We construct the authentication system for fingerprint with multi-steps, which were 3-layered neural networks with a backpropagation learning algorithm. The authentication system consists of large classification with 1 step and small classification with 16 steps. As a result, the system is useful for the authentication system with a very large number of input patterns. From the results, we found that the authentication rate at each 1 step was 99.985% and that the authentication rates of the system increased with the number of steps and were estimated by the equation, {100-(0.015)**N}, where N is the number of steps. Therefore, the authentication rates of the system are controllable by the number of steps.

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In this paper, we propose a method for automatic generation of music playlist that reflects a user's subjective preferences. The playlist is composed on top of a "Music Map" where hundreds of songs from various genres, which are subjectively characterized by the user, are topologically aligned. A playlist is generated by designing a travel path in the Music Map, visiting one song after another in a certain order. The topological nature of the Music Map ensures that the form of the travel path gives a certain character to the generated playlist. Thus, problem of generating a playlist that fulfills a given criterion can be transformed into a problem of finding an optimum path, similar to the Traveling Salesman Problem (TSP). In the experiments, we construct a Music Map containing 500 songs and automatically generate a playlist according to various criteria.

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