# Multi-View Network Representation Learning Algorithm Research
## 1 Introduction  
The network representation learning aims at learning and obtaining the low-dimensional, compressed and dense distributed representation vectors for various kinds of networks. It can be straightforwardly considered as the network encoding task for the networks, consequently, the nearest neighboring vertices have closer distance in the network representation space of lower dimension. DeepWalk is the representative algorithm of network representation learning. However, DeepWalk [1] is able to incorporate higher-order network information by multiple steps of random walks. In this respect, WALKETS [2] has conducted some positive explorations and researches and proved that multi-step random walk can encode higher-order features into the network representations. Meanwhile, high-order network representation learning can excavate valuable features only based on the existing network structural information in some sparse networks. In addition, the essence of DeepWalk based on Skip-Gram is to factorize the matrix of network structural features [3]. Fortunately, GraRep [4] and Network Embedding Update (NEU) [5] are proposed to learn the network representations, which can capture higher order network features. Thus, inspired by GraRep [4], WALKETS [2] and NEU [5], we propose a joint learning framework of multi-view network representation learning algorithm (MVNR). MNVR aims to capture higher order structural relations into lower dimension embeddings by weighting \(k\)-step network representations of higher order into a single vector. The \(k\)-th step network is denoted as the \(k\)-th viewof the original network, therefore, MVNR is a network representation learning algorithm of integrating multi-view features. The algorithm framework of MVNR is illustrated in Figure 1a,b. As shown in Figure 1a, MVNR can capture higher order structural relations, because we reconstruct \(k\)-step networks based on the length \(k\) of random walk on edges, the new network is different from the original network, the relations between of them are not the inclusive relations. In term of original network, the 2-step network is the 2 nd order feature network when \(k\) is set as 2 and so on. As shown in Figure 1b, the link weights consist of the certainty degrees of existing edges and the link probabilities of non-existing edges. The certainty degrees of existing edges are applied to 1-step network and the link probabilities of non-existing edges are used to \(k\)-step networks where \(k>2\). Most previous works on network representation learning use a \"one-size fits all\" approach to train the learning model, where the single learnt representations are applied to various tasks, for example, DeepWalk [1], Tri-Party Deep Network Representation (TriDNR) [6] and node2 vec [7] can only capture lower order features, which fails to explicitly capture higher order relations and global structural information. Especially in sparse networks, the existing network representation learning algorithms based on network structures are difficult to get valuable relations and structural features between vertices. GraRep [4] aims to factorize transition feature matrix of the network, which can explicitly encode the network features of higher order but it does not research how to weight the features form different order networks. WALKLETS [2] improves the procedure of random walk, which can capture the walk sequences by skipping pre-selected length of walk step. Nevertheless, WALKLETS [2] is still unable to obtain global features of the network, in fact, it is still the network representation learning algorithm based on local features of the network. NEU [5] can implicitly approximate higher order proximities with theoretical approximation bound. In fact, NEU [5] is more like an optimization algorithm, which optimizes the network representation obtained by DeepWalk [1], node2 vec [7] and Line [8] and so forth.