# SAES: An Introduction to Self-Adapting Exploratory Structures
## 2 Self-Adapting Exploratory Structures  
Self-adapting exploratory structures (SAES) present a uniform view of the information base consisting of multiple choices (selectors or filters) and use the same structure to set interest sets (foci) and summarize results. SAES selectors have three fundamental properties:  
* Selectors are used to set interest sets (foci), i.e., to \"query\" the information base;
* Selectors are used to summarize query results, and consequently they should be able to summarize any subset of the information base. This is a fundamental point, and intuitively, there cannot be any effective exploration capabilities in systems which do not support summaries of foci. Without summaries, users are left in the dark as to what choices are allowed to restrict the information base;
* Summaries must be produced in real time, because a slower response time would discourage users from exploration. Since exploratory systems must be able to produce summaries for any subset of the universe, naive strategies that precompute all the possibilities are obviously not applicable because of exponential growth. SAES can be further characterized according to seven dimensions:  
* _Selector composition_. In the simplest case, only one selector can be chosen. In the most general case, any boolean combination of selectors can be used;
* _Multidimensional_ vs. _monodimensional selectors_. Monodimensional selectors are characterized by a 1:N relation with items, i.e., a selector can select many items, but any specific item can be selected by only one selector. The traditional Aristotelian taxonomy is an example of a taxonomy with monodimensional selectors. Multidimensional selectors, on the other hand, have a M:N relation with items. Access through monodimensional vs. multidimensional taxonomies vs. dynamic taxonomies was studied in [PERSON] (2016). In extreme synthesis, it was shown that monodimensional taxonomies are not scalable and do not provide sufficient discrimination for large information bases. Multidimensional taxonomies are even worse from this aspect, unless selector composition (which is irrelevant in monodimensional taxonomies) is allowed. The results carry over to flat organizations;* _Completeness of iteration_. Iteration is complete if the process of selecting a focus and summarizing it can be iterated at will, or at least until a singleton result set is obtained. Incomplete iteration results in the impossibility of further restricting the information base beyond a certain point;
* _Completeness of reach_. Reach is complete if it can be guaranteed that there are no items in the information base which are not reachable through at least one selector. Incomplete reach cause a loss of potentially relevant items because some items are never considered during exploration. Consequently, reach-incomplete structures should never be used as the only access path to an information base, and their usefulness is, in general, questionable;
* _Self-sufficiency_. A SAES is self-sufficient if the use of selectors is always supported, and it is the only required operation, although other types of queries (e.g., text retrieval) can be supported. Non self-sufficient structures force the user to restrict the information base through other strategies before selectors can be used. As an example, many applications require the user to enter a text retrieval query before exploration can start. This is done primarily for performance reasons, and it results in asymmetric interactions. Most importantly, in this approach the user is unable to have summary information for the entire information base;
* _No-zero-result_. This property is satisfied when selectors which do not describe the result are pruned from summaries, or made non selectable. Consequently, the use of a selector is guaranteed never to produce an empty result;
* _Taxonomic_ vs. _flat organization_.