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METEOR is a metric

Metric (mathematics)

In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric...

for the evaluation of machine translation

Machine translation

Machine translation, sometimes referred to by the abbreviation MT is a sub-field of computational linguistics that investigates the use of computer software to translate text or speech from one natural language to another.On a basic...

output. The metric is based on the harmonic mean

Harmonic mean

In mathematics, the harmonic mean is one of several kinds of average. Typically, it is appropriate for situations when the average of rates is desired....

of unigram precision and recall

Precision and recall

In pattern recognition and information retrieval, precision is the fraction of retrieved instances that are relevant, while recall is the fraction of relevant instances that are retrieved. Both precision and recall are therefore based on an understanding and measure of relevance...

, with recall weighted higher than precision. It also has several features that are not found in other metrics, such as stemming

Stemming

In linguistic morphology and information retrieval, stemming is the process for reducing inflected words to their stem, base or root form—generally a written word form. The stem need not be identical to the morphological root of the word; it is usually sufficient that related words map to the same...

and synonymy matching, along with the standard exact word matching. The metric was designed to fix some of the problems found in the more popular BLEU

Bleu

bleu or BLEU may refer to:* the French word for blue* Three Colors: Blue, a 1993 movie* Bilingual Evaluation Understudy, a machine translation evaluation metric* Belgium–Luxembourg Economic Union...

metric, and also produce good correlation with human judgement at the sentence or segment level This differs from the BLEU metric in that BLEU seeks correlation at the corpus level.

Results have been presented which give correlation

Pearson product-moment correlation coefficient

In statistics, the Pearson product-moment correlation coefficient is a measure of the correlation between two variables X and Y, giving a value between +1 and −1 inclusive...

of up to 0.964 with human judgement at the corpus level, compared to BLEU

Bleu

bleu or BLEU may refer to:* the French word for blue* Three Colors: Blue, a 1993 movie* Bilingual Evaluation Understudy, a machine translation evaluation metric* Belgium–Luxembourg Economic Union...

's achievement of 0.817 on the same data set. At the sentence level, the maximum correlation with human judgement achieved was 0.403.

Algorithm

As with BLEU

Bleu

bleu or BLEU may refer to:* the French word for blue* Three Colors: Blue, a 1993 movie* Bilingual Evaluation Understudy, a machine translation evaluation metric* Belgium–Luxembourg Economic Union...

, the basic unit of evaluation is the sentence, the algorithm first creates an alignment (see illustrations) between two sentence

Sentence (linguistics)

In the field of linguistics, a sentence is an expression in natural language, and often defined to indicate a grammatical unit consisting of one or more words that generally bear minimal syntactic relation to the words that precede or follow it...

s, the candidate translation string, and the reference translation string. The alignment is a set of mappings between unigrams. A mapping can be thought of as a line between a unigram in one string, and a unigram in another string. The constraints are as follows; every unigram in the candidate translation must map to zero or one unigram in the reference. Mappings are selected to produce an alignment as defined above. If there are two alignments with the same number of mappings, the alignment is chosen with the fewest crosses, that is, with fewer intersections

Intersection (set theory)

In mathematics, the intersection of two sets A and B is the set that contains all elements of A that also belong to B , but no other elements....

of two mappings. From the two alignments shown, alignment (a) would be selected at this point. Stages are run consecutively and each stage only adds to the alignment those unigrams which have not been matched in previous stages. Once the final alignment is computed, the score is computed as follows: Unigram precision

is calculated as:
will be mapped by each module
|-
! Module || Candidate || Reference || Match
|-
| Exact || good || good || Yes
|-
| Stemmer || goods || good || Yes
|-
| Synonymy || well || good || Yes
|-
|}

Where

is the number of unigrams in the candidate translation that are also found in the reference translation, and

is the number of unigrams in the candidate translation. Unigram recall

is computed as:

Where

is as above, and

is the number of unigrams in the reference translation. Precision and recall are combined using the harmonic mean

Harmonic mean

In mathematics, the harmonic mean is one of several kinds of average. Typically, it is appropriate for situations when the average of rates is desired....

in the following fashion, with recall weighted 9 times more than precision:

The measures that have been introduced so far only account for congruity with respect to single words but not with respect to larger segments that appear in both the reference and the candidate sentence. In order to take these into account, longer n-gram matches are used to compute a penalty

for the alignment. The more mappings there are that are not adjacent in the reference and the candidate sentence, the higher the penalty will be.

In order to compute this penalty, unigrams are grouped into the fewest possible chunks, where a chunk is defined as a set of unigrams that are adjacent in the hypothesis and in the reference. The longer the adjacent mappings between the candidate and the reference, the fewer chunks there are. A translation that is identical to the reference will give just one chunk. The penalty

is computed as follows,

Where c is the number of chunks, and

is the number of unigrams that have been mapped. The final score for a segment is calculated as

below. The penalty has the effect of reducing the

by up to 50% if there are no bigram or longer matches.

To calculate a score over a whole corpus

Text corpus

In linguistics, a corpus or text corpus is a large and structured set of texts...

, or collection of segments, the aggregate values for

,

and

are taken and then combined using the same formula. The algorithm also works for comparing a candidate translation against more than one reference translations. In this case the algorithm compares the candidate against each of the references and selects the highest score.

Examples

Reference	the	cat	sat	on	the	mat
Hypothesis	on	the	mat	sat	the	cat



Score: 0.5000 = Fmean: 1.0000 * (1 - Penalty: 0.5000)

Fmean: 1.0000 = 10 * Precision: 1.0000 * Recall: 1.0000 / Recall: 1.0000 + 9 * Precision: 1.0000

Penalty: 0.5000 = 0.5 * (Fragmentation: 1.0000 ^3)

Fragmentation: 1.0000 = Chunks: 6.0000 / Matches: 6.0000

Reference	the	cat	sat	on	the	mat
Hypothesis	the	cat	sat	on	the	mat



Score: 0.9977 = Fmean: 1.0000 * (1 - Penalty: 0.0023)

Fmean: 1.0000 = 10 * Precision: 1.0000 * Recall: 1.0000 / Recall: 1.0000 + 9 * Precision: 1.0000

Penalty: 0.0023 = 0.5 * (Fragmentation: 0.1667 ^3)

Fragmentation: 0.1667 = Chunks: 1.0000 / Matches: 6.0000

Reference	the	cat		sat	on	the	mat
Hypothesis	the	cat	was	sat	on	the	mat



Score: 0.9654 = Fmean: 0.9836 * (1 - Penalty: 0.0185)

Fmean: 0.9836 = 10 * Precision: 0.8571 * Recall: 1.0000 / Recall: 1.0000 + 9 * Precision: 0.8571

Penalty: 0.0185 = 0.5 * (Fragmentation: 0.3333 ^3)

Fragmentation: 0.3333 = Chunks: 2.0000 / Matches: 6.0000

External links

The METEOR Automatic Machine Translation Evaluation System (including link for download)

METEOR

Algorithm

Examples

See also

External links