There are two ways that learning might be used to ease the construction of systems such as GRUFF. The first is that the rules (or proof tree) that make up GRUFF could be built by an inductive learning system. C4.5, a decision tree learner [Quinlan1992], is a good example of this class of learning systems. However, these types of inductive classification systems cannot adequately replace the functionality of the GRUFF/OMLET system. OMLET allows examples which have less than perfect membership in a class to be used for training. There is no direct way to accomplish this in a system such as C4.5. A decision-tree based system would probably require different trees to be trained for parent and child categories. The functional concepts ( provides_sittable_surface, for example) would get lost in the training process if the individual features for a chair were directly used. We could train a series of trees to learn functional concepts individually, then train a decision tree to combine the results. In such an approach the parameters of the membership functions that are learned in this paper would be learned implicitly in the construction of a decision tree for a functional concept and any resulting rules. Replacing GRUFF/OMLET with a decision tree or other general-purpose rule learner is possible, but would require extensive work to preserve the idea of functional object recognition.
OMLET is aimed at the second area in which a GRUFF-like system could benefit from learning, which is in tuning the membership functions. A knowledge primitive might be a sittable surface. Given measurements for a specific surface of an object in a specific orientation, it is necessary to develop a representation of acceptable bounds on the measurements to determine whether the surface has the area to be sittable.
Techniques from other areas of machine learning have been used to represent and learn probabilistic and fuzzy membership functions. For example, belief networks provide a mechanism for representing probabilistic relationships between features of a domain. Individual feature probabilities can be combined to generate the probability of a complex concept by propagating belief values and constraints through the network. Adaptive probabilistic networks are a kind of belief nets that can learn the individual probability values and distributions using gradient descent [Pearl1988,Cooper Herskovits1992,Spiegelhalter, Dawid, Lauritzen, \ Cowell1993]. The structure of belief nets and their update algorithms are similar to the approaches found in OMLET. However, OMLET incorporates symbolic theorem proving, a feature that is fundamental to performing function-based object recognition, as well as value propagation.
Similar research has been performed to learn fuzzy membership functions using adaptive techniques such as genetic algorithms and classifier systems [Parido Bonelli1993,Valenzuela-Rendon1991]. Much of this work can only be used to learn individual membership functions and cannot handle combinations of input. Once again, little work has been directed at learning fuzzy memberships in the context of a rule-based system. Additional refinement techniques such as reinforcement learning [Mahadevan Connell1991,Watkins1989], neural networks, and statistical learning techniques can also be used to refine confidence values.
This project represents a new direction in computer vision and machine learning research; namely, the integration of machine learning and computer vision methods to learn fuzzy membership functions for a function-based object recognition system. Although learning such functions in a rule-based context is a novel effort, similar research has been performed in the area of refining certainty factors for intelligent rule bases. For example, Mahoney and Mooney (1993) and Lacher et al. (1992) use backpropagation algorithms to adjust certainty factors of existing rules in order to improve classification of a given set of training examples. In contrast to OMLET's approach, all of these systems refine values that represent a measure of belief in a given result and are adjusted according to the combination functions of certainty factors. OMLET's measures represent degrees of fuzzy membership in an object class, and the refinement method propagates error through an AND/OR tree.
The work by Wilkins and Ma (1994) focuses on revising probabilistic rules in a classification expert system. Probabilistic weights are applied to each rule, indicating the strength of the evidence supplied by the rule. However, refinements to the rule occur in the form of modifying the applicability of the rule by generalizing, specializing, deleting or adding rules, instead of automatically refining the weight of the rule. The authors avoid automatic refinement of weights because the resulting rule base may not be interpretable by experts.
Towell and Shavlik (1993) convert a set of rules into a representation suitable for a neural net, then train the network and re-extract the refined rules. The initial network can be set up for a chain of rules. The extracted rules will not necessarily have the clear functional meaning that our approach aims at preserving.
There are several new approaches to learning and tuning fuzzy rules [Ishibuchi, Nozaki, Yamamoto1993,Berenji Khedkar1992,Jang1993,Jang Sun1995] that use genetic algorithms or specialized kinds of neural networks, some making use of reinforcement learning. These approaches might provide an alternative way to learn the membership values provided the initial functional rules are given as fuzzy rules. However, some modifications to the learning approaches would be needed as they normally work in domains without rule chaining or hierarchies of rules as there are in GRUFF/OMLET.