Spectral LDA on Spark

Note: For up-to-date version please refer to [https://github.com/Mega-DatA-Lab/SpectralLDA-Spark].

Summary

• This code implements a Spectral (third order tensor decomposition) learning method for learning LDA topic model on Spark.
• Version: 1.0

How do I get set up?

We use the sbt build system. By default we support Scala 2.11.8 and Spark 2.0.0 upward. Cross build to Scala 2.10.6 is also supported. The documentation below supposes we're using Scala 2.11.

To run from the command line

1. First compile and package the entire repo.

   sbt package

   It will produce target/scala-2.11/spectrallda-tensor_2.11-1.0.jar.

2. The command line usage is

   Spectral LDA Factorization
   Usage: SpectralLDA [options] <input>...
   
     -k, --k <value>          number of topics
     --alpha0 <value>         sum of the topic distribution prior parameter
     --min-words <value>      minimum count of words for every document. default: 0
     --idf-lb <value>         only work on terms with IDF above the lower bound. default: 1.0
     --q <value>              number of iterations q for RandSVD of M2. default: 1
     --M2-cond-num-ub <value>
                              stop if the M2 condition number is higher than the given bound. default: 1000.0
     --max-iter <value>       number of iterations of learning. default: 500
     --tol <value>            tolerance for the ALS algorithm. default: 1.0E-6
     --input-type <value>     type of input files: "obj", "libsvm" or "text". "obj" for Hadoop SequenceFile of RDD[(Long, SparseVector[Double])]. default: obj
     -o, --output-dir <dir>   output write path. default: .
     --stopword-file <value>  filepath for a list of stopwords. default: src/main/resources/Data/datasets/StopWords_common.txt
     --help                   prints this usage text
     <input>...               paths of input files   

   Only k, alpha0 and the input file paths are required parameters.

   The higher alpha0 is relative to k the more likely are we to recover only topic-specific words (vs "common" words that would exist in every topic distribution). If alpha0 = k we would allow a non-informative prior for the topic distribution, when every alpha_i = 1.0.

   M2-cond-num-ub checks the condition number (the ratio of the maximum eigenvalue to the minimum one) of the M2 moments matrix and stops if it's above the given bound. It allows to quickly check if there's any predominant topic in the input.

   input-file could be "text", "libsvm", or "obj": "text" for plain text files, "libsvm" for text files in LIBSVM format, "obj" for Hadoop SequenceFiles storing serialised RDD[(Long, SparseVector[Double])]. It is "obj" by default.

3. An example call from command line is

   spark-submit --packages com.github.scopt:scopt_2.11:3.5.0 \
   --class edu.uci.eecs.spectralLDA.SpectralLDA \
   target/scala-2.11/spectrallda-tensor_2.11-1.0.jar \
   -k 5 --alpha0 5.0 --input-type libsvm -o results \
   src/main/resources/Data/datasets/synthetic/samples_train_libsvm.txt

   It runs with alpha0 = k = 5, specifies the input file in LIBSVM format, and outputs results in result/.

API usage

The API is designed following the lines of the Spark built-in LDA class.

import edu.uci.eecs.spectralLDA.algorithm.TensorLDA
import breeze.linalg._

val lda = new TensorLDA(
  dimK = params.k,
  alpha0 = params.topicConcentration,
  maxIterations = value,            // optional, default: 500
  tol = value,                      // optional, default: 1e-6
  idfLowerBound = value,            // optional, default: 1.0
  m2ConditionNumberUB = value,      // optional, default: infinity
  randomisedSVD = true,             // optional, default: true
  numIterationsKrylovMethod = value // optional, default: 1
)

// Fit against the documents
// beta is the V-by-k matrix, where V is the vocabulary size, 
// k is the number of topics. Each column stores the word distribution per topic
// alpha is the length-k Dirichlet prior parameter for the topic distribution

// eigvecM2 is the V-by-k matrix for the top k eigenvectors of M2
// eigvalM2 is the length-k vector for the top k eigenvalues of M2
// m1 is the length-V vector for the average word distribution

val (beta: DenseMatrix[Double], alpha: DenseVector[Double], 
  eigvecM2: DenseMatrix[Double], eigvalM2: DenseVector[Double],
  m1: DenseVector[Double]) = lda.fit(documents)

If one just wants to decompose a 3rd-order symmetric tensor into the sum of rank-1 tensors, we could do

import edu.uci.eecs.spectralLDA.algorithm.ALS
import breeze.linalg._

val als = new ALS(
  dimK = value,
  thirdOrderMoments = value,        // k-by-(k*k) matrix for the unfolded 3rd-order symmetric tensor
  maxIterations = value,            // optional, default: 500
  tol = value,                      // optional, default: 1e-6
)

// We run ALS to find the best approximating sum of rank-1 tensors such that 
// $$ M3 = \sum_{i=1}^k\alpha_i\beta_i^{\otimes 3} $$

// beta is the k-by-k matrix with $\beta_i$ as columns
// alpha is the vector for $(\alpha_1,\ldots,\alpha_k)$
val (beta: DenseMatrix[Double], _, _, alpha: DenseVector[Double]) = als.run

Set up Spark 2.0.0 to use system native BLAS/LAPACK

1. In order for Spark to use system native BLAS/LAPACK, first compile Spark 2.0.0 with the option -Pnetlib-lgpl to include all the artifacts of netlib4java, following the advice here.

   mvn -Pyarn -Phadoop-2.7 -Pnetlib-lgpl -DskipTests clean package

   netlib4java includes the JNI routines to load up the system native BLAS/LAPACK libraries.

2. Now we're going to make the system native BLAS/LAPACK libraries available to netlib4java. On Mac, netlib4java will automatically find veclib; on Linux, we could use ATLAS.

3. Lastly set up symbollic links for the libblas.so.3 and liblapack.so.3 that netlib4java looks for.

   sudo alternatives --install /usr/lib64/libblas.so libblas.so /usr/lib64/atlas/libtatlas.so.3 1000
   sudo alternatives --install /usr/lib64/libblas.so.3 libblas.so.3 /usr/lib64/atlas/libtatlas.so.3 1000
   sudo alternatives --install /usr/lib64/liblapack.so liblapack.so /usr/lib64/atlas/libtatlas.so.3 1000
   sudo alternatives --install /usr/lib64/liblapack.so.3 liblapack.so.3 /usr/lib64/atlas/libtatlas.so.3 1000

Now if we run the above experiments again, any "WARN BLAS" or "WARN LAPACK" messages should have disappeared.

I have millions of small text files...

If we open them simply via sc.wholeTextFiles() the system will spend forever long time querying the file system for the list of all the file names. The solution is to first combine them in Hadoop SequenceFiles of RDD[(String, String)], then process them into word count vectors and vocabulary array.

1. We provided edu.uci.eecs.spectralLDA.textprocessing.CombineSmallTextFiles to squash many text files into a Hadoop SequenceFile. As an example, if all the Wikipedia articles are extracted under wikitext/0 to wikitext/9999, with thousands of text files under each subdirectory, we could batch combining them into a series of SequenceFiles.

   # Under wikitext/, first list all the subdirectory names,
   # then call xargs to feed, say 50 subdirectories each time to CombineSmallTextFiles
   find . -mindepth 1 -maxdepth 1 | xargs -n 50 \
   spark-submit --class edu.uci.eecs.spectralLDA.textprocessing.CombineSmallTextFiles \
   target/scala-2.11/spectrallda-tensor_2.11-1.0.jar

   When the loop finishes, we'd find a number of *.obj Hadoop SequenceFiles under wikitext/.

2. Launch spark-shell with the proper server and memory settings, and the option --jars target/scala-2.11/spectrallda-tensor_2.11-1.0.jar.

   We process the SequenceFiles into word count vectors RDD[(Long, SparseVector[Double])] and dictionary array, and save them.

   import org.apache.spark.rdd.RDD
   import edu.uci.eecs.spectralLDA.textprocessing.TextProcessor
   val (docs, dictionary) = TextProcessor.processDocumentsRDD(
     sc.objectFile[(String, String)]("wikitext/*.obj"),
     stopwordFile = "src/main/resources/Data/datasets/StopWords_common.txt",
     vocabSize = <vocabSize>
   )
   docs.saveAsObjectFile("docs.obj")

   The output file docs.obj contains serialised RDD[(Long, SparseVector[Double])]. When we run SpectralLDA later on, we could specify the input file docs.obj and the file type as obj.

References

• White Paper: http://newport.eecs.uci.edu/anandkumar/pubs/whitepaper.pdf
• New York Times Result Visualization: http://newport.eecs.uci.edu/anandkumar/Lab/Lab_sub/NewYorkTimes3.html

Who do I talk to?

• Repo owner or admin: Furong Huang
• Contact: [email protected]