Node Embeddings

start=>start: Input Graph
info=>operation: Structured Features
setCache=>operation: Learning Algorithm
end=>end: Prediction
start->info->setCache->end

Input Graph –> feature enginearing now we abrod that Automatically learn

Graph Representation Learning

Goal: Efficient task -independent feature learning for machine learning with graphs

Why Embedding

Task：map nodes into an embedding space

Setup

Shallow Encoding encoder is just an embedding-lookup

Framework Summary

Encoder + Decoder Framework - Shallow encoder:embedding looup - Parameters to optimize: Z which contains node embeddings zu for all nodes u <V

• Decoder : based on node similarity
• Objective: maximize ZvT Zu for node pairs(u,v) that are similar

Random walk Approaches for Node Embeddings

• Vector Zu:

• Probability P(v

  Zu):

• softmax
• sigmoid

Random Walk Embeddings

Unsupervised Feature Learning

Intuition:

• Find embeddding of nodes in d-dimensional space that preserves similarity idea:
• Learn node embedding such that nearby nodes are close together in the network Given a node u , how do we define nearby nodes?

Feature Learning as Optimization

Random Walk Optimization

Overview of node2vec

Goal: Embed node with similar network neighborhoods close in the feature space Key observation: Flexible notion of network neighborhood Nr of node u leads to rich node embeddings.

Embedding Entire Graph

Summary

3 ideas to graph embeddings Approach1: embed nodes and sum/avg them Approcah2: Create super-node that spans the (sub) graph and then embed that node Approach3: Annoymous Walk embeddings Idea1: sample the anon. Idea2: Embed annoymous walks

How to use embeddings zi of nodes:

• Clustering / community detection
• Node classification
• Link prediction
• Graph classification