String segment match

The string segment match algorithm computes a set of metrics - the string segment match metrics - intended to capture all the information about how well a query string matches a field string, which is useful for document ranking in search, from the limited information usually available during matching in search engines.

The algorithm works by locating segments, which are local regions in the field which contain one or more adjacent terms of the query. All segment start points in the field are explored, and the ones which produce the best overall segmentation are chosen. Informally, a segmentation is good if it contains few segments with the query matches close together. Example:

Here two segments are found to cover the query. An alternative second segment is also found, but is discarded because it has inferior query term proximity. The other lone "Bush" instance is never considered because there is no segmentation causing "Bush" to be a segment start token (i.e. there is no lone "George").

A subset of the metrics are computed from the tokens within located segments, while another subset of metrics characterizes the number and placement of the segments themselves. This allows the metrics to reflect the property of natural language that tokens which are very close are often part of the same meaning (typically as parts of the same sentence) while somewhat more distant tokens are only weakly related.

Queries typically consists of multiple intended segments, where each segment is continuous and in order, while the ordering between the segments is of little significance (although the more important segments tend to come first).

By matching the query in term order to the best and fewest segments of the field, this algorithm makes use of the available field data to discover the likely query segmentation from the evidence. Explicit segmentation information can also be used in the form of connectivity scores which influences the segment scores and thus the chosen segments.

Source information

The information used by this algorithm to calculate these metrics is (the last three are optional):

  • The position of each occurrence of a matched term in the query and field
  • The number of terms in the query and field
  • A number per query term indicating the weight (importance) of each query term
  • A number per query term indicating the relative frequency of the term
  • A number per adjacent query term pair indicating the linguistic connectivity between the terms

Algorithm

The algorithm locates segments from a given start query term as follows:

i = the position of the first query term
j = the position of the first match of the query term at i
while (i < query.length) {
    nextJ = the first location of query term i+1 at most proximityLimit steps to the right of j
    if (nextJ not found)
        nextJ = the first location query term i+1 at most proxmityLimit steps to the left backwards of j

    if (nextJ is found) { // Find next token in this segment
        i = i+1
        j = nextJ
    }
    else {
        nextJ = the first location of query term i+1 at any location to the right forwards from j
        if (nextJ not found)
            nextJ = the first location of query term i+1 at any location to the left backwards from j
        if (nextJ not found) { // Skip a non-existing query term
        	i = i+1
        }
        else { // End of segment
            return i,j as the segment end
        }
    }
}
So a segment is a set of terms in the field which corresponds to an adjacent subsection of query terms where the gap between any adjacent query term in the field is at most proximityLimit forwards or backwards, and where query terms not present in the field are ignored.

Let's call the field term search order used above the semantic distance between two field position. So, for example

  • the semantic distance between j and nextJ is n if nextJ is located n places after j and n<proximityLimit
  • the semantic distance between j and nextJ is proximityLimit+n if nextJ is located n places to the left of j and n<proximityLimit
The algorithm explores tokens and segments in the semantic distance space. The algorithm works with any definition of semantic distance. The algorithm will record for each segment start point:
  • metrics - The current best known metrics of the combined segments up to this point
  • previousJ - The end j of the previous segment in the field (if any)
  • i - the query term i which is the start of this segment
  • semanticDistanceExplored - the distance from previousJ explored so far
  • open - whether there are possibly more j's to find beyond semanticDistanceExplored
With this, we can list the high level pseudocode of the algorithm:
currentSegment=a segment start point at starting at i=0 (the start of the query)
while (there are open segment start points) {
    newSegment=find the next segment, at currentSegment.i with semanticDistance > currentsegment.semanticDistance
    if (no newSegment) {
        currentSegment.open = false
        continue;
    }
    SegmentStartPoint existingStartPoint=find stored segment at start point newSegment.i+1
    if (no existingStartPoint) {
        create and store a new (empty open) segment start point at newSegment.i+1
    }
    else {
        if (newSegment.score > existingStartPoint.score) {
            existingStartPoint.metrics.score = newSegment.metrics.score
            existingStartPoint.previousJ = newSegment.endJ
            existingStartPoint.semanticDistanceExplored = newSegment.semanticDistance+1
        }
    }
    currentSegment=the next open start point (in the order they are found)
}
finalMetrics=metrics of segmentStartPoint at query.length
The metric.score deciding which of two segmentation paths is best is absoluteProximity/segments^2. Any combination of metrics which can be calculated for a partial segmentation may be used.

Browse the code for details.

Complexity

The algorithm uses a linear programming technique to avoid recomputing earlier segments. A constant amount of data is stored per possible segment start point. Since there are at most as many start points as there are query terms, the memory complexity is:

O(query.length)
As the algorithm will try all possible segment starting points (up to a limit), and there are at most one starting point per query term, the time complexity is:
O(query.length*total number of term occurrences)
The average time complexity is:
O(average segment length/average number of term occurrences)

Metric set

The complete string segment match metrics set, computed by this algorithm, is

  • match
  • proximity
  • completeness
  • queryCompleteness
  • fieldCompleteness
  • orderness
  • relatedness
  • earliness
  • longestSequenceRatio
  • segmentProximity
  • unweightedProximity
  • absoluteProximity
  • occurrence
  • absoluteOccurrence
  • weightedOccurrence
  • weightedAbsoluteOccurrence
  • significantOccurrence
  • weight
  • significance
  • importance
  • segments
  • matches
  • outOfOrder
  • gaps
  • gapLength
  • longestSequence
  • head
  • tail
  • segmentDistance
These are documented as the features prefixed by fieldMatch(name), see the rank features reference.

The metric set contains both low level, unnormalized metrics corresponding directly to a concept in the string segment match algorithm (e.g segments, gaps), normalized basic features (e.g. proximity, queryCompleteness), normalized metrics combining lower level metrics into some useful part of the truth (e.g. completeness, orderness) as well as a metric combining most of the others into one normalized value (match). Applications will choose the subset of the metrics which captures the properties they determine is important, at the granularity which is convenient.

Configuration parameters

The algorithm has the following configuration parameters, where the three first are fundamental parameters of the algorithm, and the others are used to normalize or combine certain features. Configure using rank feature configuration:

ParameterDefaultDescription
proximityLimit10 The maximum allowed gap within a segment.
proximityTable1/(2^(i/2)/3) for i in 9..0 followed by 1/2^(i/2) for i in 0..10 The proximity table deciding the importance of separations of various distances, The table must have size proximityLimit*2+1, where the first half is for reverse direction distances. The table must only contain values between 0 and 1, where 1 is "perfect" and 0 is "worst".
maxAlternativeSegmentations10000 The maximum number of alternative segmentations allowed in addition to the first one found. This will prefer to not consider iterations on segments that are far out in the field, and which starts late in the query.
maxOccurrences100 The number of occurrences the number of occurrences of each word is normalized against. This should be set as the number above which additional occurrences of the term has no real significance.
proximityCompletenessImportance0.9 A number between 0 and 1 which determines the importance of field completeness in relation to query completeness in the match and completeness metrics.
relatednessImportance0.9 The normalized importance of relatedness used in the match metric.
earlinessImportance0.05 The importance of the match occurring early in the query, relative to segmentProximityImportance, occurrenceImportance and proximityCompletenessImportance in the match metric.
segmentProximityImportance0.05 The importance of multiple segments being close to each other, relative to earlinessImportance, occurrenceImportance and proximityCompletenessImportance in the match metric.
occurrenceImportance0.05 The importance of having many occurrences of the query terms, relative to earlinessImportance, segmentProximityImportance and proximityCompletenessImportance in the match metric.
fieldCompletenessImportance0.05 A number between 0 and 1 which determines the importance of field completeness in relation to query completeness in the match and completeness metrics.