this is interesting. but the whole idea in this case is to solve a
linear system using least squares. The standard solution involves
calculating the inverse of the matrix. what would you suggest in this
case? we can replace the inverse of the matrix by substituting it with
some form of decomposition?
On Mon, Jun 27, 2011 at 3:57 PM, Ted Dunning <ted.dunning@gmail.com> wrote:
> Formulae that involve the inverse of a matrix can be framed as solving a
> linear system. It is almost always more accurate and faster to solve that
> linear system rather than invert the matrix. Similarly, there may not be an
> actual inverse of the matrix, but there may still be good answers to the
> problem.
>
> Commonly a good way to solve the system is using a decomposition. Many
> decompositions can be framed as inverses without actually calculating the
> inverse. For instance, QR decomposition allows left or right multiplication
> by the inverse of a matrix because R has a special form and Q is a unit
> matrix.
>
> On Mon, Jun 27, 2011 at 12:36 AM, Tamas Jambor <jamborta@gmail.com> wrote:
>
>> how does that relate the inverse of the matrix?
>>
>>
>> On Thu, Jun 23, 2011 at 5:53 PM, Ted Dunning <ted.dunning@gmail.com>
>> wrote:
>> > Inverting a matrix is a bug.
>> >
>> > You should always use a decomposition method to solve a linear system.
>> QR
>> > is usually a good candidate.
>> >
>> > On Thu, Jun 23, 2011 at 8:19 AM, Sebastian Schelter (JIRA)
>> > <jira@apache.org>wrote:
>> >
>> >>
>> >> [
>> >>
>> https://issues.apache.org/jira/browse/MAHOUT737?page=com.atlassian.jira.plugin.system.issuetabpanels:commenttabpanel&focusedCommentId=13053918#comment13053918
>> ]
>> >>
>> >> Sebastian Schelter commented on MAHOUT737:
>> >> 
>> >>
>> >> I had a quick look at the patch, seems like most of the stuff could also
>> be
>> >> handled by Mahout's matrix code. There's only one issue, do we have code
>> to
>> >> invert a matrix?
>> >>
>> >> > Implicit Alternating Least Squares SVD
>> >> > 
>> >> >
>> >> > Key: MAHOUT737
>> >> > URL: https://issues.apache.org/jira/browse/MAHOUT737
>> >> > Project: Mahout
>> >> > Issue Type: Improvement
>> >> > Reporter: Tamas Jambor
>> >> > Assignee: Sebastian Schelter
>> >> > Attachments: MAHOUT737.patch, MAHOUT737.patch
>> >> >
>> >> >
>> >> > I am sharing this Java implementation of mine that is based on the
>> paper
>> >>  Collaborative Filtering with Implicit Datasets. The implementation is
>> >> multitreading and can be easily extended to use it on Hadoop. In fact
>> this
>> >> approach would possibly work with nonimplicit datasets, but further
>> testing
>> >> is needed. The algorithm is tried and tested on an implicit TVviewing
>> >> dataset, and the performance was pretty good (details to follow).
>> >>
>> >> 
>> >> This message is automatically generated by JIRA.
>> >> For more information on JIRA, see:
>> http://www.atlassian.com/software/jira
>> >>
>> >>
>> >>
>> >
>>
>
