interesting matrix decomposition idea

[Ted Dunning <te...@gmail.com>]

http://arxiv.org/pdf/1107.0789v6.pdf

The basic idea is to use randomized column sampling to divide the matrix
into parts which are then decomposed using whatever method de jour you
like.  The decompositions of the parts can then be put back together to get
a good estimate of the decomposition of the original matrix.

Combined row and column decomposition can also be used and I think
extension to row sampling (more convenient for us) is relatively trivial.

Re: interesting matrix decomposition idea

[Ted Dunning <te...@gmail.com>]

Given the authorship of the paper, I think your guess is good.


On Sun, Sep 8, 2013 at 10:00 PM, Nick Pentreath <ni...@gmail.com>wrote:

> I suspect this will be coming to Spark Mllib soon :)
>
>     —
> Sent from Mailbox for iPhone
>
> On Mon, Sep 9, 2013 at 1:40 AM, Ted Dunning <te...@gmail.com> wrote:
>
> > http://arxiv.org/pdf/1107.0789v6.pdf
> > The basic idea is to use randomized column sampling to divide the matrix
> > into parts which are then decomposed using whatever method de jour you
> > like.  The decompositions of the parts can then be put back together to
> get
> > a good estimate of the decomposition of the original matrix.
> > Combined row and column decomposition can also be used and I think
> > extension to row sampling (more convenient for us) is relatively trivial.
>

Re: interesting matrix decomposition idea

[Nick Pentreath <ni...@gmail.com>]

I suspect this will be coming to Spark Mllib soon :)

    —
Sent from Mailbox for iPhone

On Mon, Sep 9, 2013 at 1:40 AM, Ted Dunning <te...@gmail.com> wrote:

> http://arxiv.org/pdf/1107.0789v6.pdf
> The basic idea is to use randomized column sampling to divide the matrix
> into parts which are then decomposed using whatever method de jour you
> like.  The decompositions of the parts can then be put back together to get
> a good estimate of the decomposition of the original matrix.
> Combined row and column decomposition can also be used and I think
> extension to row sampling (more convenient for us) is relatively trivial.

Re: interesting matrix decomposition idea

[Andrew Musselman <an...@gmail.com>]

The divide and conquer approach sounds promising; along those lines I have
heard things about non-negative matrix factorization being worth doing
since there are methods to break the matrix into parts and then combine the
result after processing.

http://en.wikipedia.org/wiki/Non-negative_matrix_factorization

http://www.cs.helsinki.fi/u/phoyer/papers/pdf/NMFscweb.pdf


On Sun, Sep 8, 2013 at 8:47 PM, Dmitriy Lyubimov <dl...@gmail.com> wrote:

> i used to really drool over papers like this :)
>
> On Sun, Sep 8, 2013 at 4:39 PM, Ted Dunning <te...@gmail.com> wrote:
> > http://arxiv.org/pdf/1107.0789v6.pdf
> >
> > The basic idea is to use randomized column sampling to divide the matrix
> > into parts which are then decomposed using whatever method de jour you
> > like.  The decompositions of the parts can then be put back together to
> get
> > a good estimate of the decomposition of the original matrix.
> >
> > Combined row and column decomposition can also be used and I think
> > extension to row sampling (more convenient for us) is relatively trivial.
>

Re: interesting matrix decomposition idea

[Dmitriy Lyubimov <dl...@gmail.com>]

i used to really drool over papers like this :)

On Sun, Sep 8, 2013 at 4:39 PM, Ted Dunning <te...@gmail.com> wrote:
> http://arxiv.org/pdf/1107.0789v6.pdf
>
> The basic idea is to use randomized column sampling to divide the matrix
> into parts which are then decomposed using whatever method de jour you
> like.  The decompositions of the parts can then be put back together to get
> a good estimate of the decomposition of the original matrix.
>
> Combined row and column decomposition can also be used and I think
> extension to row sampling (more convenient for us) is relatively trivial.