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@@ -210,3 +210,56 @@ at each iteration.
Available algorithms for gradient descent:
* [GradientDescent](api/mllib/index.html#org.apache.spark.mllib.optimization.GradientDescent)
+
+
+
+# Singular Value Decomposition
+Singular Value Decomposition for Tall and Skinny matrices.
+Given an *m x n* matrix *A*, we can compute matrices *U, S, V* such that
+
+*A = U * S * V^T*
+
+There is no restriction on m, but we require n^2 doubles to fit in memory.
+Further, n should be less than m.
+
+The decomposition is computed by first computing *A^TA = V S^2 V^T*,
+computing svd locally on that (since n x n is small),
+from which we recover S and V.
+Then we compute U via easy matrix multiplication
+as *U = A * V * S^-1*
+
+Only singular vectors associated with singular values
+greater or equal to MIN_SVALUE are recovered. If there are k
+such values, then the dimensions of the return will be:
+
+* *S* is *k x k* and diagonal, holding the singular values on diagonal.
+* *U* is *m x k* and satisfies U^T*U = eye(k).
+* *V* is *n x k* and satisfies V^TV = eye(k).
+
+All input and output is expected in sparse matrix format, 1-indexed
+as tuples of the form ((i,j),value) all in RDDs. Below is example usage.
+
+{% highlight scala %}
+
+import org.apache.spark.SparkContext
+import org.apache.spark.mllib.linalg.SVD
+
+// Load and parse the data file
+val data = sc.textFile("mllib/data/als/test.data").map { line =>
+ val parts = line.split(',')
+ ((parts(0).toInt, parts(1).toInt), parts(2).toDouble)
+}
+val m = 4
+val n = 4
+
+// recover singular vectors for singular values at or above 1e-5
+val (u, s, v) = SVD.sparseSVD(data, m, n, 1e-5)
+
+println("singular values = " + s.toArray.mkString)
+
+{% endhighlight %}
+
+
+
+
+