Abstract
Inferring the connectivity structure of networked systems from data is an extremely important task in many areas of science. Most real-world networks exhibit sparsely connected topologies, with links between nodes that in some cases may even be associated with a binary state (0 or 1, denoting, respectively, the absence or presence of a connection). Such un-weighted topologies are elusive to classical reconstruction methods such as Lasso or compressed sensing techniques. We here introduce an approach called signal Lasso, in which the estimation of the signal parameter is subjected to 0 or 1 values. The theoretical properties and algorithm of the proposed method are studied in detail. Applications of the method are illustrated for an evolutionary game and synchronization dynamics in several synthetic and empirical networks, for which we show that our strategy is reliable and robust and outperforms the classical approaches in terms of accuracy and mean square errors.
Highlights
Complex networks have a wide range of applications in various fields of science [1,2,3,4,5,6,7]
We introduced a method for the estimation problem of signal parameters in the area of network reconstruction
By adding a control term of an L1 norm to shrink the parameters to 1 in the penalty function of Lasso, the estimated signal parameters can be compressed to 0 or 1, which ensures higher reconstruction accuracies compared with the Lasso and compressed sensing methods
Summary
Complex networks have a wide range of applications in various fields of science [1,2,3,4,5,6,7]. Evolutionary-game-based dynamics, for instance, characterizes many relevant situations and is intrinsically discrete in time In such a case, the problem can be transformed into a statistical linear model, with sparse and high-dimensional properties. The Lasso method is able to reduce the parameter estimates of unimportant predictors in X to zero, but the estimators of nonzero elements fail to be conducted towards their real values, 1. This latter feature of the methods causes the estimators of parameters with a value of 1 to have a rather low accuracy, as we will show in the present paper. Other methods, such as smoothly clipped absolute deviation (SCAD) [21], adaptive Lasso [22], group Lasso [23], and elastic net [24] and CS [25], which intrinsically focus on zero elements, suffer the same restriction as Lasso and fail to give accurate descriptions of the nonzero elements of X
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