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. >>>>> >>>> >>>> >> >
