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Posted to commits@spark.apache.org by me...@apache.org on 2015/02/06 19:26:54 UTC
spark git commit: [SPARK-5013] [MLlib] Added documentation and sample
data file for GaussianMixture
Repository: spark
Updated Branches:
refs/heads/master 37d35ab53 -> 9ad56ad2a
[SPARK-5013] [MLlib] Added documentation and sample data file for GaussianMixture
Simple description and code samples (and sample data) for GaussianMixture
Author: Travis Galoppo <tj...@columbia.edu>
Closes #4401 from tgaloppo/spark-5013 and squashes the following commits:
c9ff9a5 [Travis Galoppo] Fixed link in mllib-clustering.md Added Gaussian mixture and power iteration as available clustering techniques in mllib-guide
2368690 [Travis Galoppo] Minor fixes
3eb41fa [Travis Galoppo] [SPARK-5013] Added documentation and sample data file for GaussianMixture
Project: http://git-wip-us.apache.org/repos/asf/spark/repo
Commit: http://git-wip-us.apache.org/repos/asf/spark/commit/9ad56ad2
Tree: http://git-wip-us.apache.org/repos/asf/spark/tree/9ad56ad2
Diff: http://git-wip-us.apache.org/repos/asf/spark/diff/9ad56ad2
Branch: refs/heads/master
Commit: 9ad56ad2a2a51df449040c4f4b7c66b104883312
Parents: 37d35ab
Author: Travis Galoppo <tj...@columbia.edu>
Authored: Fri Feb 6 10:26:51 2015 -0800
Committer: Xiangrui Meng <me...@databricks.com>
Committed: Fri Feb 6 10:26:51 2015 -0800
----------------------------------------------------------------------
data/mllib/gmm_data.txt | 2000 +++++++++++++++++++++++++++++++++++++++++
docs/mllib-clustering.md | 131 ++-
docs/mllib-guide.md | 2 +
3 files changed, 2130 insertions(+), 3 deletions(-)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/spark/blob/9ad56ad2/data/mllib/gmm_data.txt
----------------------------------------------------------------------
diff --git a/data/mllib/gmm_data.txt b/data/mllib/gmm_data.txt
new file mode 100644
index 0000000..934ee4a
--- /dev/null
+++ b/data/mllib/gmm_data.txt
@@ -0,0 +1,2000 @@
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+ 3.62633110e-01 -7.46965304e-01
+ -2.44042594e+00 8.52761797e-01
+ 3.32412550e+00 -1.28439899e+00
+ 4.74860766e+00 -1.72821964e+00
+ 1.29072541e+00 -8.24872902e-01
+ -1.69450702e+00 4.09600876e-01
+ 1.29705411e+00 1.22300809e-01
+ -2.63597613e+00 8.55612913e-01
+ 9.28467301e-01 -2.63550114e-02
+ 2.44670264e+00 -4.10123002e-01
+ 1.06408206e+00 -5.03361942e-01
+ 5.12384049e-02 -1.27116595e-02
+ -1.06731272e+00 -1.76205029e-01
+ -9.45454582e-01 3.74404917e-01
+ 2.54343689e+00 -7.13810545e-01
+ -2.54460335e+00 1.31590265e+00
+ 1.89864233e+00 -3.98436339e-01
+ -1.93990133e+00 6.01474630e-01
+ -1.35938824e+00 4.00751788e-01
+ 2.38567018e+00 -6.13904880e-01
+ 2.18748050e-01 2.62631712e-01
+ -2.01388788e+00 1.41474031e+00
+ 2.74014581e+00 -1.27448105e+00
+ -2.13828583e+00 1.13616144e+00
+ 5.98730932e+00 -2.53430080e+00
+ -1.72872795e+00 1.53702057e+00
+ -2.53263962e+00 1.27342410e+00
+ 1.34326968e+00 -1.99395088e-01
+ 3.83352666e-01 -1.25683065e-01
+ -2.35630657e+00 5.54116983e-01
+ -1.94900838e+00 5.76270178e-01
+ -1.36699108e+00 -3.40904824e-01
+ -2.34727346e+00 -1.93054940e-02
+ -3.82779777e+00 1.83025664e+00
+ -4.31602080e+00 9.21605705e-01
+ 5.54098133e-01 2.33991419e-01
+ -4.53591188e+00 1.99833353e+00
+ -3.92715909e+00 1.83231482e+00
+ 3.91344440e-01 -1.11355111e-01
+ 3.48576363e+00 -1.41379449e+00
+ -1.42858690e+00 3.84532286e-01
+ 1.79519859e+00 -9.23486448e-01
+ 8.49691242e-01 -1.76551084e-01
+ 1.53618138e+00 8.23835015e-02
+ 5.91476520e-02 3.88296940e-02
+ 1.44837346e+00 -7.24097604e-01
+ -6.79008418e-01 4.04078097e-01
+ 2.87555510e+00 -9.51825076e-01
+ -1.12379101e+00 2.93457714e-01
+ 1.45263980e+00 -6.01960544e-01
+ -2.55741621e-01 9.26233518e-01
+ 3.54570714e+00 -1.41521877e+00
+ -1.61542388e+00 6.57844512e-01
+ -3.22844269e-01 3.02823546e-01
+ 1.03523913e+00 -6.92730711e-01
+ 1.11084909e+00 -3.50823642e-01
+ 3.41268693e+00 -1.90865862e+00
+ 7.67062858e-01 -9.48792160e-01
+ -5.49798016e+00 1.71139960e+00
+ 1.14865798e+00 -6.12669150e-01
+ -2.18256680e+00 7.78634462e-01
+ 4.78857389e+00 -2.55555085e+00
+ -1.85555569e+00 8.04311615e-01
+ -4.22278799e+00 2.01162524e+00
+ -1.56556149e+00 1.54353907e+00
+ -3.11527864e+00 1.65973526e+00
+ 2.66342611e+00 -1.20449402e+00
+ 1.57635314e+00 -1.48716308e-01
+ -6.35606865e-01 2.59701180e-01
+ 1.02431976e+00 -6.76929904e-01
+ 1.12973772e+00 1.49473892e-02
+ -9.12758116e-01 2.21533933e-01
+ -2.98014470e+00 1.71651189e+00
+ 2.74016965e+00 -9.47893923e-01
+ -3.47830591e+00 1.34941430e+00
+ 1.74757562e+00 -3.72503752e-01
+ 5.55820383e-01 -6.47992466e-01
+ -1.19871928e+00 9.82429151e-01
+ -2.53040133e+00 2.10671307e+00
+ -1.94085605e+00 1.38938137e+00
http://git-wip-us.apache.org/repos/asf/spark/blob/9ad56ad2/docs/mllib-clustering.md
----------------------------------------------------------------------
diff --git a/docs/mllib-clustering.md b/docs/mllib-clustering.md
index 413b824..1e9ef34 100644
--- a/docs/mllib-clustering.md
+++ b/docs/mllib-clustering.md
@@ -16,9 +16,12 @@ often used for exploratory analysis and/or as a component of a hierarchical
supervised learning pipeline (in which distinct classifiers or regression
models are trained for each cluster).
-MLlib supports
-[k-means](http://en.wikipedia.org/wiki/K-means_clustering) clustering, one of
-the most commonly used clustering algorithms that clusters the data points into
+MLlib supports the following models:
+
+### k-means
+
+[k-means](http://en.wikipedia.org/wiki/K-means_clustering) is one of the
+most commonly used clustering algorithms that clusters the data points into a
predefined number of clusters. The MLlib implementation includes a parallelized
variant of the [k-means++](http://en.wikipedia.org/wiki/K-means%2B%2B) method
called [kmeans||](http://theory.stanford.edu/~sergei/papers/vldb12-kmpar.pdf).
@@ -34,6 +37,20 @@ a given dataset, the algorithm returns the best clustering result).
* *initializationSteps* determines the number of steps in the k-means\|\| algorithm.
* *epsilon* determines the distance threshold within which we consider k-means to have converged.
+### Gaussian mixture
+
+A [Gaussian Mixture Model](http://en.wikipedia.org/wiki/Mixture_model#Multivariate_Gaussian_mixture_model)
+represents a composite distribution whereby points are drawn from one of *k* Gaussian sub-distributions,
+each with its own probability. The MLlib implementation uses the
+[expectation-maximization](http://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm)
+ algorithm to induce the maximum-likelihood model given a set of samples. The implementation
+has the following parameters:
+
+* *k* is the number of desired clusters.
+* *convergenceTol* is the maximum change in log-likelihood at which we consider convergence achieved.
+* *maxIterations* is the maximum number of iterations to perform without reaching convergence.
+* *initialModel* is an optional starting point from which to start the EM algorithm. If this parameter is omitted, a random starting point will be constructed from the data.
+
### Power Iteration Clustering
Power iteration clustering is a scalable and efficient algorithm for clustering points given pointwise mutual affinity values. Internally the algorithm:
@@ -56,6 +73,8 @@ Example outputs for a dataset inspired by the paper - but with five clusters ins
### Examples
+#### k-means
+
<div class="codetabs">
<div data-lang="scala" markdown="1">
The following code snippets can be executed in `spark-shell`.
@@ -168,6 +187,112 @@ print("Within Set Sum of Squared Error = " + str(WSSSE))
</div>
+#### GaussianMixture
+
+<div class="codetabs">
+<div data-lang="scala" markdown="1">
+In the following example after loading and parsing data, we use a
+[GaussianMixture](api/scala/index.html#org.apache.spark.mllib.clustering.GaussianMixture)
+object to cluster the data into two clusters. The number of desired clusters is passed
+to the algorithm. We then output the parameters of the mixture model.
+
+{% highlight scala %}
+import org.apache.spark.mllib.clustering.GaussianMixture
+import org.apache.spark.mllib.linalg.Vectors
+
+// Load and parse the data
+val data = sc.textFile("data/mllib/gmm_data.txt")
+val parsedData = data.map(s => Vectors.dense(s.trim.split(' ').map(_.toDouble))).cache()
+
+// Cluster the data into two classes using GaussianMixture
+val gmm = new GaussianMixture().setK(2).run(parsedData)
+
+// output parameters of max-likelihood model
+for (i <- 0 until gmm.k) {
+ println("weight=%f\nmu=%s\nsigma=\n%s\n" format
+ (gmm.weights(i), gmm.gaussians(i).mu, gmm.gaussians(i).sigma))
+}
+
+{% endhighlight %}
+</div>
+
+<div data-lang="java" markdown="1">
+All of MLlib's methods use Java-friendly types, so you can import and call them there the same
+way you do in Scala. The only caveat is that the methods take Scala RDD objects, while the
+Spark Java API uses a separate `JavaRDD` class. You can convert a Java RDD to a Scala one by
+calling `.rdd()` on your `JavaRDD` object. A self-contained application example
+that is equivalent to the provided example in Scala is given below:
+
+{% highlight java %}
+import org.apache.spark.api.java.*;
+import org.apache.spark.api.java.function.Function;
+import org.apache.spark.mllib.clustering.GaussianMixture;
+import org.apache.spark.mllib.clustering.GaussianMixtureModel;
+import org.apache.spark.mllib.linalg.Vector;
+import org.apache.spark.mllib.linalg.Vectors;
+import org.apache.spark.SparkConf;
+
+public class GaussianMixtureExample {
+ public static void main(String[] args) {
+ SparkConf conf = new SparkConf().setAppName("GaussianMixture Example");
+ JavaSparkContext sc = new JavaSparkContext(conf);
+
+ // Load and parse data
+ String path = "data/mllib/gmm_data.txt";
+ JavaRDD<String> data = sc.textFile(path);
+ JavaRDD<Vector> parsedData = data.map(
+ new Function<String, Vector>() {
+ public Vector call(String s) {
+ String[] sarray = s.trim().split(" ");
+ double[] values = new double[sarray.length];
+ for (int i = 0; i < sarray.length; i++)
+ values[i] = Double.parseDouble(sarray[i]);
+ return Vectors.dense(values);
+ }
+ }
+ );
+ parsedData.cache();
+
+ // Cluster the data into two classes using GaussianMixture
+ GaussianMixtureModel gmm = new GaussianMixture().setK(2).run(parsedData.rdd());
+
+ // Output the parameters of the mixture model
+ for(int j=0; j<gmm.k(); j++) {
+ System.out.println("weight=%f\nmu=%s\nsigma=\n%s\n",
+ gmm.weights()[j], gmm.gaussians()[j].mu(), gmm.gaussians()[j].sigma());
+ }
+ }
+}
+{% endhighlight %}
+</div>
+
+<div data-lang="python" markdown="1">
+In the following example after loading and parsing data, we use a
+[GaussianMixture](api/python/pyspark.mllib.html#pyspark.mllib.clustering.GaussianMixture)
+object to cluster the data into two clusters. The number of desired clusters is passed
+to the algorithm. We then output the parameters of the mixture model.
+
+{% highlight python %}
+from pyspark.mllib.clustering import GaussianMixture
+from numpy import array
+
+# Load and parse the data
+data = sc.textFile("data/mllib/gmm_data.txt")
+parsedData = data.map(lambda line: array([float(x) for x in line.strip().split(' ')]))
+
+# Build the model (cluster the data)
+gmm = GaussianMixture.train(parsedData, 2)
+
+# output parameters of model
+for i in range(2):
+ print ("weight = ", gmm.weights[i], "mu = ", gmm.gaussians[i].mu,
+ "sigma = ", gmm.gaussians[i].sigma.toArray())
+
+{% endhighlight %}
+</div>
+
+</div>
+
In order to run the above application, follow the instructions
provided in the [Self-Contained Applications](quick-start.html#self-contained-applications)
section of the Spark
http://git-wip-us.apache.org/repos/asf/spark/blob/9ad56ad2/docs/mllib-guide.md
----------------------------------------------------------------------
diff --git a/docs/mllib-guide.md b/docs/mllib-guide.md
index 73728bb..7779fbc 100644
--- a/docs/mllib-guide.md
+++ b/docs/mllib-guide.md
@@ -25,6 +25,8 @@ filtering, dimensionality reduction, as well as underlying optimization primitiv
* alternating least squares (ALS)
* [Clustering](mllib-clustering.html)
* k-means
+ * Gaussian mixture
+ * power iteration
* [Dimensionality reduction](mllib-dimensionality-reduction.html)
* singular value decomposition (SVD)
* principal component analysis (PCA)
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