Nikos: > > It should be the case with i.pca as well since eigen_VALUES_ (=represent > > the variances of the original dimensions that are "kept" in each > > component) are important for the interpretation of what exactly are each > > of the components. But, i.pca just does not report the eigen_VALUES_. > > > > At some point some C-expert needs to have a look in the code (i.pca) and > > correct the "bug" which does not let the eigen_VALUES_ from being > > printed.
Hamish: > done in devbr6 (6.5svn) please test, I'm not a multivariate stats guru > and may have done something dumb so didn't port to other branches yet. > > I changed the i.pca output to be like: > > Eigen (vectors) and values: > PC1 ( -0.63 -0.65 -0.43 ) 88.07 > PC2 ( 0.23 0.37 -0.90 ) 11.48 > PC3 ( 0.75 -0.66 -0.08 ) 0.45 > > As it was previously sent to stderr via G_message() I don't feel bad about > breaking output text compatibility. I wanted to add "%" to the values but > due to the sprintf()+strcat() method in the code that was a pain, so I > didn't. Wesley: > > > If this is the case then both methods still differ significantly. Is > > > this possible, and which should I use. > > Please have a look at my comments/questions in link [2]. > > i.pca follows the "SVD" method. You performed the non-standartised PCA > > using the covariance matrix. Note that you can use also the > > standartised method by using the correlation matrix. > does the r.mapcalc command at the end of the m.eigensystem help page* > do that conversion, or ...? ie how can we test these against each other? > how to do the standardized method? We can easily cross-compare now. I will run my test in GRASS and R. In GRASS: * i.pca --> SVD without data centering method * "r.covar" + "m.eigensystem" --> non-standardised PCA (about data centering I am unsure here, I will investigate the _numbers_) * "r.covar -r" + "m.eigensystem" # note the "-r" flag --> standardised PCA (about data centering I am unsure, willing to test). > [*] (is "\-" there a typo or some old mapcalc syntax?) IMHO: yes. Maybe it's some forgotten _backslash_ !? > also ISTR somebody (Dylan?) doing a comparison with the R-stats interface. > > > It would be nice to run tests using the Spearfish imagery dataset. After > my own tests I noticed it matched what was used in the m.eigensystem help > page. I will probably run the test with my own data. Since I just need to copy-paste the commands. I don't have the spearfish dataset currently. > my results follow. > > Hamish > > > ---------------------------- > #Spearfish imagery sample dataset > g.region rast=spot.ms.1 > > > # 'by-hand-method' > G65> echo "3" > test_m.eigensystem # number of input maps > G65> r.covar map=spot.ms.1,spot.ms.2,spot.ms.3 >> test_m.eigensystem > > G65> cat test_m.eigensystem > 3 > 462.876649 480.411218 281.758307 > 480.411218 513.015646 278.914813 > 281.758307 278.914813 336.326645 > > > G65> m.eigensystem < test_m.eigensystem > ----- > C The output is N sets of values. One E line and N V W lines > C > C E real imaginary percent-importance > C V real imaginary > C N real imaginary > C W real imaginary > C ... > C > C where E is the eigen value (and it relative importance) > C and V are the eigenvector for this eigenvalue. > C N are the normalized eigenvector for this eigenvalue. > C W are the N vector multiplied by the square root of the > C magnitude of the eigen value (E). > ----- > > E 1159.7452017844 0.0000000000 88.38 > V 0.6910021591 0.0000000000 > V 0.7205280412 0.0000000000 > V 0.4805108400 0.0000000000 > N 0.6236808478 0.0000000000 > N 0.6503301526 0.0000000000 > N 0.4336967751 0.0000000000 > W 21.2394712045 0.0000000000 > W 22.1470141296 0.0000000000 > W 14.7695575384 0.0000000000 > > E 5.9705414972 0.0000000000 0.45 > V 0.7119385973 0.0000000000 > V -0.6358200627 0.0000000000 > V -0.0703936743 0.0000000000 > N 0.7438340890 0.0000000000 > N -0.6643053754 0.0000000000 > N -0.0735473745 0.0000000000 > W 1.8175356507 0.0000000000 > W -1.6232096923 0.0000000000 > W -0.1797107407 0.0000000000 > > E 146.5031967184 0.0000000000 11.16 > V 0.2265837636 0.0000000000 > V 0.3474697082 0.0000000000 > V -0.8468727535 0.0000000000 > N 0.2402770238 0.0000000000 > N 0.3684685345 0.0000000000 > N -0.8980522763 0.0000000000 > W 2.9082771721 0.0000000000 > W 4.4598880523 0.0000000000 > W -10.8698904856 0.0000000000 > > > # 'all-in-one method' using r.covar+m.eigensystem: > G65> (echo 3; r.covar spot.ms.1,spot.ms.2,spot.ms.3 ) | m.eigensystem > > Then, using the W vector, new maps are created: > r.mapcalc 'pc.1 = 21.2395*map.1 + 22.1470*map.2 + 14.7696*map.3' > r.mapcalc 'pc.2 = 2.9083*map.1 + 4.4599*map.2 - 10.8699*map.3' > r.mapcalc 'pc.3 = 1.8175*map.1 - 1.6232*map.2 \- 0.1797*map.3' > > (is "\-" above a typo or some old mapcalc syntax?) Probably a typo. > which look highly similar (but not identical) to i.pca output maps. It's ok. R print's out lot's of decimals. Perhaps the difference is due to some rounding of the numbers. > (after 'r.colors color=grey') > # 'automatic method' > imagery60:G6.5svn> i.pca in=spot.ms.1,spot.ms.2,spot.ms.3 out=spot_pca > > Eigen (vectors) and values: > PC1 ( -0.63 -0.65 -0.43 ) 88.07 > PC2 ( 0.23 0.37 -0.90 ) 11.48 > PC3 ( 0.75 -0.66 -0.08 ) 0.45 _______________________________________________ grass-stats mailing list [email protected] http://lists.osgeo.org/mailman/listinfo/grass-stats
