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.