Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/1778#discussion_r17579669
 Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/RowMatrix.scala

@@ 390,6 +393,113 @@ class RowMatrix(
new RowMatrix(AB, nRows, B.numCols)
}
+ /**
+ * Compute all cosine similarities between columns of this matrix using the bruteforce
+ * approach of computing normalized dot products.
+ *
+ * @return An n x n sparse uppertriangular matrix of cosine similarities between
+ * columns of this matrix.
+ */
+ def columnSimilarities(): CoordinateMatrix = {
+ similarColumns(0.0)
+ }
+
+ /**
+ * Compute all similarities between columns of this matrix using a sampling approach.
+ *
+ * The threshold parameter is a tradeoff knob between estimate quality and computational
cost.
+ *
+ * Setting a threshold of 0 guarantees deterministic correct results, but comes at
exactly
+ * the same cost as the bruteforce approach. Setting the threshold to positive values
+ * incurs strictly less computational cost than the bruteforce approach, however the
+ * similarities computed will be estimates.
+ *
+ * The sampling guarantees relativeerror correctness for those pairs of columns that
have
+ * similarity greater than the given similarity threshold.
+ *
+ * To describe the guarantee, we set some notation:
+ * Let A be the smallest in magnitude nonzero element of this matrix.
+ * Let B be the largest in magnitude nonzero element of this matrix.
+ * Let L be the number of nonzeros per row.
+ *
+ * For example, for {0,1} matrices: A=B=1.
+ * Another example, for the Netflix matrix: A=1, B=5
+ *
+ * For those column pairs that are above the threshold,
+ * the computed similarity is correct to within 20% relative error with probability
+ * at least 1  (0.981)^(100/B)
+ *
+ * The shuffle size is bounded by the *smaller* of the following two expressions:
+ *
+ * O(n log(n) L / (threshold * A))
+ * O(m L^2)
+ *
+ * The latter is the cost of the bruteforce approach, so for nonzero thresholds,
+ * the cost is always cheaper than the bruteforce approach.
+ *
+ * @param threshold Similarities above this threshold are probably computed correctly.
 End diff 
Elaborate more on `probably computed correctly`?

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