User interaction in visual analytic systems is critical to enabling visual data exploration.Through interacting with visualizations, users engage in sensemaking, a process of developing and understanding relationships within datasets through foraging and synthesis. For example, two-dimensional layouts of high-dimensional data can be generated by dimension reduction models, and provide users with an overview of the relationships between information. However, exploring such spatializations can require expertise with the internal mechanisms and parameters of these models.The core contribution of this work is semantic interaction, capable of steering such models without requiring expertise in dimension reduction models, but instead leveraging the domain expertise of the user. Semantic interaction infers the analytical reasoning of the user with model updates, steering the dimension reduction model for visual data exploration. As such, it is an approach to user interaction that leverages interactions