Unsupervised Anomaly Detection Algorithm of Graph Data Based on Graph Kernel

Nowadays, there are a lot of graph data in many fields such as biology, medicine, social networks and so on. However, it is difficult to detect anomaly and get the useful information if we want to apply the traditional algorithms in graph data. Statistical pattern recognition and structural pattern recognition are two main methods in pattern recognition. The disadvantage of statistical pattern recognition is that it is difficult to represent the relationship. In the structural pattern recognition, the object is generally expressed as a graph, and the key point is the similarity or matching of the graphs. However, graph matching is complex and NP-hard. Recently, graph kernel is proposed to solve the graph matching problem, so we can map the graphs into vector space. As a result, the operations in the vector space are applicable to graph data. In this paper, we propose a new algorithm to detect anomaly for graph data. Firstly, we use graph kernel to define the similarity of the graphs, and then we convert graph data into vector data. After that, we use the Kernel Principal Component Analysis (KPCA) to reduce the dimension, and then train these data by one-class classifier to get the model for anomaly detection. The experiments on datasets MUTAG and ENZYMES at the end of the paper show the efficiency of proposed algorithm