From a computational standpoint, round-off error can disrupt the left-to-right pattern for the exact LS method by lengthening or shortening segment lengths by small amounts on the order of the single-precision floatingpoint variable used to represent the cut locations on the unit interval (∼ 10 -16 ). To allow the left-to-right pattern to exist for the exact LS method training data when round-off error is present, the computer is allowed to select the leftmost segment of each color whose length is within a certain tolerance of the true longest segment. Here we use the minimal tolerance necessary to produce the same left-to-right pattern in the straightforward application of the LS method, which is on the order of 10 -15 .