Hierarchical classifier
A hierarchical classifier is a classifier that maps input data into defined subsumptive output categories. The classification occurs first on a low-level with highly specific pieces of input data. The classifications of the individual pieces of data are then combined systematically and classified on a higher level iteratively until one output is produced. This final output is the overall classification of the data. Depending on application-specific details, this output can be one of a set of pre-defined outputs, one of a set of on-line learned outputs, or even a new novel classification that hasn't been seen before. Generally, such systems rely on relatively simple individual units of the hierarchy that have only one universal function to do the classification. In a sense, these machines rely on the power of the hierarchical structure itself instead of the computational abilities of the individual components. This makes them relatively simple, easily expandable, and very powerful.
Application
Many applications exist that are efficiently implemented using hierarchical classifiers or variants thereof. One such example lies in the area of computer vision. Recognizing pictures is something that hierarchical processing can do well. The reason the model is so well fit to this application is that pictures can intuitively be viewed as a collection of components or objects. These objects can be viewed as collections of smaller components like shapes, which can be viewed as collections of lines, and so on. This coincides directly with the way hierarchical processing works. If a simple unit of the processing hierarchy can classify lines into shapes, then an equivalent unit could process shapes into objects (of course, there are some intermediate steps between these, but the idea is there). Thus, if you arrange these generic classifying units in a hierarchical fashion (using a directed acyclic graph), a full step-by-step classification can ensue from pixels of color all the way up to an abstract label of what is in the picture.
There are a lot of similar applications that can also be tackled by hierarchical classification such as written text recognition, robot awareness, etc. It is possible that mathematical models and problem solving methods can also be represented in this fashion. If this is the case, future research in this area could lead to very successful automated theorem provers across multiple domains. Such developments would be very powerful, but is yet unclear how exactly these models are applicable.