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https://issues.apache.org/jira/browse/LUCENE-2089?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12832741#action_12832741
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Eks Dev commented on LUCENE-2089:
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{quote}
I assume you mean by weighted edit distance that the transitions in the state
machine would have costs?
{quote}
Yes, kind of, not embedded in the trie, just defined externally.
What I am talking about is a part of the noisy channel approach, modeling only
channel distribution. Have a look at the http://norvig.com/spell-correct.html
for basic theory. I am suggesting almost the same, just applied at character
level and without language model part. It is rather easy once you have your
dictionary in some sort of tree structure.
You guide your trie traversal over the trie by iterating on each char in your
search term accumulating log probabilities of single transformations
(recycling prefix part). When you hit a leaf insert into PriorityQueue of
appropriate depth. What I mean by "probabilities of single transformations" are
defined as:
insertion(character a)//map char->log probability (think of it as kind of "cost
of inserting this particular character)
deletion(character)//map char->log probability...
transposition(char a, char b)
replacement(char a, char b)//2D matrix <char,char>->probability (cost)
if you wish , you could even add some positional information, boosting match on
start/end of the string
I avoided tricky mechanicson traversal, insertion, deletion, but on trie you
can do it by following different paths...
the only good implementation (in memory) around there I know of is in LingPipe
spell checker (they implement full Noisy Channel, with Language model driving
traversal)... has huge educational value, Bob is really great at explaining
things. The code itself is proprietary.
I would suggest you to peek into this code to see this 2-Minute rumbling I
wrote here properly explained :) Just ignore the language model part and assume
you have NULL language model (all chars in language are equally probable) ,
doing full traversal over the trie.
{quote}
If this is the case couldn't we even define standard levenshtein very easily
(instead of nasty math), and would the beam search technique enumerate
efficiently for us?
{quote}
Standard Lev. is trivially configured once you have this, it is just setting
all these costs to 1 (delete, insert... in log domain)... But who would use
standard distance with such a beast, reducing impact of inserting/deleting
silent "h" as in "Thomas" "Tomas"...
Enumeration is trie traversal, practically calculating distance against all
terms at the same time and collectiong N best along the way. The place where
you save your time is recycling prefix part in this calculation. Enumeration is
optimal as this trie there contains only the terms from termDict, you are not
trying all possible alphabet characters and you can implement "early path
abandoning" easily ether by cost (log probability) or/and by limiting the
number of successive insertions
If interested in really in depth things, look at
http://www.amazon.com/Algorithms-Strings-Trees-Sequences-Computational/dp/0521585198
Great book, (another great tip from b...@lingpipe). A bit strange with
terminology (at least to me), but once you get used to it, is really worth the
time you spend trying to grasp it.
> explore using automaton for fuzzyquery
> --------------------------------------
>
> Key: LUCENE-2089
> URL: https://issues.apache.org/jira/browse/LUCENE-2089
> Project: Lucene - Java
> Issue Type: Wish
> Components: Search
> Reporter: Robert Muir
> Assignee: Mark Miller
> Priority: Minor
> Attachments: LUCENE-2089.patch, Moman-0.2.1.tar.gz, TestFuzzy.java
>
>
> Mark brought this up on LUCENE-1606 (i will assign this to him, I know he is
> itching to write that nasty algorithm)
> we can optimize fuzzyquery by using AutomatonTermsEnum, here is my idea
> * up front, calculate the maximum required K edits needed to match the users
> supplied float threshold.
> * for at least small common E up to some max K (1,2,3, etc) we should create
> a DFA for each E.
> if the required E is above our supported max, we use "dumb mode" at first (no
> seeking, no DFA, just brute force like now).
> As the pq fills, we swap progressively lower DFAs into the enum, based upon
> the lowest score in the pq.
> This should work well on avg, at high E, you will typically fill the pq very
> quickly since you will match many terms.
> This not only provides a mechanism to switch to more efficient DFAs during
> enumeration, but also to switch from "dumb mode" to "smart mode".
> i modified my wildcard benchmark to generate random fuzzy queries.
> * Pattern: 7N stands for NNNNNNN, etc.
> * AvgMS_DFA: this is the time spent creating the automaton (constructor)
> ||Pattern||Iter||AvgHits||AvgMS(old)||AvgMS (new,total)||AvgMS_DFA||
> |7N|10|64.0|4155.9|38.6|20.3|
> |14N|10|0.0|2511.6|46.0|37.9|
> |28N|10|0.0|2506.3|93.0|86.6|
> |56N|10|0.0|2524.5|304.4|298.5|
> as you can see, this prototype is no good yet, because it creates the DFA in
> a slow way. right now it creates an NFA, and all this wasted time is in
> NFA->DFA conversion.
> So, for a very long string, it just gets worse and worse. This has nothing to
> do with lucene, and here you can see, the TermEnum is fast (AvgMS -
> AvgMS_DFA), there is no problem there.
> instead we should just build a DFA to begin with, maybe with this paper:
> http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.652
> we can precompute the tables with that algorithm up to some reasonable K, and
> then I think we are ok.
> the paper references using http://portal.acm.org/citation.cfm?id=135907 for
> linear minimization, if someone wants to implement this they should not worry
> about minimization.
> in fact, we need to at some point determine if AutomatonQuery should even
> minimize FSM's at all, or if it is simply enough for them to be deterministic
> with no transitions to dead states. (The only code that actually assumes
> minimal DFA is the "Dumb" vs "Smart" heuristic and this can be rewritten as a
> summation easily). we need to benchmark really complex DFAs (i.e. write a
> regex benchmark) to figure out if minimization is even helping right now.
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