## [ Paper reading notes ] Network Embedding with Attribute Refinement

## The structure of this paper

- solve the problem
- Main contributions
- Algorithm principle
- reference

#### (1) solve the problem

According to the homogeneity Hypothesis , Similar nodes tend to be linked together , Nodes with similar properties are also topologically connected by . But some of the properties of real networks are not very good , namely ** Node attributes and topology are often inconsistent **, This makes some pairs of nodes similar in topology , But it's not necessarily the same in node properties , vice versa .

#### (2) Main contributions

**Contribution 1：** It is found that the node attribute is inconsistent with the node topology .

**Contribution 2：** A novel unsupervised framework is proposed **NEAR**, It uses an attribute filter guided by homogeneity to optimize the attributes and solve the inconsistency between node attributes and node topology , So as to improve the accuracy of attribute network representation .

#### (3) Algorithm principle

**NEAR The main framework of the algorithm is shown in the figure below ：** From the frame diagram, we can see the general idea of the algorithm ：（** Firstly, it is clear that the parameters to be learned by the network are filters F、 Hidden layer weight matrix W、 Topological information matrix B And the node context vector U'**） Second, let's look at the introduction of attribute information , Attribute matrix A With a filter F The optimized data matrix is obtained by multiplication A~,A~ And the corresponding weight matrix in the network W Multiply to get a n x d Attribute based node representation vector matrix , Plus the bias matrix in the network B（ Represents the network embedding matrix based on topology information ） We can get the node center vector （ The nodes in the neural network are represented by two vectors , Center node vector and context vector , Analogy to Skip-Gram）, The node center vector matrix and the node context vector matrix get a similar node similarity matrix , Again softmax Normalization can predict the possible context of the central node （ namely Skip-Gram Model ）, The loss function of this part is Skip-Gram Loss function of （ Maximize the co-occurrence probability of nodes ）. also , Let's look at the introduction of topological information , Topology information is used to calculate the node similarity matrix n x n （ Introduction ） And A~ Attribute matrix n x n combination , As a term in the loss function .** You can see , The final loss function consists of two parts ,Skip-Gram Loss function + Based on the homogeneity assumption, it is used to optimize the node properties （ Solve the problem of inconsistent properties and topology ） Loss function （ Introduction ）**. About the network training part , Training samples are generated either by sampling neighbors or by random walk .

** The loss function consists of two parts , The following is an introduction to each part ：**

**Skip-Gram The loss function is as follows （ The detailed derivation process is shown in DeepWalk The original paper ）：**Minimizing the objective function is to find the node vector , It maximizes the co-occurrence probability of nodes in the window .

**Based on the homogeneity assumption, it is used to optimize the node properties （ Solve the problem of inconsistent properties and topology ） Loss function ：**sim_t It is the similarity of node pairs in topology （ The homogeneity hypothesis can be expressed by the similarity of nodes' neighborhood ）, In this paper, I use Adar index To measure （**The two nodes Adar index Measurement calculation**： Of all the common neighbors of two nodes*logk*Divided 1 Sum up ）.sim_a Is the attribute similarity of a node pair , In this paper, the cosine of node attribute vector is used to measure .**Then minimize the following objective function to express the meaning of**： somehow （ Such as filter F） Adjust the attribute vector of the node pair , The product of structural similarity and attribute similarity of node pairs is the largest （ It's the biggest when it's equal ）, This ensures that the nodes are in the structure （ attribute ） Similar at the same time in the properties （ structure ） It's similar to , That is to solve the problem of inconsistency between node attribute and node topology .

** The final objective function is as follows （ Weighted sum of the above two objective functions ）：**

#### (4) reference

Xiao T, Fang Y, Yang H, et al. Network Embedding with Attribute Refinement[J].