Visual summarization of clinical data collected on patients contained within the electronic health record (EHR) may enable precise and rapid triage at the time of patient presentation to an emergency department (ED). The triage process is critical in the appropriate allocation of resources and in anticipating eventual patient disposition, typically admission to the hospital or discharge home. EHR data are high-dimensional and complex, but offer the opportunity to discover and characterize underlying data-driven patient phenotypes. These phenotypes will enable improved, personalized therapeutic decision making and prognostication. In this work, we focus on the challenge of two-dimensional patient projections. A low dimensional embedding offers visual interpretability lost in higher dimensions. While linear dimensionality reduction techniques such as principal component analysis are often used towards this aim, they are insufficient to describe the variance of patient data. In this work, we employ the newly-described non-linear embedding technique called uniform manifold approximation and projection (UMAP). UMAP seeks to capture both local and global structures in high-dimensional data. We then use Gaussian mixture models to identify clusters in the embedded data and use the adjusted Rand index (ARI) to establish stability in the discovery of these clusters. This technique is applied to five common clinical chief complaints from a real-world ED EHR dataset, describing the emergent properties of discovered clusters. We observe clinically-relevant cluster attributes, suggesting that visual embeddings of EHR data using non-linear dimensionality reduction is a promising approach to reveal data-driven patient phenotypes. In the five chief complaints, we find between 2 and 6 clusters, with the peak mean pairwise ARI between subsequent training iterations to range from 0.35 to 0.74.