In the Mahout Spark R-like DSL [A’A] and [AA’] doesn’t actually do a transpose—it’s optimized out. Mahout has had a stand alone row matrix transpose since day 1 and supports it in the Spark version. Can’t really do matrix algebra without it even though it’s often possible to optimize it away. 

Row similarity with LLR is much simpler than cosine since you only need non-zero sums for column, row, and matrix elements so rowSimilarity is implemented in Mahout for Spark. Full blown row similarity including all the different similarity methods (long since implemented in hadoop mapreduce) hasn’t been moved to spark yet.

Yep, rows are not covered in the blog, my mistake. Too bad it has a lot of uses and can at very least be optimized for output matrix symmetry.

On Jan 17, 2015, at 11:44 AM, Andrew Musselman <> wrote:

Yeah okay, thanks.

On Jan 17, 2015, at 11:15 AM, Reza Zadeh <> wrote:

Pat, columnSimilarities is what that blog post is about, and is already part of Spark 1.2.

rowSimilarities in a RowMatrix is a little more tricky because you can't transpose a RowMatrix easily, and is being tracked by this JIRA:

Andrew, sometimes (not always) it's OK to transpose a RowMatrix, if for example the number of rows in your RowMatrix is less than 1m, you can transpose it and use rowSimilarities.

On Sat, Jan 17, 2015 at 10:45 AM, Pat Ferrel <> wrote:
BTW it looks like row and column similarities (cosine based) are coming to MLlib through DIMSUM. Andrew said rowSimilarity doesn’t seem to be in the master yet. Does anyone know the status?

Also the method for computation reduction (make it less than O(n^2)) seems rooted in cosine. A different computation reduction method is used in the Mahout code tied to LLR. Seems like we should get these together.
On Jan 17, 2015, at 9:37 AM, Andrew Musselman <> wrote:

Excellent, thanks Pat.

On Jan 17, 2015, at 9:27 AM, Pat Ferrel <> wrote:

Mahout’s Spark implementation of rowsimilarity is in the Scala SimilarityAnalysis class. It actually does either row or column similarity but only supports LLR at present. It does [AA’] for columns or [A’A] for rows first then calculates the distance (LLR) for non-zero elements. This is a major optimization for sparse matrices. As I recall the old hadoop code only did this for half the matrix since it’s symmetric but that optimization isn’t in the current code because the downsampling is done as LLR is calculated, so the entire similarity matrix is never actually calculated unless you disable downsampling. 

The primary use is for recommenders but I’ve used it (in the test suite) for row-wise text token similarity too.  

On Jan 17, 2015, at 9:00 AM, Andrew Musselman <> wrote:

Yeah that's the kind of thing I'm looking for; was looking at SPARK-4259 and poking around to see how to do things.

On Jan 17, 2015, at 8:35 AM, Suneel Marthi <> wrote:

Andrew, u would be better off using Mahout's RowSimilarityJob for what u r trying to accomplish.

 1.  It does give u pair-wise distances
 2.  U can specify the Distance measure u r looking to use
 3.  There's the old MapReduce impl and the Spark DSL impl per ur preference.

From: Andrew Musselman <>
To: Reza Zadeh <>
Cc: user <>
Sent: Saturday, January 17, 2015 11:29 AM
Subject: Re: Row similarities

Thanks Reza, interesting approach.  I think what I actually want is to calculate pair-wise distance, on second thought.  Is there a pattern for that?

On Jan 16, 2015, at 9:53 PM, Reza Zadeh <> wrote:

You can use K-means with a suitably large k. Each cluster should correspond to rows that are similar to one another.

On Fri, Jan 16, 2015 at 5:18 PM, Andrew Musselman <> wrote:
What's a good way to calculate similarities between all vector-rows in a matrix or RDD[Vector]?

I'm seeing RowMatrix has a columnSimilarities method but I'm not sure I'm going down a good path to transpose a matrix in order to run that.