Abstract: Methods and systems for identifying and classifying multilinear data sets into a plurality of classes using invariant theory are disclosed herein. An example method includes receiving an input data set; computing a change of coordinates for each mode of the plurality of modes for the input data set using an invariant theory optimization algorithm by (i) constructing a chosen group and (ii) determining a group element in the chosen group; transforming the input data set into a relocated data set by applying each change of coordinates for each respective mode of the plurality of modes for the input data set by multiplying the subset of the input data set for each mode by the at least one matrix corresponding to each respective mode; and classifying, based on distances between coordinates in the relocated data set, the input data set into the plurality of classes.