Ok, then what would you think to be the minimum number of columns in the dataset for Lanczos to give a reasonable result?
Thanks, -Trevor > A gazillion rows of 2-columned data is really much better suited to doing > the following: > > if each row is of the form [a, b], then compute the matrix > > [[a*a, a*b], [a*b, b*b]] > > (the outer product of the vector with itself) > > Then take the matrix sum of all of these, from each row of your input > matrix. > > You'll now have a 2x2 matrix, which you can diagonalize by hand. It will > give you your eigenvalues, and also the right-singular vectors of your > original matrix. > > -jake > > 2011/6/23 <[email protected]> > >> Yes, exactly why I asked it for only 2 eigenvalues. So what is being >> said, >> is if I have lets say 50M rows of 2 columned data, Lanczos can't do >> anything with it (assuming it puts the 0 eigenvalue in the mix - of the >> 2 >> eigenvectors only 1 is returned because of the 0 eigenvalue taking up a >> slot)? >> >> If the eigenvalue of 0 is invalid, then should it not be filtered out so >> that it returns "rank" number of eigenvalues that could be valid? >> >> -Trevor >> >> > Ah, if your matrix only has 2 columns, you can't go to rank 10. Try >> on >> > some slightly less synthetic data of more than rank 10. You can't >> > ask Lanczos for more reduced rank than that of the matrix itself. >> > >> > -jake >> > >> > 2011/6/23 <[email protected]> >> > >> >> Alright I can reorder that is easy, just had to verify that the >> ordering >> >> was correct. So when I increased the rank of the results I get >> Lanczos >> >> bailing out. Which incidentally causes a NullPointerException: >> >> >> >> INFO: 9 passes through the corpus so far... >> >> WARNING: Lanczos parameters out of range: alpha = NaN, beta = NaN. >> >> Bailing out early! >> >> INFO: Lanczos iteration complete - now to diagonalize the >> tri-diagonal >> >> auxiliary matrix. >> >> Exception in thread "main" java.lang.NullPointerException >> >> at >> >> org.apache.mahout.math.DenseVector.assign(DenseVector.java:133) >> >> at >> >> >> >> >> org.apache.mahout.math.decomposer.lanczos.LanczosSolver.solve(LanczosSolver.java:160) >> >> at pca.PCASolver.solve(PCASolver.java:53) >> >> at pca.PCA.main(PCA.java:20) >> >> >> >> So I should probably note that my data only has 2 columns, the real >> data >> >> will have quite a bit more. >> >> >> >> The failing happens with 10 and more for rank, with the last, and >> >> therefore most significant eigenvector being <NaN,NaN>. >> >> >> >> -Trevor >> >> > The 0 eigenvalue output is not valid, and yes, the output will list >> >> the >> >> > results >> >> > in *increasing* order, even though it is finding the largest >> >> > eigenvalues/vectors >> >> > first. >> >> > >> >> > Remember that convergence is gradual, so if you only ask for 3 >> >> > eigevectors/values, you won't be very accurate. If you ask for 10 >> or >> >> > more, >> >> > the >> >> > largest few will now be quite good. If you ask for 50, now the top >> >> 10-20 >> >> > will >> >> > be *extremely* accurate, and maybe the top 30 will still be quite >> >> good. >> >> > >> >> > Try out a non-distributed form of what is in the >> EigenverificationJob >> >> to >> >> > re-order the output and collect how accurate your results are (it >> >> computes >> >> > errors for you as well). >> >> > >> >> > -jake >> >> > >> >> > 2011/6/23 <[email protected]> >> >> > >> >> >> So, I know that MAHOUT-369 fixed a bug with the distributed >> version >> >> of >> >> >> the >> >> >> LanczosSolver but I am experiencing a similar problem with the >> >> >> non-distributed version. >> >> >> >> >> >> I send a dataset of gaussian distributed numbers (testing PCA >> stuff) >> >> and >> >> >> my eigenvalues are seemingly reversed. Below I have the output >> given >> >> in >> >> >> the logs from LanczosSolver. >> >> >> >> >> >> Output: >> >> >> INFO: Eigenvector 0 found with eigenvalue 0.0 >> >> >> INFO: Eigenvector 1 found with eigenvalue 347.8703086831804 >> >> >> INFO: LanczosSolver finished. >> >> >> >> >> >> So it returns a vector with eigenvalue 0 before one with an >> >> eigenvalue >> >> >> of >> >> >> 347?. Whats more interesting is that when I increase the rank, I >> get >> >> a >> >> >> new >> >> >> eigenvector with a value between 0 and 347: >> >> >> >> >> >> INFO: Eigenvector 0 found with eigenvalue 0.0 >> >> >> INFO: Eigenvector 1 found with eigenvalue 44.794928654801566 >> >> >> INFO: Eigenvector 2 found with eigenvalue 347.8286920203704 >> >> >> >> >> >> Shouldn't the eigenvalues be in descending order? Also is the 0.0 >> >> >> eigenvalue even valid? >> >> >> >> >> >> Thanks, >> >> >> Trevor >> >> >> >> >> >> >> >> > >> >> >> >> >> >> >> > >> >> >> >
