Outlier mining in high-dimensional data using the Jensen–Shannon divergence and graph structure analysis

Reliable anomaly/outlier detection algorithms have practical applications in many fields. For instance, anomaly detection allows to filter and clean the data used to train machine learning algorithms, improving their performance. However, outlier mining is challenging when the data is high-dimensional, and different approaches have been proposed for different types of data (temporal, spatial, network, etc). Here we propose a methodology to mine outliers in generic datasets in which it is possible to define a meaningful distance between elements of the dataset. The methodology is based on defining a fully connected, undirected graph, where the nodes are the elements of the dataset and the links have weights that are the distances between the nodes. Outlier scores are defined by analyzing the structure of the graph, in particular, by using the Jensen–Shannon (JS) divergence to compare the distributions of weights of different nodes. We demonstrate the method using a publicly available database of credit-card transactions, where some of the transactions are labeled as frauds. We compare with the performance obtained when using Euclidean distances and graph percolation, and show that the JS divergence leads to performance improvement, but increases the computational cost.