What do you think about the best way to perform a search for two discrete group membership in data that consist of four Fourier series coefficients like this:
$an
[1] -1.099759e+02 -3.277411e+01 -2.069982e+01 1.294945e+00 -4.557681e+00
[6] 3.659611e+00 -2.266350e+00 2.290051e+00 -1.165922e+00 4.290447e-01
[11] -5.157878e-01 -4.373163e-02 -9.627400e-02 -2.160347e-01 -8.664855e-02
[16] -7.125669e-02 -1.661091e-01 5.034174e-02 -5.773743e-02 9.070195e-02
[21] -1.103436e-01 4.968477e-02 -3.843040e-02 -3.539704e-02 -2.001452e-03
[26] -6.103696e-02 5.080494e-03 -8.438730e-02 9.728283e-02 -1.201637e-01
[31] 5.214383e-03 -3.097534e-02
$bn
[1] -9.950280480 21.060718135 1.749972609 3.125969744 -1.221718994
[6] -0.366008050 0.134939868 -1.433288279 1.286034494 -0.793100554
[11] 1.024338370 -0.645426109 0.752002518 -0.354023866 0.371995040
[16] -0.079819647 0.093705335 -0.085753179 0.062387444 -0.007351952
[21] 0.112815714 -0.071472761 0.180375050 -0.155871666 0.165280059
[26] -0.084238927 0.157971637 -0.115017123 0.058533444 0.021303459
[31] -0.009807206 -0.037191448
$cn
[1] 186.42631186 -48.82963771 -13.05530543 -17.63800716 -8.78793762
[6] -5.13169720 -4.05998782 -1.53832276 -1.92963513 -1.04525653
[11] -0.80438591 -0.98701575 -0.24698734 -1.00053803 -0.21660353
[16] -0.85765069 -0.32822392 -0.54232592 -0.39971080 -0.22425141
[21] -0.46861898 -0.05909403 -0.45459051 -0.03218630 -0.39596045
[26] -0.06020157 -0.25675128 -0.08580023 -0.16002496 -0.14539536
[31] -0.13190927 -0.12939389
$dn
[1] -60.193804743 17.089146986 -5.359459446 9.834089998 -1.841459861
[6] 2.894124403 -1.229890034 -0.060334681 -0.383461709 -0.414984724
[11] 0.161235406 -0.209664090 0.133169983 0.114066031 -0.113437218
[16] 0.326989075 -0.353357830 0.366442458 -0.379583013 0.327422310
[21] -0.253858236 0.177601217 -0.120553856 0.010128884 0.009787827
[26] -0.048527754 0.075992199 -0.090581996 0.043151283 -0.050768870
[31] 0.022838609 0.004311564
when I have 26 of such sets (and choosing the first 8 of each coefficient excluding the first one). These coefficients describe shape in mountain goat horns, and I need the best way to separate them according to sex which is accounting for horn curvature and other shape features. Now, PCA or LDA separate the extreme shapes well but what about the intermediate ones?
I tried numerous partitional clustering approaches but found no consistent grouping pattern with them. Also the majority of parametric statistic methods do not work because of high degree of correlation and non-normality of such data. Any advice?
