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Reza Zadeh authored
# All-pairs similarity via DIMSUM
Compute all pairs of similar vectors using brute force approach, and also DIMSUM sampling approach.

Laying down some notation: we are looking for all pairs of similar columns in an m x n RowMatrix whose entries are denoted a_ij, with the i’th row denoted r_i and the j’th column denoted c_j. There is an oversampling parameter labeled ɣ that should be set to 4 log(n)/s to get provably correct results (with high probability), where s is the similarity threshold.

The algorithm is stated with a Map and Reduce, with proofs of correctness and efficiency in published papers [1] [2]. The reducer is simply the summation reducer. The mapper is more interesting, and is also the heart of the scheme. As an exercise, you should try to see why in expectation, the map-reduce below outputs cosine similarities.

![dimsumv2](https://cloud.githubusercontent.com/assets/3220351/3807272/d1d9514e-1c62-11e4-9f12-3cfdb1d78b3a.png)

[1] Bosagh-Zadeh, Reza and Carlsson, Gunnar (2013), Dimension Independent Matrix Square using MapReduce, arXiv:1304.1467 http://arxiv.org/abs/1304.1467

[2] Bosagh-Zadeh, Reza and Goel, Ashish (2012), Dimension Independent Similarity Computation, arXiv:1206.2082 http://arxiv.org/abs/1206.2082

# Testing

Tests for all invocations included.

Added L1 and L2 norm computation to MultivariateStatisticalSummary since it was needed. Added tests for both of them.

Author: Reza Zadeh <rizlar@gmail.com>
Author: Xiangrui Meng <meng@databricks.com>

Closes #1778 from rezazadeh/dimsumv2 and squashes the following commits:

404c64c [Reza Zadeh] Merge remote-tracking branch 'upstream/master' into dimsumv2
4eb71c6 [Reza Zadeh] Add excludes for normL1 and normL2
ee8bd65 [Reza Zadeh] Merge remote-tracking branch 'upstream/master' into dimsumv2
976ddd4 [Reza Zadeh] Broadcast colMags. Avoid div by zero.
3467cff [Reza Zadeh] Merge remote-tracking branch 'upstream/master' into dimsumv2
aea0247 [Reza Zadeh] Allow large thresholds to promote sparsity
9fe17c0 [Xiangrui Meng] organize imports
2196ba5 [Xiangrui Meng] Merge branch 'rezazadeh-dimsumv2' into dimsumv2
254ca08 [Reza Zadeh] Merge remote-tracking branch 'upstream/master' into dimsumv2
f2947e4 [Xiangrui Meng] some optimization
3c4cf41 [Xiangrui Meng] Merge branch 'master' into rezazadeh-dimsumv2
0e4eda4 [Reza Zadeh] Use partition index for RNG
251bb9c [Reza Zadeh] Documentation
25e9d0d [Reza Zadeh] Line length for style
fb296f6 [Reza Zadeh] renamed to normL1 and normL2
3764983 [Reza Zadeh] Documentation
e9c6791 [Reza Zadeh] New interface and documentation
613f261 [Reza Zadeh] Column magnitude summary
75a0b51 [Reza Zadeh] Use Ints instead of Longs in the shuffle
0f12ade [Reza Zadeh] Style changes
eb1dc20 [Reza Zadeh] Use Double.PositiveInfinity instead of Double.Max
f56a882 [Reza Zadeh] Remove changes to MultivariateOnlineSummarizer
dbc55ba [Reza Zadeh] Make colMagnitudes a method in RowMatrix
41e8ece [Reza Zadeh] style changes
139c8e1 [Reza Zadeh] Syntax changes
029aa9c [Reza Zadeh] javadoc and new test
75edb25 [Reza Zadeh] All tests passing!
05e59b8 [Reza Zadeh] Add test
502ce52 [Reza Zadeh] new interface
654c4fb [Reza Zadeh] default methods
3726ca9 [Reza Zadeh] Remove MatrixAlgebra
6bebabb [Reza Zadeh] remove changes to MatrixSuite
5b8cd7d [Reza Zadeh] Initial files
587a0cd7
History

Apache Spark

Spark is a fast and general cluster computing system for Big Data. It provides high-level APIs in Scala, Java, and Python, and an optimized engine that supports general computation graphs for data analysis. It also supports a rich set of higher-level tools including Spark SQL for SQL and structured data processing, MLlib for machine learning, GraphX for graph processing, and Spark Streaming for stream processing.

http://spark.apache.org/

Online Documentation

You can find the latest Spark documentation, including a programming guide, on the project web page. This README file only contains basic setup instructions.

Building Spark

Spark is built using Apache Maven. To build Spark and its example programs, run:

mvn -DskipTests clean package

(You do not need to do this if you downloaded a pre-built package.) More detailed documentation is available from the project site, at "Building Spark".

Interactive Scala Shell

The easiest way to start using Spark is through the Scala shell:

./bin/spark-shell

Try the following command, which should return 1000:

scala> sc.parallelize(1 to 1000).count()

Interactive Python Shell

Alternatively, if you prefer Python, you can use the Python shell:

./bin/pyspark

And run the following command, which should also return 1000:

>>> sc.parallelize(range(1000)).count()

Example Programs

Spark also comes with several sample programs in the examples directory. To run one of them, use ./bin/run-example <class> [params]. For example:

./bin/run-example SparkPi

will run the Pi example locally.

You can set the MASTER environment variable when running examples to submit examples to a cluster. This can be a mesos:// or spark:// URL, "yarn-cluster" or "yarn-client" to run on YARN, and "local" to run locally with one thread, or "local[N]" to run locally with N threads. You can also use an abbreviated class name if the class is in the examples package. For instance:

MASTER=spark://host:7077 ./bin/run-example SparkPi

Many of the example programs print usage help if no params are given.

Running Tests

Testing first requires building Spark. Once Spark is built, tests can be run using:

./dev/run-tests

Please see the guidance on how to run all automated tests.

A Note About Hadoop Versions

Spark uses the Hadoop core library to talk to HDFS and other Hadoop-supported storage systems. Because the protocols have changed in different versions of Hadoop, you must build Spark against the same version that your cluster runs.

Please refer to the build documentation at "Specifying the Hadoop Version" for detailed guidance on building for a particular distribution of Hadoop, including building for particular Hive and Hive Thriftserver distributions. See also "Third Party Hadoop Distributions" for guidance on building a Spark application that works with a particular distribution.

Configuration

Please refer to the Configuration guide in the online documentation for an overview on how to configure Spark.