On the E ciency of Learning in Spatial Domains and Relational Evidence Theory

In this paper two di erent approaches to evidential learning are investigated in how they apply to generalizing within spatial domains. We present a systematic evaluation of learning to identify unconstrained spatial data. The e ciency of di erent approaches to evidential theory for relational problems is compared. Many real-world identi cation and planning tasks involve the interpretation of data encoded at one level by classi cation categories at another level. In spatial domains image interpretation involves the labeling of image regions corresponding to di erent objects or world structures. For example, in handwritten text and symbol recognition the classi cation of di erent types of strokes or symbols and the ability to assign higherlevel descriptions to collections of such labeled regions is critical to e cient interpretation. Recognition processes need to be robust with respect to distortions, missing data and invariant to shifts, rotations and scales. All spatial interpretation systems must be able to generalize from training in all the above ways. Further, such generalizing in learning systems involves binding di erent levels of representation and this typically comes about by two di erent types of theories: Causal modeling, a universal approach based on determining dependencies in data and, Constraint Interpretation, an empirical approach which determines association between states of the world. For spatial classi cation systems there has been a move away from global representation toward the use of relational structures which encode local information. Queries in these domains are delineated from simple database operations like sorting and attributed lookup in that the data is relational. This is re ected in the form of input data used, whether it be in the form of simple attribute lists or relations which encode speci c instantiations and combinations of evidence. Image interpretation hierarchies must include both a notion of what a visual event is combined with relative location to other events, event relations. Interpretation tasks involving montages or scenes of di erent patterns rely on the relative layout and positioning of events as an important component of the interpretation process. The use of pure deductive, explanation-based or theorem proving approaches to interpretation has proven too di cult because of the limited nature of the background knowledge and the di culty in providing suitable hand-coded speci cations. As a result inductive learning procedures have proven to be an important factor in allowing systems to improve their behavior over time, particularly for the tasks of database query optimizing and generalizing over the input data. In the context of evidence-based learning [3, 8] the process of generalizing not only requires a way to partition the data, a kind of generalizing engine, but also a way to evaluate the representation which addresses the process of searching for the best solution. Two aspects of representational selection emerge and are based on di erent evidential approaches. First, causal modeling has been used to register degrees of implication, or evidence weights, for representations during data partitioning and is based on conditioning over events which have been provided a priori. Second, constraint interpretation may be used to resolve con ict between di erent representational entities after partitioning, a posteriori, and is based on the association between speci c instantiations of events, label-compatibility.