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https://issues.apache.org/jira/browse/MAHOUT-1853?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15391126#comment-15391126
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Pat Ferrel edited comment on MAHOUT-1853 at 8/4/16 4:15 PM:
------------------------------------------------------------
To reword this issue...
The CCO analysis code currently only employs a single # of values per row of
the P’X matrices. This has proven an insufficient threshold for many of the
possible cross-occurrence types. The problem is that for a user * item input
matrix, which becomes an item * item output a fixed # per row is fine but the
implementation is a bit meaningless when there are only 20 columns of the X
matrix. For instance if X = C category preferences, there may be only 20
possible categories and with a threshold of 100 and the fact that users often
have enough usage to trigger preference events on all categories (though
resulting in a small LLR value), the P’C matrix is almost completely full. This
reduces any value in P’C.
There are several ways to address:
1) have a # of indicators per row threshold for every P'X matrix, not one for
all (the current impl)
2) use a fixed LLR threshold value per matrix
3) use a confidence of correlation value (a % maybe) that is calculated from
the data by looking at the distribution in P’C or other. This is potentially
O(n^2) where n = number of items in the matrix. This may be practical to
calculate for some types of data since n may be very small.
1 and 2 are easy in the extreme, #3 can actually be calculated after the fact
and used in #2 even if it is not included in Mahout.
I've started work on #1 and #2
[~ssc][~tdunning] I'm especially looking for comments on #3 above, calculating
a % confidence of correlation. The function we use for LLR scoring is
https://github.com/apache/mahout/blob/master/math-scala/src/main/scala/org/apache/mahout/math/cf/SimilarityAnalysis.scala#L210
was (Author: pferrel):
To reword this issue...
The CCO analysis code currently only employs a single # of values per row of
the P’? matrices. This has proven an insufficient threshold for many of the
possible cross-occurrence types. The problem is that for a user * item input
matrix, which becomes an item * item output a fixed # per row is fine but the
implementation is a bit meaningless when there are only 20 columns of the ?
matrix. For instance if ? = C category preferences, there may be only 20
possible categories and with a threshold of 100 and the fact that users often
have enough usage to trigger preference events on all categories (though
resulting in a small LLR value), the P’C matrix is almost completely full. This
reduces any value in P’C.
There are several ways to address:
1) have a # of indicators per row threshold for every matrix, not one for all
(the current impl)
2) use a fixed LLR threshold value per matrix
3) use a confidence of correlation value (a % maybe) that is calculated from
the data by looking at the distribution in P’C or other. This is potentially
O(n^2) where n = number of items in the matrix. This may be practical to
calculate for some types of data since n may be very small.
1 and 2 are easy in the extreme, #3 can actually be calculated after the fact
and used in #2 even if it is not included in Mahout.
starting work on #1 and #2
> Improvements to CCO (Correlated Cross-Occurrence)
> -------------------------------------------------
>
> Key: MAHOUT-1853
> URL: https://issues.apache.org/jira/browse/MAHOUT-1853
> Project: Mahout
> Issue Type: New Feature
> Affects Versions: 0.12.0
> Reporter: Andrew Palumbo
> Assignee: Pat Ferrel
> Fix For: 0.13.0
>
>
> Improvements to CCO (Correlated Cross-Occurrence) to include auto-threshold
> calculation for LLR downsampling, and possible multiple fixed thresholds for
> A’A, A’B etc. This is to account for the vast difference in dimensionality
> between indicator types.
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