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Register a new userMemory effect of the online user preference
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The mechanism of the online user preference evolution is of great significance for understanding the online user behaviors and improving the quality of online services. Since users are allowed to rate on objects in many online systems, ratings can well reflect the users preference. With two benchmark datasets from online systems, we uncover the memory effect in users selecting behavior which is the sequence of qualities of selected objects and the rating behavior which is the sequence of ratings delivered by each user. Furthermore, the memory duration is presented to describe the length of a memory, which exhibits the power-law distribution, i.e., the probability of the occurring of long-duration memory is much higher than that of the random case which follows the exponential distribution. We present a preference model in which a Markovian process is utilized to describe the users selecting behavior, and the rating behavior depends on the selecting behavior. With only one parameter for each of the users selecting and rating behavior, the preference model could regenerate any duration distribution ranging from the power-law form (strong memory) to the exponential form (weak memory).
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Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an analytical expression for the effect of memory on the spectral gap and thus, equivalently, on the characteristic time needed for the stochastic process to asymptotically reach equilibrium. Perturbation analysis shows that standard first-order Markov models can either overestimate or underestimate the diffusion rate of flows across the modular structure of a system captured by a second-order Markov network. We test the theoretical predictions on a toy example and on numerical data, and discuss their implications for network theory, in particular in the case of temporal or multiplex networks.
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