Fuzzy filtering and string similarity scoring - compatible with fuzzaldrin
npm install fuzzaldrin-plusCore vs. Controller size is a good indicator of quality, but not so much in Controller vs. ExtentionCore. This situation happens because match compactness matters more than haystack size. Match compactness is the principle behind the scoring of the Selecta project.
indexOf call. However, there are times where a single query can target multiple parts of a candidate.
git push vs. Git Plus: Push
email handler vs. email/handler.py
toLowerCase
toLocaleString
toLocalLowerCase
tololo to select the third option of these.
itc, we should match
core against controller_core leftmost alignment miss the consecutive run:
install should result be in this order ?
git push, should we order result in that order ?
Plus Stage Hunk? PSH is very close to 'push' (And Plus contains u).
push:
Plus: Stage Hunk: we have P + u + SH grouped as 1, 1, 2
push: we have a single group of 4.
psh:
Plus: Stage Hunk: we have PSH so a single group of 3
push: we have p + sh so grouped as 1, 2
itc?
diag preferring diagnostic to Diagnostics.
install prefer "Uninstall" over "Install" ? Or should it be the other way around? In this case, we have to consider the relative priority of case-sensitivity and start-of-word.
model user vs models/user.rb or moderator_column_users.rb)
CamelCase acronym using lowercase query cc.
Git Push the P of push will be recognised as CamelCase because we consider score(query,query) whatever that number is. A longer query will have a greater maximal score.
ssrb against Set Syntax Ruby we'll score it like so
012345678901234
"Set Syntax Ruby"
"000 SSR0b0 0000"
``
- Acronym scored as three consecutive character at start-of-word + an isolated letter.
- Here we have a wrong-case match. "SSRb" or "SSRB" would have case-sensitive points on the acronym pattern (case of isolated letter is not important)
- Position of the equivalent consecutive match is the average position of acronym characters.
- For scoring, we use the size of the original candidate.
Another example is matching gaa against Git Plus: Add All we'll score it like so
``
01234567890123456
"Git Plus: Add All"
"000000 GAA00 0000"
``
- here we conveniently allow to skip the P of Plus.
Then what about something like "git aa" ?
This is a current limitation. We do not support acronym pattern outside of the prefix. Mostly for performance reason.
Acronym outside of the acronym prefix will have some bonus, scoring between isolated character and 2 consecutive.
There are multiple thing we can improve if one day we implement a proper multiple word query support, and this is one of them.
$3
Legacy fuzzaldrin had some support for optional characters (Mostly space, see SpaceRegEx). Because the scoring does not support errors, the optional character was simply removed from the query.
With this PR, optimal alignment algorithm supports an unlimited number of errors. The strict matching requirement is handled by a separate method isMatch. The optional character implementation is done by building a subset of the query containing only non-optional characters (coreQuery) and passing that to isMatch.
This new way of doing thing means that while some characters are optional, candidates that match those characters have a better score. What this allow is to add characters to the optional list without compromising ranking.
Optional character contains space, but also - and _ because multiple specs require that we should treat them as space. Also \ and : are also optional to support searching a file using the PHP or Ruby name-space. Finally / is optional to mirror \ and support a better workflow in a multi-OS environment.
Finally option allowErrors would make any character optional. Expected effect of that options would be some forgiveness on the spelling at the price of a slower match.
$3
- Score for a given path is computed from the score of the fullpath and score of the filename. For low directory depth, the influence of both is about equal. But, for deeper directory, there is less retrieval effect (importance of basename)
- The full path is penalized twice for size. Once for its own size, then a second time for the size of the basename. Extra basename penalty is dampened a bit.
- The basename is scored as if allowErrors was set to true. (Full-path must still pass isMatch test). This choice is made to support query such as model user against path model/user. Previously, the basename score would be 0 because it would not find model inside basename user. Variable queryHasSlashes partially addressed this issue, but was inconsistent with usage of as folder separator
- When query has slashes (path.sep) the last or last few folder from the path are promoted to the basename. (as many folder from the path as folder in the query)
-------------
Algorithm (Optimal alignment)
$3
Let's compare A:surgery and B:gsurvey.
To do so we can try to match every letter of A against every letter of B.
This problem can be solved using a score matrix.
- The match starts at [0,0] trying to compare the first letter of each.
- The match end at [m,n] comparing the last letter of each.
At each position [i,j] the best move can be one of the 3 options.
- match A[i] with B[j] (move diagonal, add 1 to score)
- skip A[i] (move left, copy score)
- skip B[j] (move down, copy score)
We do not know which one of these 3 is the best move until we reach the end, so we record the score of the best move so far. The last cell contains the score of the best alignment. If we want to output that alignment we need to rebuild it backward from the last cell.
``
s u r g e r y
g [0,0,0,1,1,1,1] : best move is to align g of gsurvey with g of surgery, score 1
s [1,1,1,1,1,1,1] : we can align s, but doing so invalidate g. Both score 1, we cannot decide
u [1,2,2,2,2,2,2] : if we align s, we can also align u, we have a winner
r [1,2,3,3,3,3,3] : we can align r
v [1,2,3,3,3,3,3] : nothing we can do with that v, score stay the same
e [1,2,3,3,4,4,4] : we can align e (we skipped g the same way we skipped v)
y [1,2,3,3,4,4,5] : align y (we skipped r )
``
Best alignment is
``
gsur-ve-y
-|||--|-|
-surg-ery
``
For those familiar with code diff, this is essentially the same problem. Except, in this case, we the do the alignment of characters in a word and a diff performs alignment of lines in a file. Characters present in the second word but not in the first counts as additions; characters present only in the first word are deletions and characters present in both are matches - like unchanged lines in a diff.
To get that alignment, we start from the last character and trace back the best option. The pattern to looks for an alignment is the corner increase (diagonal+1 is greater than left or up.)
``
4,4 3,3 2,2 1,1 0,0
4,5 3,4 2,3 1,2 0,1
``
- (There are an implicit row and column of 0 before the matrix)
The pattern to look for to move left is:
``
3,3
4,4
``
The pattern to look for to move up is:
``
3,4
3,4
``
We try to resolve equality the following way:
``
3,3
3,3
``
1. Prefer moving UP: toward the start of the candidate. This strategy ensures we highlight toward the start of string instead of the end when all else is equal.
2. If not available, prefer moving LEFT (optional character)
3. Only accept alignment DIAG when it is the absolute best option.
$3
The LCS algorithm allows to detect which character of the query are common to both words while being in proper order. (For example g is common to both word but discarded because out of order.)
LCS is not immediately useful for fuzzaldrin needs. Because fuzzaldrin require ALL characters of the query to be in subject to have a score greater than 0, LCS for all positive candidates would be the length of the query.
However, the dynamic programming table used to solve LCS is very useful to our need. The ability to select the best path and skip that g even if it is present in both query and candidate is the key to improves over left-most alignment. All we need for this to works is a bit more detail in score than 0 or 1.
$3
Matching character does not have to be binary. Case sensitive match can still prefer proper case, same goes with accents. A diff tools can decide a line has been modified, instead of registering an addition and a deletion. A handwriting recognition tool can decide a and o are somewhat more similar to each other than they are to w, and so on.
We use character similarity as a way to build and score patterns. That is, we consider that character are similar from their own quality ( such as case) as well of being part of a similar neighborhood (consecutive letters or acronyms)
There are some rules that limit our scoring ability (for example we cannot go back in time and correct the score based on future choice) but overall that scheme is very flexible.
$3
While the programming table describes computation, we do not need to store the whole matrix when we only output the score. Fundamentally when computing a score, we only need 3other previously computed cell: UP, LEFT and DIAG.
Suppose we process the cell [3,5]
20, 21, 22, 23, 24, 25, 26, 27, 28, 29
30, 31, 32, 33, 34, 35, 36, 37, 38, 39
To build that score we only need values 24(DIAG), 25(UP), 34(LEFT).
So instead of a whole matrix we can keep only the two current lines.
Furthermore, anything on the left of 24 on the first line is not needed anymore. Also, anything to the right of 35 on the second line has not yet been computed. So we can build a more compact structure using one composite row + one diagonal.
score_diag = 24
score_row = 30, 31, 32, 33, 34, 25, 26, 27, 28, 29
#### Preparing next value
Once we have computed the value of the cell [3,5], we can insert that value into the structure, taking care of saving next diagonal before overwriting it.
diag = 25
row = 30, 31, 32, 33, 34, 35, 26, 27, 28, 29
To compute value of cell [3,6] we take
- UP value (26) from the row.
- DIAG value, from the diag register.
- LEFT value from the previously computed value: 35
$3
Before entering the matching process, the row is initialized with 0. Before scoring each row, the LEFT and DIAG register are reset to 0.
That strategy has the effect of placing a virtual row and column of 0 before the matrix. Moreover, it allows to deal with boundary condition without any special case.
$3
We set up the row vector with the size of the query. Using a full matrix, scoring a query of size 5 against a path of size 100, would require a 500 cells. Instead, we use a 5 item row + some registers. This should ease memory management pressure.
Each character of the query manages its best score. More precisely, each cell row[j] manage the best score so far of matching query[0..j] against candidate[0..i].
$3
We cache the consecutive score in a virtual matrix following the same composite row scheme that we do with score values.
In fuzzaldrin.score The candidate entirely determines the Neighbourhood quality. It is not affected by which character has been chosen. In highlight, (fuzzaldrin.match) we further refine the formula to make the consecutive bonus conditional to not breaking the consecutive chain:
For example query abcdz vs. subject abcdzbcdz. Between abcd and bcdz, abcd wins for being sooner in the string. Now between the two z, the first one is isolated and the second one is part of a rank 4 group. However given that bcd are matched sooner, the second z is an isolated match, so the first z wins.
-------------
Performance
Let's consider the following autocomplete scenario.
- Symbol bank has 1000 items.
- The user receives about 5 suggestion for its query.
- Of those 5, 1 is a exact case-sensitive match.
- That particular user almost always wants that case sensitive match.
Should we optimize for case sensitive indexOf before trying other things? Our answer to that question is no.
Case sensitive exact match are valuable because they are rare. Even if the user tries to get them, for each one of those we have to reject 995 entry and deal with 4 other kinds of matches.
This is our first principle for optimization: Most of the haystack is not the needle. Because rejection of candidate happens often, we should be very good at doing that.
Failing a test for case-sensitive indexOf tell us exactly nothing for case-insensitive indexOf, or acronyms, or even scattered letters.
That test is too specific. To reject match efficiently, we should aim for the lowest common denominator: scattered case-insensitive match.
This is exactly the purpose of isMatch.
$3
We just have shown how that sentence applies at the candidate level, but it is also at the character level.
Let's consider this line: if (subject_lw[i] == query_lw[j])
This test is for match points (or hits). It refers to the diag+1 in the algorithm description, with the +1 being refined to handle the differents levels of character and neighborhood similarity.
How often is that condition true ?
Let's consider an alphabet that contain 26 lowercase letters, 10 numbers, a few symbols _!?=<>. That is a 40+ symbol alphabet. Under a uniform usage model of those symbols, we have the hit condition occurs about 2.5% of the time (1/40). If we suppose only 10-20 of those characters are popular, the hit rate is about 5-10%.
This means we'll try to minimize the number of operation that happens outside of math points. In that context, increasing the cost of a hit, while decreasing the cost of non-hits looks like a possibly worthwhile proposition.
A canonical example of this is that, instead of testing each character against the list of separators, setting a flag for next character being a start-of-word, we first confirm a match then look behind for separator. This characterization work is sometimes repeated more than once, but so far this scheme benchmarked better than alternatives we have tried to avoid doing extra work.
Having work concentrated at hit points is also a natural fit to our logic, the most expensive part being to determine how to score similarity between characters (including context similarity). However, it also means we'll want to have some control over the number of positive hits we'll compute - that is the purpose of missed hit optimisation.
$3
To the extent the user is searching for a specific resource, this should be uncommon.
It can still happen in some situation such as:
- Search is carried as user type (the query is not intentional)
- The intentional query is not fully typed, match-all is a temporary step.
One way to deal with that is not to use the full matching algorithm when we can deal with something simpler. This is what we have done while searching for indexOf instance.
One special note: Acronym still have to be checked even if we have an exact match: for example query su against StatusUrl. As an exact match it is poor: 'StatusUrl' is a middle of word match and have the wrong case. However as an acronym it is great: 'StatusUrl'. That motivated us to create the specialized scoreAcronyms.
What is nice is that while scoreAcronyms was created to speed up exact matches search, it also provided very valuable information for accuracy. It later became a corner stone in the processing of accidental acronym.
The result is that for exact matches and exact acronym matches we bypass the optimal alignment algorithm, giving very fast results.
We still have to deal with fuzzier stacks of needles and the next two optimization address this.
$3
A hit occurs when character of query is also in the subject.
- Every (i,j) such that subject[i] == query[j], in lowercase.
A missed hit occurs when a hit does not improve the score.
To guarantee optimal alignment, every hit has to be considered.
However when candidate are long (deep path) & query contains common use character, for example, vowels , we can spend a huge amount of time scoring accidental hits.
So we use the number of missed hit as a heuristic for current score that are unlikely to improve. Let's score itc vs ImportanceTableControl
- I of Importance: First occurrence, improve over none.
- t of Importance: First occurrence, improve over none.
- c of Importance: First occurrence, improve over none.
- T of Table : Acronym match, improve over an isolated middle of word.
- C of Control : Acronym match, improve over an isolated middle of word.
- t of Control: no improvement over acronym T: first hit miss.
- After a certain threshold of missed hit we can consider it is unlikely the score will improve by much.
- Despite above example hit miss optimization do not affect scoring of exact match (sub-string or acronym)
- There are some legitimate use for hit miss, for example while scoring query Mississippi each positive match for s or i may trigger up to 3 hit miss on the other occurrence of that letter in query.
- For that reason, we propose counting consecutive hit miss and having a maximum of one hit miss per character of the subject.
Q: Does this grantee improvement over leftmost alignment?
A: It'll often be the case but no guarantee on pathological matches.
For example, in query abcde against candidate 'abcabcabcabcabcabcabczde' we may trigger the miss count before matching de. It'll still be registered as a match and probably a good one with abc at the start, de will be scored as optional characters not present.
Candidate 'abcabcabcabcabcabcabcde' will not have any problem because it does not affect exact match.
A real world example is searching index in the benchmark. Where i, n, d, e exist scattered in folder name, but x exist in the extension .txt. However, the whole point of this project is to prefer structured match to scattered one so this might not be a problem.
$3
[option maxInners, disabled by default]
A lot of the speed of this PR come from the idea that rejection happens often, and we need to be very efficient on them to offset slower higher quality match. Unfortunately, some query will match against almost everything.
- Fast short-circuit path for exact substring acronym help a lot.
- Missed hit heuristic also help a lot for general purpose match.
However, we may still be too slow for interactive time query on large data set. This is why maxInners option is provided.
This is the maximum number of positive candidate we collect before sorting and returning the list.
The realization is that a query that match everything on a 50K item data set is unlikely to show anything useful to the user above the fold (say in the first 15 results).
So then the priority is to detect such case of low quality (low discrimination power) query and report fast to the user so user can refine its query.
A maxInners size of about 20% of the list works well. It is not needed on a smaller list.
$3
Before the first occurrence of the first char of query in the subject, or after the last occurrence of the last char of query in the subject it is impossible to make a match. So we'll trim the subject to that active region. The search for those boundaries is linear while the optimal alignment algorithm is quadratic, so it is an improvement, however, little or large we move.
$3
- All test compare this PR to previous version (legacy)
- The first test index is a typical use case, 10% positive, 1/3 of positive are exact matches.
- We are about 2x faster
- Second test indx remove exact matches. Just under 2x faster
- Third test walkdr, 1% positive, mostly testing isMatch(), above 2x faster.
- Fourth test node, exact match, 98% positive, bit under 2x faster.
- Test 5 nm, exact acronym match, 98% positive, about 10% slower.
- Test 6 nodemodules is special in that it use a string that score on almost every candidate, often multiple time per candidate and individuals characters are popular. It also avoid exact match speed-up. About 2x slower, but unlikely to happens in real life. maxInners mitigation cover that case.
``
Filtering 66672 entries for 'index' took 62ms for 6168 results (~10% of results are positive, mix exact & fuzzy)
Filtering 66672 entries for 'index' took 120ms for 6168 results (~10% of results are positive, Legacy method)
======
Filtering 66672 entries for 'indx' took 69ms for 6192 results (~10% of results are positive, Fuzzy match)
Filtering 66672 entries for 'indx' took 126ms for 6192 results (~10% of results are positive, Fuzzy match, Legacy)
======
Filtering 66672 entries for 'walkdr' took 30ms for 504 results (~1% of results are positive, fuzzy)
Filtering 66672 entries for 'walkdr' took 70ms for 504 results (~1% of results are positive, Legacy method)
======
Filtering 66672 entries for 'node' took 112ms for 65136 results (~98% of results are positive, mostly Exact match)
Filtering 66672 entries for 'node' took 213ms for 65136 results (~98% of results are positive, mostly Exact match, Legacy method)
======
Filtering 66672 entries for 'nm' took 60ms for 65208 results (~98% of results are positive, Acronym match)
Filtering 66672 entries for 'nm' took 56ms for 65208 results (~98% of results are positive, Acronym match, Legacy method)
======
Filtering 66672 entries for 'nodemodules' took 602ms for 65124 results (~98% positive + Fuzzy match, [Worst case scenario])
Filtering 66672 entries for 'nodemodules' took 123ms for 13334 results (~98% positive + Fuzzy match, [Mitigation])
Filtering 66672 entries for 'nodemodules' took 295ms for 65124 results (Legacy)
```