Space: Apache Mahout (https://cwiki.apache.org/confluence/display/MAHOUT)
Page: Stochastic Singular Value Decomposition
(https://cwiki.apache.org/confluence/display/MAHOUT/Stochastic+Singular+Value+Decomposition)
Edited by Dmitriy Lyubimov:
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Stochastic SVD method in Mahout produces reduced rank Singular Value
Decomposition output in its strict mathematical definition: A=USV'.
h5. The benefits over other methods are:
* reduced flops required compared to Krylov subspace methods
* In map-reduce world, a fixed number of MR iterations required regardless of
rank requested
* Tweak precision/speed balance with options.
* A is a Distributed Row Matrix where rows may be identified by any Writable
(such as a document path). As such, it would work directly on the output of
seq2sparse.
* Now includes PCA and dimensionality reduction workflow.
map-reduce characteristics:
SSVD uses at most 3 MR _sequential_ steps (map-only + map-reduce + 2 optional
parallel map-reduce jobs) to produce reduced rank approximation of U, V and S
matrices. Additionally, two more map-reduce steps are added for each power
iteration step if requested.
h5. Potential drawbacks:
* potentially less precise (but adding even one power iteration seems to fix
that quite a bit).
h5. Documentation
[Overview and Usage|^SSVD-CLI.pdf]
Note: Please use 0.6 or later! for PCA workflow, please use 0.7 or later.
h5. R simulation
[SSVD implementation flow in R with power iterations and PCA options|^ssvd.R].
Note that this implementation is not most optimal for sequential flow solver,
but it is for demonstration purposes only.
However, try this R code to simulate a meaningful input:
{code:title=tests.R}
n<-1000
m<-2000
k<-10
qi<-1
#simulated input
svalsim<-diag(k:1)
usim<- qr.Q(qr(matrix(rnorm(m*k, mean=3), nrow=m,ncol=k)))
vsim<- qr.Q(qr( matrix(rnorm(n*k,mean=5), nrow=n,ncol=k)))
x<- usim %*% svalsim %*% t(vsim)
{code}
and try to compare ssvd.svd\(x\) and stock svd\(x\) performance for the same
rank k, notice the difference in the running time. Also play with power
iterations (qIter) and compare accuracies of standard svd and SSVD.
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