Opening the Black Box: the Relationship between Neural Networks and Linear Discriminant Functions

Over the last ten years feed‐forward neural networks have become a popular tool for statistical decision making. During this time, they have been applied in many fields, including cytological classification. Neural networks are often treated as a black box, whose inner workings are concealed from the researcher. This is unfortunate, since the inner workings of a neural network can be understood in a manner similar to that of a linear discriminant function, which is the standard tool that researchers use for decision making. This paper discusses feed‐forward neural networks and some methods to improve their performance for classification problems. Their relationship to discriminant functions will be examined for a simple two‐dimensional classification problem.