The Identification of the influential nodes in networks is one of the most promising domains. In this paper, we present an improved iterative resource allocation (IIRA) method by considering the centrality information of neighbors and the influence o
f spreading rate for a target node. Comparing with the results of the Susceptible Infected Recovered (SIR) model for four real networks, the IIRA method could identify influential nodes more accurately than the tradition IRA method. Specially, in the Erdos network, the Kendalls tau could be enhanced 23% when the spreading rate is 0.12. In the Protein network, the Kendalls tau could be enhanced 24% when the spreading rate is 0.08.
With great theoretical and practical significance, identifying the node spreading influence of complex network is one of the most promising domains. So far, various topology-based centrality measures have been proposed to identify the node spreading
influence in a network. However, the node spreading influence is a result of the interplay between the network topology structure and spreading dynamics. In this paper, we build up the systematic method by combining the network structure and spreading dynamics to identify the node spreading influence. By combining the adjacent matrix $A$ and spreading parameter $beta$, we theoretical give the node spreading influence with the eigenvector of the largest eigenvalue. Comparing with the Susceptible-Infected-Recovered (SIR) model epidemic results for four real networks, our method could identify the node spreading influence more accurately than the ones generated by the degree, K-shell and eigenvector centrality. This work may provide a systematic method for identifying node spreading influence.
Identifying the node spreading influence in networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the shortest distance between a target node
and the node set with the highest $k$-core value, we present an improved method to generate the ranking list to evaluate the node spreading influence. Comparing with the epidemic process results for four real networks and the Barab{a}si-Albert network, the parameterless method could identify the node spreading influence more accurately than the ones generated by the degree $k$, closeness centrality, $k$-shell and mixed degree decomposition methods. This work would be helpful for deeply understanding the node importance of a network.
A key challenge of the collaborative filtering (CF) information filtering is how to obtain the reliable and accurate results with the help of peers recommendation. Since the similarities from small-degree users to large-degree users would be larger t
han the ones opposite direction, the large-degree users selections are recommended extensively by the traditional second-order CF algorithms. By considering the users similarity direction and the second-order correlations to depress the influence of mainstream preferences, we present the directed second-order CF (HDCF) algorithm specifically to address the challenge of accuracy and diversity of the CF algorithm. The numerical results for two benchmark data sets, MovieLens and Netflix, show that the accuracy of the new algorithm outperforms the state-of-the-art CF algorithms. Comparing with the CF algorithm based on random-walks proposed in the Ref.7, the average ranking score could reach 0.0767 and 0.0402, which is enhanced by 27.3% and 19.1% for MovieLens and Netflix respectively. In addition, the diversity, precision and recall are also enhanced greatly. Without relying on any context-specific information, tuning the similarity direction of CF algorithms could obtain accurate and diverse recommendations. This work suggests that the user similarity direction is an important factor to improve the personalized recommendation performance.
The class of generating functions for completely monotone sequences (moments of finite positive measures on $[0,1]$) has an elegant characterization as the class of Pick functions analytic and positive on $(-infty,1)$. We establish this and another s
uch characterization and develop a variety of consequences. In particular, we characterize generating functions for moments of convex and concave probability distribution functions on $[0,1]$. Also we provide a simple analytic proof that for any real $p$ and $r$ with $p>0$, the Fuss-Catalan or Raney numbers $frac{r}{pn+r}binom{pn+r}{n}$, $n=0,1,ldots$ are the moments of a probability distribution on some interval $[0,tau]$ {if and only if} $pge1$ and $pge rge 0$. The same statement holds for the binomial coefficients $binom{pn+r-1}n$, $n=0,1,ldots$.
We provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency and noise i
ntensity depend on a measure of the local alignment. We show that, in the spatially homogeneous case, the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment. In the spatially inhomogeneous case, we derive the macroscopic models associated to the stable equilibria and classify their hyperbolicity according to the same function.
Random walks have been successfully used to measure user or object similarities in collaborative filtering (CF) recommender systems, which is of high accuracy but low diversity. A key challenge of CF system is that the reliably accurate results are o
btained with the help of peers recommendation, but the most useful individual recommendations are hard to be found among diverse niche objects. In this paper we investigate the direction effect of the random walk on user similarity measurements and find that the user similarity, calculated by directed random walks, is reverse to the initial nodes degree. Since the ratio of small-degree users to large-degree users is very large in real data sets, the large-degree users selections are recommended extensively by traditional CF algorithms. By tuning the user similarity direction from neighbors to the target user, we introduce a new algorithm specifically to address the challenge of diversity of CF and show how it can be used to solve the accuracy-diversity dilemma. Without relying on any context-specific information, we are able to obtain accurate and diverse recommendations, which outperforms the state-of-the-art CF methods. This work suggests that the random walk direction is an important factor to improve the personalized recommendation performance.
Heat conduction process has recently found its application in personalized recommendation [T. Zhou emph{et al.}, PNAS 107, 4511 (2010)], which is of high diversity but low accuracy. By decreasing the temperatures of small-degree objects, we present a
n improved algorithm, called biased heat conduction (BHC), which could simultaneously enhance the accuracy and diversity. Extensive experimental analyses demonstrate that the accuracy on MovieLens, Netflix and Delicious datasets could be improved by 43.5%, 55.4% and 19.2% compared with the standard heat conduction algorithm, and the diversity is also increased or approximately unchanged. Further statistical analyses suggest that the present algorithm could simultaneously identify users mainstream and special tastes, resulting in better performance than the standard heat conduction algorithm. This work provides a creditable way for highly efficient information filtering.
Motivated by a phenomenon of phase transition in a model of alignment of self-propelled particles, we obtain a kinetic mean-field equation which is nothing else than the Doi equation (also called Smoluchowski equation) with dipolar potential. In a se
lf-contained article, using only basic tools, we analyze the dynamics of this equation in any dimension. We first prove global well-posedness of this equation, starting with an initial condition in any Sobolev space. We then compute all possible steady-states. There is a threshold for the noise parameter: over this threshold, the only equilibrium is the uniform distribution, and under this threshold, there is also a family of non-isotropic equilibria. We give a rigorous prove of convergence of the solution to a steady-state as time goes to infinity. In particular we show that in the supercritical case, the only initial conditions leading to the uniform distribution in large time are those with vanishing momentum. For any positive value of the noise parameter, and any initial condition, we give rates of convergence towards equilibrium, exponentially for both supercritical and subcritical cases and algebraically for the critical case.
Recommender systems use data on past user preferences to predict possible future likes and interests. A key challenge is that while the most useful individual recommendations are to be found among diverse niche objects, the most reliably accurate res
ults are obtained by methods that recommend objects based on user or object similarity. In this paper we introduce a new algorithm specifically to address the challenge of diversity and show how it can be used to resolve this apparent dilemma when combined in an elegant hybrid with an accuracy-focused algorithm. By tuning the hybrid appropriately we are able to obtain, without relying on any semantic or context-specific information, simultaneous gains in both accuracy and diversity of recommendations.
