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We live in an age where data is plentiful but finding patterns in the data is hard. We need automated ways to do so. Given a large cloud of data points in a high dimensional space, a classical technique, Principal Component Analysis (PCA), computes the affine subspace of a given dimension that is closest to the data. But suppose the data lies on the surface of a two dimensional sphere in a higher dimensional space. PCA with given dimension three yields the three dimensional subspace that contains the sphere. PCA with given dimension two yields a random two dimensional subspace close to the center of the sphere. PCA is oblivious to the geometry of the sphere. New techniques are needed that capture the intrinsic geometry of the data. Thomas Hunt and I have developed a nonlinear version of PCA called Nonlinear Simplicial Principal Component Analysis (SNPCA) that captures the intrinsic geometry of data on a sphere by approximating it by a two dimensional simplicial complex. A two dimensional simplicial complex is a set vertices (points), edges (line segments) and triangles such that triangles meet at edges and edges meet at vertices. SNPCA is a novel and easily parallelizable algorithm that takes as input a point cloud in R^n, e.g. n = 50, and outputs a triangulization that fits the point cloud. The algorithm grows the triangulation using an advancing front method that only needs the points in the cloud near the frontier of the advancing triangulation, followed by a stage that closes holes in the triangulation. Consequently, the algorithm can handle point clouds that grow as they are triangulated.