Blind Identification of A number of Graph Filters(arXiv)
Creator : Yu Zhu, Fernando J. Iglesias, Antonio G. Marques, Santiago Segarra
Summary : This paper research the issue of collectively estimating a number of community processes pushed by a typical unknown enter, thus successfully generalizing the classical blind multi-channel identification drawback to graphs. Extra exactly, we mannequin community processes as graph filters and contemplate the commentary of a number of graph indicators similar to outputs of various filters outlined on a typical graph and pushed by the identical enter. Assuming that the underlying graph is understood and the enter is unknown, our objective is to get better the specs of the community processes, specifically the coefficients of the graph filters, solely counting on the commentary of the outputs. Being generated by the identical enter, these outputs are intimately associated and we leverage this relationship for our estimation functions. Two settings are thought of, one the place the orders of the filters are identified and one other one the place they aren’t identified. For the previous setting, we current a least-squares method and supply circumstances for restoration. For the latter state of affairs, we suggest a sparse restoration algorithm with theoretical efficiency ensures. Numerical experiments illustrate the effectiveness of the proposed algorithms, the affect of various parameter settings on the estimation efficiency, and the validity of our theoretical claims.
