Wouldn't I expect to get similar results using Mahout's SSVD vs. R's SVD?
Note the second component of each vector in U and V is the negative of what
R gives me. Also, R includes a third singular value even when I ask it to
calculate a rank-2 decomposition.
The output of Mahout's SSVD run on the 3x3 matrix
$ cat a
1 (0.0,0.25,0.25)
2 (0.75,0.0,0.25)
3 (0.25,0.75,0.5)
$ mahout ssvd -k 2 -p 1 -q 1 --input kv-pairs --output ssvd-out --tempDir
tmp-ssvd-2 --reduceTasks 1
$ mahout seqdumper -i ssvd-out/U -o ssvd-dump-U -b 200
$ mahout seqdumper -i ssvd-out/V -o ssvd-dump-V -b 200
$ mahout seqdumper -i ssvd-out/sigma -o ssvd-dump-sigma -b 200
$ cat ssvd-dump-U; cat ssvd-dump-V; cat ssvd-dump-sigma
Input Path: hdfs://localhost:9010/user/akm/ssvd-out/U/part-m-00000
Key class: class org.apache.hadoop.io.IntWritable Value Class: class
org.apache.mahout.math.VectorWritable
Key: 1: Value: {0:-0.27511654723856177,1:-0.2590650410646752}
Key: 2: Value: {0:-0.5012740900141649,1:0.8604052567841447}
Key: 3: Value: {0:-0.8203872086496734,1:-0.43884860555363264}
Count: 3
Input Path: hdfs://localhost:9010/user/akm/ssvd-out/V/part-m-00000
Key class: class org.apache.hadoop.io.IntWritable Value Class: class
org.apache.mahout.math.VectorWritable
Key: 0: Value: {0:-0.5370130951532543,1:0.8012749902922572}
Key: 1: Value: {0:-0.6322223639715111,1:-0.5893002821703531}
Key: 2: Value: {0:-0.5584906607349807,1:-0.10336134367394931}
Count: 3
Input Path: ssvd-out/sigma
Key class: class org.apache.hadoop.io.IntWritable Value Class: class
org.apache.mahout.math.VectorWritable
Key: 0: Value: {0:1.0820078223739025,1:0.6684244456504859}
Count: 1
Versus the output of R's SVD run on the same 3x3 matrix
> mp
[,1] [,2] [,3]
[1,] 0.00 0.25 0.25
[2,] 0.75 0.00 0.25
[3,] 0.25 0.75 0.50
> s <- svd(mp,2,2)
> s
$d
[1] 1.08200782 0.66842445 0.08641662
$u
[,1] [,2]
[1,] -0.2751165 0.2590650
[2,] -0.5012741 -0.8604053
[3,] -0.8203872 0.4388486
$v
[,1] [,2]
[1,] -0.5370131 -0.8012750
[2,] -0.6322224 0.5893003
[3,] -0.5584907 0.1033613
