note that to estimate variance retained approximately only, you probably don't need to run it with q=1 so you can run with q=0 and not request either V or U but singular values only. That will reduce running time dramatically (perhaps up to 2-5 times faster compared to with q=1 and U and V).
On Fri, Aug 10, 2012 at 2:31 PM, Dmitriy Lyubimov <[email protected]> wrote: > With PCA, there's a metric, something called "variance retained". > > One idea of mine to estimate k is described in footnote discussion on > page 5. While it is not possible to compute "PCA variance retained" > metric exactly with an application of a thin SVD (the metric assumes > use of a full rank SVD) it is possible to infer upper estimate for k > given target variance retained (say, 99%) or try some sort of > polynomialy approximated value for the sum of all singular values > given visible decay. Probably requires some simple code in R or matlab > to get reasonable estimate. > > This technique requires running PCA one time and then estimate > sufficient k given singular values produced on your corpus. If the > action is repetetive and corpus is not changing drastically, you may > infer if you spending too much (or too little) on k for future uses. > > But pragmatically i just use the best k my cluster can compute in the > time i need. my corpus is relatively small and i don't run full corpus > run too often so i can afford some time spent. > > On Fri, Aug 10, 2012 at 2:14 PM, Pat Ferrel <[email protected]> wrote: >> The built-in PCA option is one reason I wanted to try SSVD. Building the >> test was to make sure I understood the external matrix operations before >> diving in. I expect one primary decision is how to choose k for reduction. >> I'm hoping to get some noise rejection so not using it for reduced matrix >> size so much. We are starting with m = 500,000 and a million or so docs. We >> get many dups and low value docs in a small web crawl, so lots of noise. >> >> You mention in your paper: >> >> "The valueof k + p directly impacts running time and memory requirements. >> k+p=500 is probably more than reasonable. Typically k + p >> is taken within range 20…200" >> >> So I guess we might start with >> -p 15 (default) >> -q 1 >> -k 200 >> >> Is there any use in hand inspecting the eigen vectors before choosing the >> final k? If so do you get those by choosing k nearly = m or is something >> like k = 1000 (or ?) good enough to for inspection? >> >> On Aug 10, 2012, at 12:53 PM, Dmitriy Lyubimov <[email protected]> wrote: >> >> BTW if you really are trying to reduce dimensionality, you may want to >> consider --pca option with SSVD, that [i think] will provide with much >> better preserved data variance then just clean SVD (i.e. essentially >> run a PCA space transformation on your data rather than just SVD) >> >> -d >> >> On Fri, Aug 10, 2012 at 11:57 AM, Pat Ferrel <[email protected]> wrote: >>> Got it. Well on to some real and much larger data sets then… >>> >>> On Aug 10, 2012, at 11:53 AM, Dmitriy Lyubimov <[email protected]> wrote: >>> >>> i think actually Mahout's Lanczos requires external knowledge of input >>> size too, in part for similar reasons. SSVD doesn't because it doesn't >>> have "other" reasons to know input size but fundamental assumption >>> rank(input)>=rank(thin SVD) still stands about the input but the >>> method doesn't have a goal of verifying it explicitly (which would be >>> kind of hard), and instead either produces 0 eigenvectors or runs into >>> block deficiency. >>> >>> It is however hard to assert whether block deficiency stemmed from >>> input size deficiency vs. split size deficiency, and neither of >>> situations is typical for a real-life SSVD applications, hence error >>> message is somewhat vague. >>> >>> On Fri, Aug 10, 2012 at 11:39 AM, Dmitriy Lyubimov <[email protected]> >>> wrote: >>>> The easy answer is to ensure (k+p)<= m. It is mathematical constraint, >>>> not a method pecularity. >>>> >>>> The only reason the solution doesn't warn you explicitly is because >>>> DistributedRowMatrix format, which is just a sequence file of rows, >>>> would not provide us with an easy way to verify what m actually is >>>> before it actually iterates over it and runs into block size >>>> deficiency. So if you now m as an external knowledge, it is easy to >>>> avoid being trapped by block height defiicency. >>>> >>>> >>>> On Fri, Aug 10, 2012 at 11:32 AM, Pat Ferrel <[email protected]> wrote: >>>>> This is only a test with some trivially simple data. I doubt there are >>>>> any splits and yes it could easily be done in memory but that is not the >>>>> purpose. It is based on testKmeansDSVD2, which is in >>>>> mahout/integration/src/test/java/org/apache/mahout/clustering/TestClusterDumper.java >>>>> I've attached the modified and running version with testKmeansDSSVD >>>>> >>>>> As I said I don't think this is a real world test. It tests that the code >>>>> runs, and it does. Getting the best results is not part of the scope. I >>>>> just thought if there was an easy answer I could clean up the parameters >>>>> for SSVDSolver. >>>>> >>>>> Since it is working I don't know that it's worth the effort unless people >>>>> are likely to run into this with larger data sets. >>>>> >>>>> Thanks anyway. >>>>> >>>>> >>>>> >>>>> >>>>> On Aug 10, 2012, at 11:07 AM, Dmitriy Lyubimov <[email protected]> wrote: >>>>> >>>>> It happens because of internal constraints stemming from blocking. it >>>>> happens when a split of A (input) has less than (k+p) rows at which >>>>> point blocks are too small (or rather, to short) to successfully >>>>> perform a QR on . >>>>> >>>>> This also means, among other things, k+p cannot be more than your >>>>> total number of rows in the input. >>>>> >>>>> It is also possible that input A is way too wide or k+p is way too big >>>>> so that an arbitrary split does not fetch at least k+p rows of A, but >>>>> in practice i haven't seen such cases in practice yet. If that >>>>> happens, there's an option to increase minSplitSize (which would >>>>> undermine MR mappers efficiency somewhat). But i am pretty sure it is >>>>> not your case. >>>>> >>>>> But if your input is shorter than k+p, then it is a case too small for >>>>> SSVD. in fact, it probably means you can solve test directly in memory >>>>> with any solver. You can still use SSVD with k=m and p=0 (I think) in >>>>> this case and get exact (non-reduced rank) decomposition equivalent >>>>> with no stochastic effects, but that is not what it is for really. >>>>> >>>>> Assuming your input is m x n, can you tell me please what your m, n, k >>>>> and p are? >>>>> >>>>> thanks. >>>>> -D >>>>> >>>>> On Fri, Aug 10, 2012 at 9:21 AM, Pat Ferrel <[email protected]> wrote: >>>>>> There seems to be some internal constraint on k and/or p, which is >>>>>> making a test difficult. The test has a very small input doc set and >>>>>> choosing the wrong k it is very easy to get a failure with this message: >>>>>> >>>>>> java.lang.IllegalArgumentException: new m can't be less than n >>>>>> at >>>>>> org.apache.mahout.math.hadoop.stochasticsvd.qr.GivensThinSolver.adjust(GivensThinSolver.java:109) >>>>>> >>>>>> I have a working test but I had to add some docs to the test data and >>>>>> have tried to reverse engineer the value for k (desiredRank). I came up >>>>>> with the following but I think it is only an accident that it works. >>>>>> >>>>>> int p = 15; //default value for CLI >>>>>> int desiredRank = sampleData.size() - p - 1;//number of docs - p - 1, >>>>>> ?????? not sure why this works >>>>>> >>>>>> This seems likely to be an issue only because of the very small data set >>>>>> and the relationship of rows to columns to p to k. But for the purposes >>>>>> of creating a test if someone (Dmitriy?) could tell me how to calculate >>>>>> a reasonable p and k from the dimensions of the tiny data set it would >>>>>> help. >>>>>> >>>>>> This test is derived from a non-active SVD test but I'd be up for >>>>>> cleaning it up and including it as an example in the working but >>>>>> non-active tests. I also fixed a couple trivial bugs in the non-active >>>>>> Lanczos tests for what it's worth. >>>>>> >>>>>> >>>>>> On Aug 9, 2012, at 4:47 PM, Dmitriy Lyubimov <[email protected]> wrote: >>>>>> >>>>>> Reading "overview and usage" doc linked on that page >>>>>> https://cwiki.apache.org/confluence/display/MAHOUT/Stochastic+Singular+Value+Decomposition >>>>>> should help to clarify outputs and usage. >>>>>> >>>>>> >>>>>> On Thu, Aug 9, 2012 at 4:44 PM, Dmitriy Lyubimov <[email protected]> >>>>>> wrote: >>>>>>> On Thu, Aug 9, 2012 at 4:34 PM, Pat Ferrel <[email protected]> wrote: >>>>>>>> Quoth Grant Ingersoll: >>>>>>>>> To put this in bin/mahout speak, this would look like, munging some >>>>>>>>> names and taking liberties with the actual argument to be passed in: >>>>>>>>> >>>>>>>>> bin/mahout svd (original -> svdOut) >>>>>>>>> bin/mahout cleansvd ... >>>>>>>>> bin/mahout transpose svdOut -> svdT >>>>>>>>> bin/mahout transpose original -> originalT >>>>>>>>> bin/mahout matrixmult originalT svdT -> newMatrix >>>>>>>>> bin/mahout kmeans newMatrix >>>>>>>> >>>>>>>> I'm trying to create a test case from testKmeansDSVD2 to use >>>>>>>> SSVDSolver. Does SSVD require the EigenVerificationJob to clean the >>>>>>>> eigen vectors? >>>>>>> >>>>>>> No >>>>>>> >>>>>>>> if so where does SSVD put the equivalent of >>>>>>>> DistributedLanczosSolver.RAW_EIGENVECTORS? Seems like they should be >>>>>>>> in V* but SSVD creates V so should I transpose V* then run it through >>>>>>>> the EigenVerificationJob? >>>>>>> no >>>>>>> >>>>>>> SSVD is SVD, meaning it produces U and V with no further need to clean >>>>>>> that >>>>>>> >>>>>>>> I get errors when I do so trying to figure out if I'm on the wrong >>>>>>>> track. >>>>>> >>>>> >>>>> >>> >>
