Bankruptcy analysis with self-organizing maps in learning metrics

We introduce a method for deriving a metric, locally based on the Fisher in formation matrix, into the data space. A self-organizing map (SOM) is compu ted in the new metric to explore financial statements of enterprises. The m etric measures local distances in terms of changes in the distribution of a n auxiliary random variable that reflects what is important in the data. In this paper the variable indicates bankruptcy within the next few years. Th e conditional density of the auxiliary variable is first estimated, and the change in the estimate resulting from local displacements in the primary d ata space is measured using the Fisher information matrix. When a self-orga nizing 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.