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 <[email protected]> wrote: > how does that relate the inverse of the matrix? > > > On Thu, Jun 23, 2011 at 5:53 PM, Ted Dunning <[email protected]> > 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) > > <[email protected]>wrote: > > > >> > >> [ > >> > https://issues.apache.org/jira/browse/MAHOUT-737?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13053918#comment-13053918 > ] > >> > >> Sebastian Schelter commented on MAHOUT-737: > >> ------------------------------------------- > >> > >> 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: MAHOUT-737 > >> > URL: https://issues.apache.org/jira/browse/MAHOUT-737 > >> > Project: Mahout > >> > Issue Type: Improvement > >> > Reporter: Tamas Jambor > >> > Assignee: Sebastian Schelter > >> > Attachments: MAHOUT-737.patch, MAHOUT-737.patch > >> > > >> > > >> > I am sharing this Java implementation of mine that is based on the > paper > >> - Collaborative Filtering with Implicit Datasets. The implementation is > >> multi-treading and can be easily extended to use it on Hadoop. In fact > this > >> approach would possibly work with non-implicit datasets, but further > testing > >> is needed. The algorithm is tried and tested on an implicit TV-viewing > >> 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 > >> > >> > >> > > >
