Clearly, one's ability to build, explore, and compare alternatives can lead to better decision making, problem solving, and design outcomes. However, I find that all too often many systems still work in a single state mode where the user can only see the result from one set of inputs at a time. Here I propose a formalism designed to represent alternatives and spaces of alternatives using the propagation-based parametric models. I choose the inputs (source nodes' independent properties) as the representation of an alternative, which I have labeled variation heads. A variation head may contain one or several inputs to the model. The information carried by several variation heads can be unified to create a new variation head. Then I define the concept of the variation space as a collection of many variation heads. A variation space is structured by an indexed array. Two key operations, Index Unification and Cartesian Unification, can be used to unify two or more spaces. The user defines a series of variation heads as a variation space and indexes them based on his/her preference, uses unification to unify the many variation spaces to create a space of the inputs for the system, and then generates a space of results based on these inputs. This research adopts design science research methodology to iteratively refine the formalism through loops of problem awareness, design, and evaluation. A prototypical system has been developed as a formative evaluation in order to confirm, explore, and expand the formalism from a purely mathematical perspective by testing out many varied and differing kinds of data organizations. To demonstrate its usage, I show how this formalism can be used on a specific visual analytics tool (CZSaw) in order to create a space of visualization variations; I then explain both how this formalism can be used to enrich the user's interaction in the variation space and how the indices of the space can help the user to navigate through the space.
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Thesis advisor: Woodbury, Robert
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