Probabilistic Modeling of State Transitions on the Self-Organizing Map: Some Temporal Financial Applications

Self-organizing maps (SOM) have been commonly used in temporal financial applications. This paper enhances the SOM paradigm for temporal data by presenting a framework for computing, summarizing and visualizing transition probabilities on the SOM. The framework includes computing matrices of node-to-node and node-to-cluster transitions and summarizing maximum state transition. The computations are visualized using feature plane representations. The future state transitions can also be used for finding low- and high-risk profiles as well as for assessing the evolution of probabilities over time, where the cluster centers express the representative financial states while the probability fluctuations represent their variation over time. We demonstrate the usefulness of the framework on two previously presented SOM models for temporal financial analysis: financial benchmarking of banks and monitoring indicators of currency crises.