US Patent 9551567 Reducing noise in spectral data from polishing substrates

Among other things, a machine based method includes representing a plurality of spectra reflected from one or more substrates at a plurality of different positions on the one or more substrates in the form of a first matrix; decomposing, by one or more computers, the first matrix into products of at least two component matrixes of a first set of component matrixes; reducing dimensions of each of the at least two component matrixes to produce a second set of component matrixes containing the at least two matrixes with reduced dimensions; and generating, by the one or more computers, a second matrix by taking a product of the matrixes of the second set of component matrixes.