Bankruptcy analysis with self-organizing maps in learning metrics

We introduce a method for deriving a metric, locally based on the Fisher information matrix, into the data space. A self-organizing map (SOM) is computed in the new metric to explore financial statements of enterprises. The metric measures local distances in terms of changes in the distribution of an auxiliary random variable that reflects what is important in the data. In this paper the variable indicates bankruptcy within the next few years. The conditional density of the auxiliary variable is first estimated, and the change in the estimate resulting from local displacements in the primary data space is measured using the Fisher information matrix. When a self-organizing map is computed in the new metric it still visualizes the data space in a topology-preserving fashion, but represents the (local) directions in which the probability of bankruptcy changes the most.