Determining symmetry within a collection of spatially oriented points is a problem that occurs in many fields. In these applications, large amounts of data are generally collected, and it is desirable to approximate this data with a compressed representation. In some situations, the data is known to obey certain symmetry conditions, and it is profitable to preserve such symmetry in the compressed approximation. I accomplish this task by providing a symmetry preserving singular value decomposition. I will present the formulation of this factorization along with an application of this method to molecular dynamics.