## 2 Related Works  
As far as multi-hop range-free localization algorithms are concerned, some popular ones include DV-hop (Distance Vector hop) [13; 14], Amorphous [15], and MDS-MAP (Multidimensional scaling MDP) [16]. The DV-hop method was first proposed by [PERSON] at the University of Bucharest, and the basic idea is that one node estimates the distance to another node using the product of the network per-hop distance and the shortest path between them. The DV-hop algorithm does not need distance measurement equipment nor angle measurement hardware, and thus it is one of the most widely used algorithms for wireless sensor networks. It can be simply divided into three steps. First of all, the unknown nodes calculate the minimal hop counts to anchor nodes by the AODV (Ad hoc On-demand Distance Vector Routing) protocol. Then, the unknown nodes estimate their Euclidean distances to anchors by multiplying the minimum hop counts and the per-hop distance together. At last, the locations of unknown nodes are estimated by using the trilateration or maximum likelihood method. The Amorphous algorithm is an improved version of DV-hop. Unlike the first step used in DV-hop, Amorphous relies on another way that is called local hop counts to calculate the minimum number of hop counts. Furthermore, it also uses a different method to compute the average per-hop distance. In this way, Amorphous can generally achieve better performance than DV-hop. MDS-MAP, as another popular method, is a localization method that is based on multidimensional scaling (MDS). MDS-MAP uses the distance or connectivity information between all nodes at the same time and only uses the information between the unknown and anchor nodes. It can be used as either a range-based or a range-free algorithm. In the case of the range-free method, it rebuilds the relative coordinators of nodes by taking advantage of the pair distance, and obtains the absolute coordinators of nodes by using coordinate transformation with the help of anchor nodes. The above localization methods all assume that the nodes are distributed uniformly and densely in networks. However, the real deployment environment is often complex and changeable; thus, it is almost impossible to satisfy the ideal condition of uniformity and denseness for nodes to be located. For example, in anisotropic networks, such as networks with existing obstacles or noise corruption, these multi-hop range-free localization methods will probably demonstrate poor positioning accuracy. Recently, designing localization algorithms through machine learning theory has drawn a lot of attention. These machine-learning-based localization algorithms utilize the correlations between nodal distribution characteristics and measurement information to construct a mapping model, which is then applied to estimate the positions of unknown nodes. Compared with the existing methods, machine-learning-based approaches can more effectively retrieve the fuzzy relations that are hidden behind information and data. [PERSON] et al. proposed a localization method named Proximity-Distance Map (PDM) [17], which creates the mapping relationship between hop counts and the real distances of anchor nodes. Then, this mapping relationship is used to estimate the distance from the unknown nodes to the anchor nodes. Inspired by the PDM method in [17], [PERSON] et al. presented two improved localization methods, i.e., Localized Support Vector Regression (LSVR) and Multi-dimensional Support Vector Regression (MSVR) [18], which regard the relationship between hop counts and distances as nonlinear and estimate distances by the regression method relying on a Support Vector Machine (SVM) [19]. Although the methods mentioned above can effectively improve the positioning accuracy in anisotropic networks, the computational complexity of their core algorithms is very high, which will cause sensor nodes to fail or die earlier because such nodes will estimate the locations by themselves, and they are short of computation and memory resources as well.