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## What changes were proposed in this pull request?

Implement Locality Sensitive Hashing along with approximate nearest neighbors and approximate similarity join based on the [design doc](https://docs.google.com/document/d/1D15DTDMF_UWTTyWqXfG7y76iZalky4QmifUYQ6lH5GM/edit).

Detailed changes are as follows:
(1) Implement abstract LSH, LSHModel classes as Estimator-Model
(2) Implement approxNearestNeighbors and approxSimilarityJoin in the abstract LSHModel
(3) Implement Random Projection as LSH subclass for Euclidean distance, Min Hash for Jaccard Distance
(4) Implement unit test utility methods including checkLshProperty, checkNearestNeighbor and checkSimilarityJoin

Things that will be implemented in a follow-up PR:
 - Bit Sampling for Hamming Distance, SignRandomProjection for Cosine Distance
 - PySpark Integration for the scala classes and methods.

## How was this patch tested?
Unit test is implemented for all the implemented classes and algorithms. A scalability test on Uber's dataset was performed internally.

Tested the methods on [WEX dataset](https://aws.amazon.com/items/2345) from AWS, with the steps and results [here](https://docs.google.com/document/d/19BXg-67U83NVB3M0I84HVBVg3baAVaESD_mrg_-vLro/edit).

## References
Gionis, Aristides, Piotr Indyk, and Rajeev Motwani. "Similarity search in high dimensions via hashing." VLDB 7 Sep. 1999: 518-529.
Wang, Jingdong et al. "Hashing for similarity search: A survey." arXiv preprint arXiv:1408.2927 (2014).

Author: Yunni <Euler57721@gmail.com>
Author: Yun Ni <yunn@uber.com>

Closes #15148 from Yunni/SPARK-5992-yunn-lsh.
ac26e9cf
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Apache Spark

Spark is a fast and general cluster computing system for Big Data. It provides high-level APIs in Scala, Java, Python, and R, 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 DataFrames, 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 and project wiki. This README file only contains basic setup instructions.

Building Spark

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

build/mvn -DskipTests clean package

(You do not need to do this if you downloaded a pre-built package.)

You can build Spark using more than one thread by using the -T option with Maven, see "Parallel builds in Maven 3". More detailed documentation is available from the project site, at "Building Spark". For developing Spark using an IDE, see Eclipse and IntelliJ.

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" 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 tests for a module, or individual 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.

Configuration

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

## Contributing

Please review the Contribution to Spark wiki for information on how to get started contributing to the project.