1. A computer implemented method for improving, using multi-dimensional indexing data structures, a process of finding nearest neighbors for points, in multi-dimensional spaces, associated with a manufacturing process, the computer comprising a processor and memory, the method comprising: powering the computer; in response to powering the computer, executing an initialization procedure for the computer, the initialization procedure comprising configuring the memory and initializing one or more device drivers for communicating with one or more devices; providing a multi-dimensional indexing data structure in the memory, the multi-dimensional indexing data structure comprising at least one of an R-tree data structure or a KD-tree data structure; projecting, using at least one processor associated with the multi-dimensional indexing data structure, an n-dimension space Θ, with a dissimilarity measure μ into an m-dimensional space P with a dissimilarity measure μ′ by a projection function p, wherein: 
 1<m<n; and 
 μ′( p ( v 1), p ( v 2))≤μ( v 1, v 2) for all points v 1 and v 2 in Θ; selecting, using the at least one processor associated with the multi-dimensional indexing data structure, a point v in Θ; performing, using the at least one processor associated with the multi-dimensional indexing data structure, a search in P for a set S′ of k nearest neighbors of the point p(v) in P; finding, using the at least one processor associated with the multi-dimensional indexing data structure, a set S of all points in Θ that project to the set S′; and determining, using the at least one processor associated with the multi-dimensional indexing data structure, whether a point of the set S is a nearest neighbor of the point v, wherein determining whether the point of the set S is the nearest neighbor of the point v enables determination of a problem or an issue associated with the manufacturing process.