In the second row of figure 1, \(\tau _i^*\)against \({\tau _i}\) are plotted, where \({\tau _i}\)’s are the computed coordinates by LTSA. From these figures, \(\left( {\tau _i^*,{\tau _i}} \right)\) forms a straight line with either a \(\frac{\pi}{4}\) and \(-\frac{\pi}{4}\) slope. Because it is difficult to align the locale tangent information if some of the matrix \({P_i}'s\) are close to be singular. The computed coordinates \({\tau _i}\) and its neighbors maybe compressed together.