A Comparison between Neural Network Methods for Learning Aggregate Functions

In various application domains, data can be represented as bags of vectors instead of single vectors. Learning aggregate functions from such bags is a challenging problem. In this paper, a number of simple neural network approaches and a combined approach based on cascade-correlation are examined in order to handle this kind of data. Adapted feedforward networks, recurrent networks and networks with special aggregation units integrated in the network can all be used to construct networks that are capable of learning aggregate function. A combination of these three approaches is possible by using cascade-correlation, creating a method that automatically chooses the best of these options. Results on artificial and multi-instance data sets are reported, allowing a comparison between the different approaches.