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References: <13685.1265255859@buffalo.edu>
Date: Thu, 4 Feb 2010 02:56:08 -0800 (PST)
From: Tran Son <sondt1@yahoo.com>
Subject: Re: Re: Inverse of a matrix using Map - Reduce
To: common-user@hadoop.apache.org, aa225@buffalo.edu,
  Ganesh Swami <ganesh@iamganesh.com>
In-Reply-To: <13685.1265255859@buffalo.edu>
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Hi,=0AAs far as i know, inversion of matrix need a lot of loops which are n=
ot supported well in Hadoop MapRed. Hadoop MapRed is working well with bloc=
k algorithms, especially for simple operations such are addition, transposi=
tion and possibly multiplication. However, with inversion, there is no (as =
I search up to now) algorithms support blocking, i mean working in each sma=
ll parts of matrix and combine to final result. There are several algorithm=
s such as Gaussian (as you said) or Csanky, but i think you will need more =
conplex implementation with ChainMapper/ChainReducer and/or using multiple =
contrained job.=0AHowever, I think it does not effective much and convenien=
t. So I am developing another version of Map Reduce which support staging o=
f Reducer: 1 job =3D Mapper Reducer*. I test it with Csanky algorithm and i=
t work quite well but I'm still on the way to improve the scheduling mechan=
ism.=0A=0A=0A=0A=0A=0A________________________________=0AFrom: "aa225@buffa=
lo.edu" <aa225@buffalo.edu>=0ATo: common-user@hadoop.apache.org; aa225@buff=
alo.edu; Ganesh Swami <ganesh@iamganesh.com>=0ASent: Thursday, February 4, =
2010 3:57:39=0ASubject: Re: Re: Inverse of a matrix using Map - Reduce=0A=
=0AHi,=0A   Any idea how this method will scale for dense matrices ?The kin=
d of matrices I=0Aam going to be working with are 500,000*500,000. Will thi=
s be a problem. Also=0Ahave you used this patch ?=0A=0ABest Regards from Bu=
ffalo=0A=0AAbhishek Agrawal=0A=0ASUNY- Buffalo=0A(716-435-7122)=0A=0AOn Wed=
 02/03/10  1:41 AM , Ganesh Swami ganesh@iamganesh.com sent:=0A> What about=
 the Moore-Penrose inverse?=0A> =0A> http://en.wikipedia.org/wiki/Moore-Pen=
rose_pseudoinverse=0A> =0A> The pseudo-inverse coincides with the regular i=
nverse when the matrix=0A> is non-singular. Moreover, it can be computed us=
ing the SVD.=0A> =0A> Here's a patch for a MapReduce version of the SVD:=0A=
> https://issues.apache.org/jira/browse/MAHOUT-180=0A> Ganesh=0A> =0A> On T=
ue, Feb 2, 2010 at 10:11 PM,  <aa225@buffa=0A> lo.edu> wrote:> Hello People=
,=0A> > =C2  =C2  =C2 =0A> =C2  =C2  =C2 My name is Abhishek Agrawal. For=
=0A> the last few days I have been trying> to figure out how to calculate t=
he=0Ainverse of a=0A> matrix using Map Reduce. Matrix> inversion has 2 comm=
on approaches. Gaussian-=0A> Jordan and the cofactor of transpose> method. =
But both of them dont seem to be=0Asuited=0A> too well for Map- Reduce.> Ga=
ussian Jordan involves blocking co factoring a=0A> matrix requires repeated=
> calculation of determinant.=0A> >=0A> > Can some one give me any pointers=
 so as to how=0A> to solve this problem ?>=0A> > Best Regards from Buffalo=
=0A> >=0A> > Abhishek Agrawal=0A> >=0A> > SUNY- Buffalo=0A> > (716-435-7122=
)=0A> >=0A> >=0A> >=0A> >=0A> =0A> =0A> =0A> =0A> =0A=0A=0A      New Email =
names for you! =0AGet the Email name you&#39;ve always wanted on the new @y=
mail and @rocketmail. =0AHurry before someone else does!=0Ahttp://mail.prom=
otions.yahoo.com/newdomains/aa/
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