Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/1778#discussion_r17579676
--- 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 brute-force
+ * approach of computing normalized dot products.
+ *
+ * @return An n x n sparse upper-triangular 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 trade-off 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 brute-force approach. Setting the threshold to
positive values
+ * incurs strictly less computational cost than the brute-force
approach, however the
+ * similarities computed will be estimates.
+ *
+ * The sampling guarantees relative-error 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 non-zero element of this matrix.
+ * Let B be the largest in magnitude non-zero element of this matrix.
+ * Let L be the number of non-zeros 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 brute-force approach, so for non-zero
thresholds,
+ * the cost is always cheaper than the brute-force approach.
+ *
+ * @param threshold Similarities above this threshold are probably
computed correctly.
+ * Set to 0 for deterministic guaranteed correctness.
+ * @return An n x n sparse upper-triangular matrix of cosine similarities
+ * between columns of this matrix.
+ */
+ def similarColumns(threshold: Double): CoordinateMatrix = {
+ require(threshold >= 0 && threshold <= 1, s"Threshold not in [0,1]:
$threshold")
+
+ val gamma = if (math.abs(threshold) < 1e-6) {
+ Double.PositiveInfinity
+ } else {
+ 100 * math.log(numCols()) / threshold
+ }
+
+ similarColumnsDIMSUM(computeColumnSummaryStatistics().normL2.toArray,
gamma)
+ }
+
+ /**
+ * Find all similar columns using the DIMSUM sampling algorithm,
described in two papers
+ *
+ * http://arxiv.org/abs/1206.2082
+ * http://arxiv.org/abs/1304.1467
+ *
+ * @param colMags A vector of column magnitudes
+ * @param gamma The oversampling parameter. For provable results, set to
100 * log(n) / s,
+ * where s is the smallest similarity score to be estimated,
+ * and n is the number of columns
+ * @return An n x n sparse upper-triangular matrix of cosine similarities
+ * between columns of this matrix.
+ */
+ private[mllib] def similarColumnsDIMSUM(colMags: Array[Double],
+ gamma: Double): CoordinateMatrix
= {
--- End diff --
4-space indentation
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