Much research has been done regarding how to visualize and interact with observations and attributes of high-dimensional data for exploratory data analysis. From the analyst's perceptual and cognitive perspective, current visualization approaches typically treat the observations of the high-dimensional dataset very differently from the attributes. Often, the attributes are treated as inputs (e.g., sliders), and observations as outputs (e.g., projection plots), thus emphasizing investigation of the observations. However, there are many cases in which analysts wish to investigate both the observations and the attributes of the dataset, suggesting a symmetry between how analysts think about attributes and observations. To address this, we define SIRIUS (Symmetric Interactive Representations In a Unified System), a symmetric, dual projection technique to support exploratory data analysis of high-dimensional data. We provide an example implementation of SIRIUS and demonstrate how this symmetry affords additional insights.