Approximation Analysis of Multi-Step Material Diffusion Recommendation Algorithm Based on Bipartite Network

Material diffusion recommendation algorithm has received wide attention for its simplicity and effectiveness. However, up to now, most of researches on this algorithm were confined to two-step diffusion process of a bipartite network. In this paper, we use the method of matrix analysis to study the multi-step material diffusion process in the bipartite network. By analyzing the nature of the diffusion transfer matrix of W, we prove that W^N converges when the diffusion step N tends to infinity. Eventually, the distribution of resources will reach a steady state. At this point, the number of resources that each node obtains is proportional to its degree, but not the proportion of the initial distribution of resources. At the same time, the algorithm is transformed into a global recommendation algorithm and the recommendation result is no longer personalized. It reveals that the material diffusion recommendation algorithm will gradually lose its personalized feature with the increase of the number of diffusion steps.