3.1 Linguistically agnostic evaluation metrics

Linguistically agnostic metrics can be further classified into mention, link, optimal mapping-based or link-based and entity-aware metrics (Sukthanker et al. Reference Sukthanker, Poria, Cambria and Thirunavukarasu2018). But a common feature of all of these metrics is that they treat coreference evaluation task as a clustering task and do not take in mind linguistic information of coreference chain elements into consideration.

3.1.1 Basic precision, recall, and F-measure metric

Basic metrics of precision (P), recall (R), and F-measure (F) are often used to evaluate various NLP tasks. Precision, (1) formula, shows the percentage of correctly resolved (C) coreference expressions against the actual number of provided coreferences (A) by the annotator:

(1) \begin{equation} P = \frac{C}{A} \end{equation}

Recall, (2) formula, shows the percentage of correctly resolved (C) coreference expressions against the total amount (T) of expressions pre-annotated in the text:

(2) \begin{equation} R = \frac{C}{T} \end{equation}

While the precision metric is rather straightforward, the recall has certain limitations. For example, not all coreferences might be in the scope of the research. As a result, the total amount of pre-annotated expressions might vary even if the evaluation is run against the same text corpus.

There have been suggestions made for result reporting guidelines proposing additional metric called resolution rate (RR), (3) formula, that would replace recall and next to the total amount of pre-annotated expressions would add coreferences that were excluded (E) by the annotator that is being evaluated (Byron Reference Byron2001):

(3) \begin{equation} \text{RR} = \frac{C}{T+E} \end{equation}

The obvious question here is, how to define what is excluded and what should not be covered by coreference resolution in general? In related literature, there are many different types of expressions (presuppositions, appositions, etc.) that sometimes are treated as coreferences by some researches and not treated as such by others (Ceberio et al. Reference Ceberio, Aduriz, de Ilarraza and Garcia-Azkoaga2018; Hou, Markert, and Strube Reference Hou, Markert and Strube2013; Rösiger and Teufel Reference Rösiger and Teufel2014; Souza et al. Reference Souza, Glauber, de Oliveira, Sena and Claro2017; Van Deemter and Kibble Reference Van Deemter and Kibble1999).

Lastly, F-measure, (4) formula, is a harmonic mean of precision and recall. There is also a possibility, (5) formula, to assign an additional weight to either precision or recall. Newer metrics usually provide different formulas for precision and recall calculations, while F-measure calculations remain largely unchanged:

(4) \begin{equation} F = \frac{2PR}{P+R} \end{equation}

(5) \begin{equation} F_{\beta } = \frac{(\beta ^{2}+1)PR}{(\beta ^{2})P+R} \end{equation}

3.1.2 Trivial, nontrivial, and critical success rates

Mitkov proposed to calculate three separate scores depending on the complexity of the coreference expression (Mitkov Reference Mitkov2014). He defines N as a set of all coreferences present in the evaluation and S as a set of correctly resolved coreferences by the annotator. Following that K is defined as a set of resolved trivial coreferences where each referent has only one candidate antecedent. And M is defined as a set of resolved coreferences where each referent has more than one candidate, but the correct resolution is made by applying gender and number agreement. With these variables success rate, (6) formula, nontrivial success rate, (7) formula, and critical success rate, (8) formula, are calculated:

(6) \begin{equation}{\text{success rate}} = \frac{S}{N} \end{equation}

(7) \begin{equation}{\text{non-trivial success rate}} = \frac{S-N}{N-K} \end{equation}

(8) \begin{equation}{\text{critical success rate}} = \frac{S-N-M}{N-K-M} \end{equation}

Since the critical success rate evaluates more complex coreference expressions, it is considered to be the most important metric of the proposed three.

3.1.3 MUC link-based metric

An alternative strategy was proposed for MUC-6 evaluation (Vilain et al. Reference Vilain, Burger, Aberdeen, Connolly and Hirschman1995). The proposed model is link-based and assumes that each reference links two mentions, and it attempts to solve the transitivity problem. For example:

• In the text, there are three coreferences marked: A $\rightarrow$ B, B $\rightarrow$ C, and D $\rightarrow$ E.

• Annotator that is being evaluated marks: A $\rightarrow$ C and D $\rightarrow$ E.

Going with the basic precision metric, it would get 1/2 score and basic recall would get a 1/3 score. But assuming that A, B, and C have a transitive relationship, it is reasonable to claim that A $\rightarrow$ C marking is correct as well. The proposed model constructs two groups of equivalence classes. Gold set:

• {A B C} and {D E}

Response set:

• {A C} and {D E}

For recall calculation, the size of the gold set class is taken as S, and it is subtracted by the number of partitions required from response set class p(S) to match it. Then each equivalence class is added up for total recall. The author proposes to calculate recall, (9) formula, by using the size of S and p(S) sets:

(9) \begin{equation} R_{T} = \frac{\sum |S| - |p(S)|}{\sum |S| - 1} \end{equation}

For the precision process is inverse, (10) formula, the size of response set class is taken as S’ and it is subtracted by the number of partitions required from gold set class p(S’) to match it. Then each equivalence class is added up for total precision:

(10) \begin{equation} P_{T} = \frac{\sum |S'| - |p(S')|}{\sum |S'| - 1} \end{equation}

As the author notes, such an approach works only with equivalence classes and when the transitivity is enforced. It also favors results that over-merge entities. For example, if all mentions of different discourse-world entities in the text were merged into one coreference chain, then it would result in a 100 $\%$ recall and very high precision score.

3.1.4 B-cubed (B $^3$ ) metric

This mention-based metric was proposed as a response to MUC-6’s evaluation model. It raises the important question of not all precision errors being equal when looking at the task from the information extraction viewpoint (Bagga and Baldwin Reference Bagga and Baldwin1998). For example, we have three different equivalence classes: {A B}, {C E}, and{D F G}. If the annotator would make a mistake by marking B $\rightarrow$ C relationship and as such merging the first two classes, then it should be considered as a smaller error than if it marked E $\rightarrow$ D relationship and merged the last two classes. The weight of the error is based on the size of the newly created class. This is relevant to information extraction tasks, since the size of the error can greatly impact the result. On the other hand, from a linguistic standpoint, both errors could be treated equally.

Precision ( $P_i$ ) for each entity is calculated, (11) formula, by taking the number of correctly annotated entities in the equivalence class (C) and the total number of entities in the equivalence class (A):

(11) \begin{equation} P_{i} = \frac{C}{A} \end{equation}

Recall ( $R_i$ ) for each entity is calculated, (12) formula, by taking the number of correctly annotated entities in the equivalence class (C) and the total number of entities in the pre-annotated equivalence class (T):

(12) \begin{equation} R_{i} = \frac{C}{T} \end{equation}

Then final precision, (13) formula, and recall, (14) formula, are calculated. All (N) previously calculated precision ( $P_i$ ) and recall ( $R_i$ ) values are added up and multiplied by their assigned weight ( $w_i$ ). By default, the author suggests dividing 1 by the number of total entities present in the text. But if required weights can be altered for each specific entity:

(13) \begin{equation} \text{Precision} = \sum _{i=1}^{N} (w_i * P_i) \end{equation}

(14) \begin{equation} \text{Recall} = \sum _{i=1}^{N} (w_i * R_i) \end{equation}

One of the arguments in favor of B-cubed against the MUC link-based approach was that MUC evaluation did not deal with singleton mentions. Yet, if the annotator marked all mentions as singletons B-cubed evaluation would result in 100 $\%$ precision.

3.1.5 ACE value

This metric was created for the ACE task (Doddington et al. Reference Doddington, Mitchell, Przybocki, Ramshaw, Strassel and Weischedel2004). It scores entities, relations, and events separately. The value is computed by counting the number of following errors: missed mentions, false positives, and misclassifications. Calculation of entity, composed of all (N) its mentions, value can be seen in (15) formula:

(15) \begin{align} \text{Value}_{\text{response}\_\text{entity}} = \text{Entity}\_\text{value}(\text{response}\_\text{entity}) \cdot \sum _{i=1}^{N} (\text{Mention}\_\text{value}(\text{response}\_\text{mention}_{i})) \end{align}

Entity_value assigns value depending on whether the same entity is present in the gold set. Mention_value assigns value to each mention of the entity based on its presence in the gold set. Each error is assigned a weight based on the type of entity (person, location, etc.) and mention type (nominal, pronominal, etc.); therefore, it does include some linguistic information in the evaluation process.

ACE value is considered to be task-specific and not very useful for general purpose coreference evaluation (Zitouni Reference Zitouni2014). Furthermore, it has been criticized for being hard to interpret (Luo Reference Luo2005).

3.1.6 CEAF metric

CEAF is an entity-based metric (Luo Reference Luo2005) and attempts to evaluate similarities between entities. Entities, in this case, are similar to coreference chains – all mentions of one object in the text form one entity. It provides two ways of scoring the coreference resolution approach, mention-based and entity-based. Both use R (gold set) and S (response set) for calculations.

Entity-based approach (CEAFE) measures, (16) formula, how many same mentions two entities (R and S) share. It can also function as F-measure, (17) formula:

(16) \begin{equation} \phi = |R \cap S| \end{equation}

(17) \begin{equation} F(R, S) = \frac{2|R \cap S|}{|R|+|S|} \end{equation}

The mention-based approach (CEAFM) calculates recall, (18) formula, and precision, (19) formula, separately:

(18) \begin{equation} \text{Recall} = \frac{\phi (g^*)}{\sum _{i=1}^{N} \phi (R_i, R_i)} \end{equation}

(19) \begin{equation} \text{Precision} = \frac{\phi (g^*)}{\sum _{i=1}^{N} \phi (S_i, S_i)} \end{equation}

Here, $g^*$ represents Kuhn–Munkers algorithm, (20) formula, that is used to find the best mapping of the two entities. $R^*_m$ refers to gold set subset where $g^*$ is attained:

(20) \begin{equation} \phi (g^*) = \sum _{R \epsilon R^*_m} \phi (R, g^* (R)) \end{equation}

One of the flaws of this approach is that it does not take into consideration unaligned entities in the response set. The annotator might make a mistake and create two entities instead of one. CEAF would ignore the second entity even if it had multiple right mentions linked.

3.1.7 CoNLL score

CoNLL score is not a separate evaluation metric, but it is often used in the coreference evaluation. During CoNLL-2012 shared task on coreference resolution, it was decided that MUC, B $^3$ , and CEAF metrics have their benefits and drawbacks (Pradhan et al. Reference Pradhan, Moschitti, Xue, Uryupina and Zhang2012). Therefore, instead of introducing a completely new metric, it was decided to take an average of their F-measures, (21) formula, as the evaluation score:

(21) \begin{equation} \text{CoNLL} = \frac{F_{\text{MUC}}+F_{B^3}+F_{\text{CEAF}}}{3} \end{equation}

This approach was originally proposed earlier (Denis and Baldridge Reference Denis and Baldridge2009), but it is not clear why the average of three flawed numbers would not result in a fourth flawed number (Moosavi and Strube Reference Moosavi and Strube2016).

3.1.8 BLANC

BLANC is a link-based approach that adapts the Rand index (Luo et al. Reference Luo, Pradhan, Recasens and Hovy2014; Pradhan et al. Reference Pradhan, Luo, Recasens, Hovy, Ng and Strube2014; Recasens Reference Recasens2010). It constructs four sets. There are two gold sets, one representing all coreference links ( $C_k$ ) in the text and another representing all non-coreference links ( $N_k$ ). Same for response set, $C_r$ and $N_r$ .

Recall, (22) and (23) formulas, and precision, (24) and (25) formulas, are calculated for both coreference and non-coreference links:

(22) \begin{equation} R_c = \frac{|C_k \cap C_r|}{|C_k|} \end{equation}

(23) \begin{equation} R_n = \frac{|N_k \cap N_r|}{|N_k|} \end{equation}

(24) \begin{equation} P_c = \frac{|C_k \cap C_r|}{|C_k|} \end{equation}

(25) \begin{equation} P_n = \frac{|N_k \cap N_r|}{|N_k|} \end{equation}

After this F-measure is calculated for both corefering and non-corefering links. Their average is used as BLANC’s final score. The problem with this approach lies in the fact that if the text has a high number of corefering links, then naturally it also will have a very high number of non-corefering links due to different coreference chains not referring to each other. This might result in higher precision and recall values than if the same annotator marked the text with fewer coreference expressions in it.

3.1.9 LEA metric

LEA attempts to combine link and entity-based approaches for coreference resolution (Moosavi and Strube, Reference Moosavi and Strube2016). It is one of the newest evaluation methods and attempts to tackle various issues with previously covered metrics. It has a weighting mechanism called importance, but it functions similarly to B $^3$ weights. It is based on the size of the entity ( $|e|$ ) but can be adjusted according to domain needs. Additionally, the number of links, (26) formula, for each entity (e) with the number of mentions (n) is calculated:

(26) \begin{equation} \text{links}(e) = n * \frac{n - 1}{2} \end{equation}

As in other approaches, gold set (k) and response set (r) sets are used for recall, (27) formula, and precision, (28) formula, calculations. For precision, the role of gold and response sets are reversed:

(27) \begin{equation} R = \frac{\sum _{k_i \epsilon K} \left(|k_i|*\sum _{r_j \epsilon R}\frac{\text{links}|k_i \cap r_j|}{\text{links}|k_i|}\right)}{\sum _{k_z \epsilon K} (|k_z|)} \end{equation}

(28) \begin{equation} P = \frac{\sum _{r_i \epsilon R} \left(|k_i|*\sum _{k_j \epsilon K}\frac{\text{links}|r_i \cap k_j|}{\text{links}|r_i|}\right)}{\sum _{r_z \epsilon R} (|r_z|)} \end{equation}

A common issue with linguistically agnostic metrics is that they treat coreference evaluation as a generic clustering problem. But in practice, a hierarchy of importance can be established, where a definitive noun phrase stating the full name of the person has a higher value than a generic pronoun that might refer to that person (Chen and Ng Reference Chen and Ng2013). This results in the possible loss of semantic information being not addressed in the linguistically agnostic evaluation metrics (Holen Reference Holen2013).

3.2 Linguistically aware evaluation metrics

One of the noted issues with linguistically agnostic metrics is that they treat coreference evaluation as a generic clustering problem. This results in the possible loss of semantic information being not addressed in the linguistically agnostic evaluation metrics. While not as important in linguistic researches, this is a vital problem for information extraction tasks.

3.2.1 LMetrics

LMetrics (Chen and Ng Reference Chen and Ng2013) proposes to solve this problem by extending some of the already existing metrics. Authors identified the common weight functions in MUC, B $^3$ , and CEAF metrics:

• Weight of common subset in response and gold sets (w $_c$ ).

• Weight of gold set (w $_k$ ).

• Weight of response set (w $_s$ ).

Then these weight functions are redefined into linguistically aware versions: w $^L_c$ , w $^L_k$ , and w $^L_s$ . For example, w $_c$ is redefined, in (29) formula:

(29) \begin{equation} w^L_c(C^i_j) = \left\{\begin{array}{ll} \sum _{e_l \epsilon E}w_l(e_l) & \text{if}(C^i_j) \gt 1 \\ w_{\text{sing}} & \text{if} |(C^i_j)|, |K_i|, |S_j| = 1 \\ 0 & \text{otherwise} \end{array}\right\} \end{equation}

Here, e $_l$ is coreference link, and C $^i_j$ is a common subset in response (S $_j$ ) and gold (K $_i$ ) sets. W $_l$ is additional weight based on the coreference link: name, nominal, or pronominal. If the coreference set is singleton, then a different weight is used (w $ _{\text{sing}}$ ).

3.2.2 ARCS

Instead of redefining existing metrics, Tuggener proposes new ARCS evaluation framework (Tuggener Reference Tuggener2014, Reference Tuggener2016). To determine if the suggested link is correct, separate strategies are suggested for different types of higher-level applications that would use coreference annotations:

• An application that investigates distributions and patterns of entity occurrences in discourse. In such a case, immediate antecedent should be selected for referent.

• Summarization and machine translation applications. In such case, the closest nominal antecedent should be selected for referent.

• Query-driven applications. In such a case, anchor mention should be selected for referent. Anchor mention is the first nominal mention in the coreference chain. It is assumed that the first nominal mention in the text best describes the underlying discourse-world entity.

Four scores are aggregated over gold and response sets:

• TP, true positive, where the referent is in the gold and response sets and the suggested link is correct.

• WL, wrong linkage, where the referent is in the gold and response sets, but the suggested link is incorrect.

• FP, false positive, where the referent is in the response set, but not in the gold one.

• FN, false negative, where the referent is in the gold set, but not in the suggested one.

F-measure is the standard harmonic mean of precision, (30) formula, and recall, (31) formula:

(30) \begin{equation} P = \frac{\text{TP}}{\text{TP + FP + WL}} \end{equation}

(31) \begin{equation} R = \frac{\text{TP}}{\text{TP + FN + WL}} \end{equation}

3.2.3 Prague Anaphora Score

Similar to Tuggener’s approach is Prague Anaphora Score (Novák Reference Novák2018). Next to four ARCS scores, it adds spurious zero positive (SZP) variable that deals with ellipses that should not be resolved. It is language-dependent and is used in precision, (32) formula, calculation. Recall and F-measure calculations are the same as in ARCS:

(32) \begin{equation} P = \frac{\text{TP + SZP}}{\text{TP + FN + WL + SZP}} \end{equation}

However, Prague Anaphora Score does not use any of the three strategies outlined in ARCS to determine the correctness of the response set. Instead, a link to any antecedent in the chain, which does not refer to another antecedent, is considered valid. Ideally, the coreference chain should contain only one such element.

3.2.4 PARENT

PARENT metric (Kaczmarek and Marcińczuk Reference Kaczmarek and Marcińczuk2015) also attempts to better evaluate correct information returned by the coreference resolution approaches. It divides all mentions present in the text into two disjoint subsets: defining and non-defining. Defining mentions are those that carry enough semantic information that allows them to identify as discourse-world entities. A non-defining subset can be further divided into referring and ignored, not relevant for the evaluation process, subsets. This provides certain flexibility for the evaluation process. For example, if we want to evaluate pronoun linkage to definitive nouns, then all other types of mentions would be contained in an ignored subset. It focuses on finding relations between referring and defining mentions, since they are more valuable than relations between two different referring mentions.

All mentions of one entity constitute one gold set cluster ( $C_i^{\text{key}}$ ) and a response set cluster ( $ C_i^{\text{sys}} $ ). Relations for gold (G) set are defined in (33) formula:

(33) \begin{equation} G = \{(m^i_{rl},C_i^{\text{key}})|\forall C_i^{\text{key}} \epsilon C^{\text{key}}\forall m^i_{rl}, \epsilon C_i^{\text{key}} \} \end{equation}

Here, $m^i_{rl}$ is referring to mention that belongs to the gold set cluster. Relations for response (S) set are defined in (34) formula:

(34) \begin{equation} S = \{(m^i_{rl},[[m^i_{dk}]]\text{key})|\forall C_i^{\text{sys}} \epsilon C^{\text{sys}}\forall m^i_{rl}, \epsilon C_i^{\text{sys}} \forall m^i_{dk}, \epsilon C_i^{\text{sys}} \} \end{equation}

Here, $m^i_{rl}$ is referring mention that belongs to response set cluster and $m^i_{dk}$ is defining mention that it links to. Precision, (35) formula, and recall, (36) formula, are calculated using G and S. F-measure is calculated in a standard way:

(35) \begin{equation} P = \frac{|G \cap S|}{|S|} \end{equation}

(36) \begin{equation} R = \frac{|G \cap S|}{|G|} \end{equation}

While the problem of all mentions being treated equally has been addressed by these linguistically aware metrics, they still lack in extendibility. Extendibility in this context determines how easy it would be to add additional linguistic information into the evaluation process. The need to introduce new coreference data might come from the requirements of the higher-level applications that are being developed. New data would lead to potential new types of errors that would not be covered by these metrics. Due to that linguistically aware evaluation metrics should be easily expandable and be able to address potential new types of errors.

3.3 Coreference resolution error analysis

During the development of coreference resolution approach phase, many different types of coreferences are identified and analyzed (Delmonte Reference Delmonte2002; Fischer Reference Fischer2015; Hou et al. Reference Hou, Markert and Strube2013; King and Lewis Reference King and Lewis2018; Saeboe Reference Saeboe1996; Van Deemter and Kibble Reference Van Deemter and Kibble1999). Different types often require different techniques to resolve. But this information is relevant not only for the development of new approaches but also for interpretations of the results. Currently, coreference type identification is not addressed by any coreference evaluation metric.

This problem is partially addressed by coreference resolution error categorization tools (Kummerfeld and Klein Reference Kummerfeld and Klein2013). They take the response sets from the annotators that participated in ConLL 2011 task and attempt to categorize underlying error types. But since coreference resolution evaluation metrics do not require providing information on what kind of coreference was resolved, such tools are limited to categorizing along the part of speech and span errors. Often this does not provide the required detail to properly evaluate the performance, since very different types of coreferences can be constructed with the same type of speech. For example, a name repetition, certain feature, synonym, metonym, or hypernym/hyponym can be used to refer to the same discourse-world entity. In all cases, noun phrase would be used. Therefore, stating that a specific coreference resolution approach has incorrectly resolved a certain number of noun phrases would not be informative enough to determine the exact weak points of the coreference resolution approach.

Another option would be adding such information to coreference resolution response sets (and gold sets) after the fact with automated tools, but it would introduce additional errors since the determination of what kind of coreference relationship two phrases have is not a trivial task. Additionally, after adding such information to response sets, it becomes questionable if it is the coreference resolution system being evaluated or these were the tools that added this information.

In many coreference resolution systems, especially rule-based ones, such information is already available internally since usually different strategies are used for solving different coreference constructions. Therefore, the main issue here is that coreference resolution evaluation metrics do not require providing this information in response sets.

4.1 Coreference annotation scheme

To provide a context for our proposed evaluation strategy at first, we introduce the coreference annotation scheme that was used during the development. Usually, the coreference annotation scheme does not influence coreference resolution evaluation when applying existing evaluation approaches. Our proposed evaluation strategy is a bit different. It requires dominant mentions (or other, similar concept, covered in Section 4.2) and that annotation scheme would classify different coreference expressions (covered in this section). Different annotation schemes might use different classification, important point is that classification is done.

Our coreference annotation scheme and the first version of coreference resolution algorithm were implemented as part of NLP tools for the Lithuanian language in 2014. It allowed us to create a Semantic Search Framework for Lithuanian Language (SSFLL) Internet corpus extracted from public news portals (Vileiniškis, Šukys, and Butkienė Reference Vileiniškis, Šukys and Butkienė2015). Initial resolution approach was limited to pronoun resolution only but eventually was expanded to cover nouns as well. For this reason, coreference annotation scheme for the Lithuanian language was updated as well and the last version can be seen in Table 1 (Žitkus and Butkienė Reference Žitkus and Butkienė2018).

Table 1. Structure of coreference annotation scheme

A distinguishable feature of our annotation schema is that it requires to specify to which class each identified coreference belongs. This information can be valuable to a higher-level application. Furthermore, enforcing such classification allows us to evaluate implemented coreference resolution more precisely, especially in cases when for different classes of coreferences a separate resolution algorithm (or model) is implemented.

Proposed coreference annotation scheme covers only endophoric expressions and is of four levels. In the first level, coreference dependency to one of the five broad classes is specified: pronominal (p), nominal (further divided into generic (g) and definitive nouns (d)), ellipsis (e), and adverbs (a). Further in the second level, more specific classes, specifying their parent classes, are indicated. At the moment, in the second level, only nominal, pronominal, and ellipsis coreferences are specified. Third and fourth levels are global and are used by all types of coreferences. The third level determines if the referring object is pointing backward (a), forward (p), or is the direction irrelevant (i). The fourth level defines if the referring object is referring to one antecedent (s) or group of antecedents (g). Third option is for those cases where, due to authors intention or mistake, it is ambiguous (a) to which antecedent referring object is referring to.

Technically, all four level features of the specific coreference are encoded using certain letters specified in brackets (see Table 1). These letters are combined to define a specific code for each type of coreference. For example, if in cases where the coreference is pronominal (p), personal (p), pointing backward (a) and refers to multiple antecedents (g), then the final combination can be reduced to “ppag” as the code of that specific coreference:

• Tom and Jim are very good friends. They know each other since second grade.

• Word “they” refers to “Tom” and “Jim.”

In the case of adverbs, since they do not have the second level specified, they would form codes like this: “a-is.” Adverbs do not have three-letter code because we want to preserve a common format in case of future research that would make second-level classification of adverbs meaningful.

Same entity can be mentioned multiple times in the text with different phrases and if we linked them in different order, then different annotations might have different coreference types specified for the same text. Due to that we recommend linking each referent to the closest, more dominant antecedent. Determination of the more dominant antecedent is covered in Section 4.2.

Since Lithuanian language has free word order, one of the goals of this annotation scheme was to have a scheme that would produce comparable results for different coreference expressions regardless of the used word order. This fits the overall trends in annotation schemes. For example, new time expressions and named entity annotation scheme TOMN/UGTO (Zhong et al. Reference Zhong, Cambria and Hussain2020) attempts to solve similar problem—same date written in different formats.

It is important to mention that in our evaluation model when we refer to coreference class we mean first-level values. When we refer to coreference type, we mean full four-letter code.

As can be seen, our annotation scheme does not cover cases where the discourse-world entity is mentioned only once, such cases are usually called singletons. We assume that the scope of the coreference resolution task requires at least two mentions (one antecedent and one referent) of the same entity in the text that is being analyzed. Singletons can be successfully identified by other NLP components such as mention identification, which is very important to coreference resolution approaches, but at the same time should not necessarily be considered as part of coreference resolution itself.

It could be argued that such information could be added at a later date by semantic annotator (or another higher-level application), but it would be just duplicating work already done by coreference resolution approach and likely have worse results since it is not designed for identifying and resolving coreferences.

4.2 Dominant mentions

The same discourse-world entity can be referenced in the text by different mentions: proper noun, generic noun, pronoun, or a gap. In linguistically agnostic evaluation strategies, all of these different mentions are treated as equal. Looking from the information extraction viewpoint and the needs of higher-level applications, it is obvious that it should be possible to determine which of those mentions best describes a discourse-world entity that it refers to. Naturally, such mentions tend to be semantically richest mentions. Due to that, other linguistically aware evaluation metrics introduced concepts like anchor mentions and defining mentions that were overviewed in Section 3.2. They help in evaluating whether the coreference resolution approach correctly identified the most relevant mention(s) of the entity. For the same purpose, we use the concept of dominant mention.

A dominant mention is an expression that carries the richest semantics or describes most precisely the discourse-world entity (Ogrodniczuk et al. Reference Ogrodniczuk, Głowińska, Kopeć, Savary and Zawisławska2013). The authors of this paper propose ordering expressions by their dominance in the following order: full proper noun, abbreviated proper noun, partial proper noun, NP, and ellipsis referring back to the same object. Certain expressions like pronouns, adverbs, and other types of ellipsis cannot be dominant, since they do not carry much semantic information on their own. If two or more expressions are of the same dominance level, then preference should be given to expression that appeared earlier in the text.

Let’s take this abridged text fragment for an example:

• Early in the morning president declared that $\ldots$ He hopes $\ldots$ . This was unusual for B. Obama. Earlier in the year, Obama was criticized $\ldots$ But his position $\ldots$ It looks like Barack Obama is not doubting himself. But critics said that Barack Obama is $\ldots$

From this text fragment, we can create the following collection of coreferences referring to the same discourse-world entity: President $\leftarrow$ He, He $\leftarrow$ B. Obama, B. Obama $\leftarrow$ Obama, Obama $\leftarrow$ His, His $\leftarrow$ Barack Obama, Barack Obama $\leftarrow$ Himself, Himself $\leftarrow$ Barack Obama.

To determine the dominant mention, all mentions of the same entity should be listed first. This can be done either at the same time as individual coreference relationships are resolved or after it. It depends entirely on the specific implementation. Listed mentions have to be ordered by their appearance in the text starting from the earliest to the latest. Going with the previous example, we would have this list of mentions created:

• { [President] $_1$ [He] $_2$ [B. Obama] $_3$ [Obama] $_4$ [His] $_5$ [Barack Obama] $_6$ [Himself] $_7$ [Barack Obama] $_8$ }

Next pronouns are filtered out since they do not carry much semantic information on their own:

• { [President] $_1$ [B. Obama] $_3$ [Obama] $_4$ [Barack Obama] $_6$ [Barack Obama] $_8$ }

Then elements are ordered by their dominance:

• { [Barack Obama] $_6$ [Barack Obama] $_8$ [B. Obama] $_3$ [Obama] $_4$ [President] $_1$ }

After these steps, the first element in the list is selected as the dominant mention. The sixth overall mention gets preference over the eighth one due to it being present earlier in the text. Same mention is selected as dominant mention for the entire chain. All remaining mentions are treated as referents of the selected dominant mention. But their types of coreference that were initially assigned to them are preserved, this is done so that type validity can be checked when performing the evaluation. Asides from coreference type preservation, dominant mentions could be integrated into any other annotation scheme without any issues.

If anchor mentions were used instead of proposed dominant mentions, then the first mention present in the text, in this case, “President,” would be selected. Certainly, it is not the mention present in the text that best describes the discourse-world entity. Defining mentions would take all named entities in this case and treat them as equally important, yet it is natural to assume that “Barack Obama” better describes the discourse-world entity than “B. Obama” and due to that is more important. Asides from evaluation strategies, Stanford CoreNLP solution has incorporated representative mentions into their coreference annotation scheme (Lee et al. Reference Lee, Peirsman, Chang, Chambers, Surdeanu and Jurafsky2011).

Representative mentions are similar to dominant mentions but do not take in mind the order in which mentions were presented in the text. Additionally, instead of making a distinction between full, abbreviated and partial named entities preference is given to the longest mention. While most of the time it provides the same results, it can also cause inaccuracies. For example, the last name of the person usually better describes him than his first name, yet the first name can be longer and, in such case, a less descriptive proper noun would be selected. Due to these reasons, we believe that dominant mentions provide an advantage over the anchor, representative and defining mentions.

Outside of evaluation purposes, dominant mentions can also be useful for the resolution of exophoric expressions. If we can determine semantically richest mentions of the same entity from two or more different data sources, then it is easier to determine if they refer to the same discourse-world entity and are coreferent or not.

4.3 Proposed evaluation strategy

In this section, a new, linguistically aware evaluation strategy is presented. Compared to other linguistically aware evaluation strategies, it adds additional linguistic information with coreference type identification and dominant mention usage. Furthermore, classification of errors (with added coefficients) allows adjusting the evaluation process if certain errors are deemed to be more, or less, severe.

Concepts and their relationships which we use to explain the evaluation strategy are depicted in Figure 2 using UML class diagram notation. Concepts relevant to the coreference annotations themselves (the Annotation package) are defined in Appendix A, Table A1. The Evaluation package covers concepts relevant to the process of the evaluation, and it is defined in Appendix A, Table A2.

Figure 2. Conceptual data model of coreference evaluation

As shown in Figure 2, annotations are classified into six classes: Correct annotation, Correct annotation with the wrong type, Correct annotation with the wrong dominant mention, Correct annotation with wrong dominant mention and type, Missed annotation, and False positive annotation. While other linguistically aware evaluation metrics have a similar classification as dominant mentions (Tuggener Reference Tuggener2016; Kaczmarek and Marcińczuk Reference Kaczmarek and Marcińczuk2015), to our knowledge they are not being combined with coreference type classification like in our evaluation strategy.

Asides from dominant mentions, we do not make any distinctions between types of speech used in coreference expression. In the information extraction context, it is important to determine not only what phrases are used to construct coreference relationships but also what kind of semantic information can be extracted near them. Therefore, a generic noun, or even a pronoun, can be linked to more valuable semantic information than a definitive noun. Different types of systems might also value the same semantic information differently. For example:

• Tom was feeling sick. The boy wandered the house for a while until he decided to call the ambulance.

In this example, “The boy” mention itself is semantically richer than “he” mention. The pronoun “he” implies gender and number of the discourse-world entity, while the noun phrase “The boy” has those too and additionally implies the age of the discourse-world entity. Yet semantic information near “he” mention is more valuable: fact that he called the ambulance would be more important in most cases than the fact that he wandered the house for a while. It depends entirely on the sentence and the context, therefore, assigning a higher value to, for example, noun than to pronoun is not useful and can be counterproductive as in the given example.

As explained in Section 3.3, including coreference type into annotation would increase the overall quality of the error analysis. But such information can be valuable for higher-level application as well.

For our example, we used English text and Stanford CoreNLP coreference annotator (text and annotation available in Appendix B). One of the created coreference chains has the following structure: We $\leftarrow$ We $\leftarrow$ us $\leftarrow$ We $\leftarrow$ We $\leftarrow$ We $\leftarrow$ We $\leftarrow$ We.

It is unlikely that someone is going to search for information with “we” or “us” keywords. And even in such a case, it would be difficult to find useful information since pronouns are very common in various documents. For this reason, such coreference annotation is not very useful from the higher-level application (like semantic search) perspective. If coreference type would be included in the annotation, then the application could be optimized by filtering out coreferences that are not relevant to its tasks.

In our opinion, having coreference type in coreference annotations can provide many fine-tuning opportunities to higher-level applications. For example, coreference annotator has high precision with synonyms, but noticeably lower precision with metonyms. With coreference type provided semantic search application can rank query results by giving priority to synonyms over metonyms since they are more likely to be correct. Therefore, it is worthwhile to include such information in coreference annotations and evaluate them during the evaluation process.

However, naturally, some coreference types like repetition, partial repetition, or abbreviation might be deemed to be not informative enough and coreference resolution approach should not be penalized for incorrectly identifying them. For example:

• Barack Obama was elected the 44th president of the United States on Tuesday. B. Obama is the first black US president. The newly elected president will be in charge of the armed forces. He is scheduled to appear at the press conference tomorrow.

Here we have “B. Obama,” being an abbreviation of “Barack Obama” and “president” a feature (referring to his specific occupation). Coreference resolution approach might label “B. Obama” as a partial repetition of “Barack Obama,” which would be technically incorrect, but it still allows us to identify that this is an alternate name for the same discourse-world entity. On the other hand, if “president” was mislabeled as a partial repetition then it could cause problems since it is not an alternate name, but a specific feature of the discourse-world entity by which it was referred to. Which type identification errors can be ignored should be determined either by a specific annotation scheme being used or higher-level application needs.

Going with previous example, coreference annotator might make a mistake and create two separate coreference clusters instead of one:

• Cluster A: Barack Obama, B. Obama

• Cluster B: president, He

Items in the second cluster will be assigned Correct annotation with the wrong dominant mention class since they are not linked to “Barack Obama.” Additionally, there will be one missing annotation connecting “president” to “B. Obama.” Additional penalties for creating misleading clusters are not applied. Calculation of precision and recall for this example are provided in Appendix C.

One of the issues with the evaluation process that is usually not addressed in other evaluation metrics is the overrepresentation of certain expressions in the corpus that evaluation was performed on. Usage of coreference expressions can vary depending on the type and style of the text. For example, technical manuals tend not to have many such expressions and avoid complex constructions in general, while literary works often employ them for stylistic and other purposes. Let’s assume that we have two coreference resolution approaches. The first one focuses on pronouns and solves them very well yet struggles with other expressions. The second one does well with all types of expressions. If the selected corpus is dominated by pronominal coreference expressions, then the first coreference resolution approach can score higher despite the second coreference resolution approach being more useful in general.

One solution to this problem is to run an evaluation with multiple different corpora and compare their results. This approach is not straightforward and unfortunately not applicable to less researched languages. For example, recent study on text classification lists 24 datasets for English language (Minaee et al. Reference Minaee, Kalchbrenner, Cambria, Nikzad, Chenaghlu and Gao2021). Less researched languages often have only few, or even one, such datasets. Another possibility is the usage of micro and macro F-measure averages.

Micro average pools the performance over the smallest possible unit, in the context of coreference resolution it would be all coreference annotations. High micro F score indicates that the coreference resolution approach has a good overall performance. On the other hand, macro average pools the performance from large groups, in the context of coreference resolution that would be different coreference classes (Manning et al. Reference Manning, Raghavan and Schütze2010). High macro F score indicates that the CR approach has good performance for each coreference class. Unfortunately, in related literature, it is rarely specified if micro or macro evaluation should be performed and it is usually assumed that micro is used by default. Some papers present micro and macro evaluation numbers for the developed coreference resolution approaches, but usually, it is also not specified and can cause confusion when interpreting provided results.

One of the main advantages of macro average is that it adjusts for imbalanced coreference class distribution. It could be argued that this is the case with natural language texts. For example, we are bound to find noticeably more nouns and pronouns in texts than an ellipsis. It is not realistic to expect that corpus would be constructed in such a way that each possible coreference class would be equally represented. Moreover, if such a corpus would be constructed, then it would have to be altered each time the annotation scheme was changed to adjust for possible imbalances created by that change. On the other hand, it could be argued that such imbalance actually represents discourse-world data and as such micro average is preferable. Due to that, we propose to use both micro and macro averages when evaluating coreference resolution approaches.

The separate precision, recall, and F-measure calculations for each coreference class are useful in case we want to find a specialized coreference resolution approach that is suitable for a specific task. While papers presenting new coreference resolution approaches often tend to detail how well certain types of coreferences are solved, coreference evaluation metrics themselves usually do not provide recommendations on how it should be done, or should it be done at all. We propose to always follow the classification of the annotation scheme that is being used and provide a separate evaluation for each coreference class when reporting results.

For the calculation of precision and recall, additional weighting coefficients are assigned to each coreference depending on which of the six annotation classes (see Figure 2 and Appendix A, Table A2) it was assigned to:

• A number of annotations assigned to Correct annotation (True Positive, TP) concept get $k_1$ coefficient.

• A number of annotations assigned to Correct annotation with the wrong type (Wrong Type, WT) concept get $k_2$ coefficient.

• A number of annotations assigned to Correct annotation with the wrong dominant mention (Wrong Linkage, WL) concept get $k_3$ coefficient.

• A number of annotations assigned to Correct annotation with wrong dominant mention and type (Wrong Type and Linkage, WTL) concept get $k_4$ coefficient.

• A number of annotations assigned to Missed annotation (False Negative, FN) and False positive annotation (FP) concepts do not get any coefficients.

These coefficients allow differentiating among different types of errors by assigning different values to them. The values of the coefficients range from 0 to 1. In our proposal, the values of the coefficients are proportionally lowered depending on how severe the error of a certain type is. These values are not universal as they could be a starting point for further refinements to the evaluation model. Current coefficients’ values are as follows:

• $k_1$ – 1;

• $k_2$ – 0.75;

• $k_3$ – 0.5;

• $k_4$ – 0.25.

The evaluation process is not tied to six annotation classes that are shown in the conceptual data model (Figure 2). Depending on the annotation scheme, it can have different numbers of classes. For example, if we wanted to evaluate how well coreference annotator resolves exophoric coreferences, then we would add new classes related to their evaluation. Or if we decided that type identification is not relevant to our evaluation, then we can remove second and fourth classes. Naturally, after such additions or subtractions number of coefficients, and their values, would also have to be adjusted accordingly.

The annotation scheme that was used in this work has five coreference classes, but the evaluation model is not tied to that number. There can be from 1 to n different coreference classes defined. Calculations of precision ( $P_i$ ), (37) formula, recall ( $R_i$ ), (38) formula, and F-measure ( $F_i$ ), (39) formula, for each coreferences class, are identical:

(37) \begin{equation} P_i = \frac{k_1\text{TP} + k_2\text{WT}+k_3\text{WL}+k_4\text{WTL}}{\text{TP + WT + WL + WTL + FP}} = \frac{\text{TP}+0.75*\text{WT}+0.5*\text{WL}+0.25*\text{WTL}}{\text{TP + WT + WL + WTL + FP}} \end{equation}

(38) \begin{equation} R_i = \frac{k_1\text{TP} + k_2\text{WT}+k_3\text{WL}+k_4\text{WTL}}{\text{TP + WT + WL + WTL + FN}} = \frac{\text{TP}+0.75*\text{WT}+0.5*\text{WL}+0.25*\text{WTL}}{\text{TP + WT + WL + WTL + FN}} \end{equation}

(39) \begin{equation} F_i = \frac{2P_iR_i}{P_i+R_i} \end{equation}

To diminish the impact of overrepresented classes of coreferences for final evaluation scoring, macro precision ( $ P_{\text{macro}} $ ), (40) formula, recall ( $R_{\text{macro}} $ ), (41) formula, and F-measure ( $F_{\text{macro}} $ ), (42) formula, are used. Here, $n_a$ is a number of coreference classes that coreference resolution approach attempted to resolve:

(40) \begin{equation} P_{\text{macro}} = \frac{\sum _{i}^{n_a}P_i}{n_a} \end{equation}

(41) \begin{equation} R_{\text{macro}} = \frac{\sum _{i}^{n_a}R_i}{n_a} \end{equation}

(42) \begin{equation} F_{\text{macro}} = \frac{2P_{\text{macro}}R_{\text{macro}}}{P_{\text{macro}}+R_{\text{macro}}} \end{equation}

Next, we also calculate micro precision ( $ P_{\text{micro}} $ ), (43) formula, recall ( $R_{\text{micro}} $ ), (44) formula, and F-measure ( $F_{\text{micro}} $ ), (45) formula:

(43) \begin{equation} P_{\text{micro}} = \frac{\sum _{i}^{n_a}k_1\text{TP}_i + k_2\text{WT}_i + k_3\text{WL}_i + k_4\text{WTL}_i}{\text{TP}_i + \text{WT}_i + \text{WL}_i + \text{WTL}_i + \text{FP}_i} \end{equation}

(44) \begin{equation} R_{\text{micro}} = \frac{\sum _{i}^{n_a}k_1\text{TP}_i + k_2\text{WT}_i + k_3\text{WL}_i + k_4\text{WTL}_i}{\text{TP}_i + \text{WT}_i + \text{WL}_i + \text{WTL}_i + \text{FN}_i} \end{equation}

(45) \begin{equation} F_{\text{micro}} = \frac{2P_{\text{micro}}R_{\text{miro}}}{P_{\text{micro}}+R_{\text{micro}}} \end{equation}

The purpose of these scores is to evaluate how well the coreference resolution approach resolves coreferences that it attempts to resolve. Naturally, the annotation scheme might have more coreference classes than the specific coreference resolution approach attempted to resolve. To determine how well the proposed coreference resolution approach covers the used annotation scheme, separate calculations should be made. For that purpose, we introduced precision ( $P_{\text{scheme}} $ ), (46) formula, recall ( $ R_{\text{scheme}} $ ), (47) formula, and F-measure ( $F_{\text{scheme}} $ ), (48) formula, values for annotation scheme coverage:

(46) \begin{equation} P_{\text{scheme}} = \frac{\sum _{i}^{n_a}P_i}{n} \end{equation}

(47) \begin{equation} R_{\text{scheme}} = \frac{\sum _{i}^{n_a}R_i}{n} \end{equation}

(48) \begin{equation} F_{\text{scheme}} = \frac{2P_{\text{scheme}}R_{\text{scheme}}}{P_{\text{scheme}}+R_{\text{scheme}}} \end{equation}

These look similar to macro formulas, but the difference is that division is performed not only by $n_a$ but also by $n$ —the number of coreference classes present in the annotation scheme. Scheme coverage score heavily penalizes coreference resolution approaches that do not attempt to solve certain coreference classes.

Overall, our presented evaluation strategy provides the following advantages:

1. 1. The use of both macro and micro averages allows diminishing the impact of imbalanced classes to the final score and at the same time provides a score that is more representative of the discourse-world data.

2. 2. Performing separate calculation for scheme coverage allows distinguishing between how well coreferences resolution approach is doing what it attempts to do and how well does it cover the annotation scheme.

3. 3. Addition of coreference type identification in the evaluation process allows to better identify the weak points of the evaluated coreference resolution approach.

4. 4. Combination of coreference type and dominant mentions to the evaluation process allows to better evaluate to what extent additional semantic information is added by the coreference resolution approach.

4.4 Compatibility with other annotation schemes

The evaluation process will be demonstrated with our annotation scheme, but it can easily work with other annotation schemes as well. The only requirements are that the annotation scheme would classify different coreference expressions and that mention that best describes the entity would be selected.

Our annotation scheme is divided into four levels and together they form a four-letter code that is used in the evaluation process. But for the process to work code can be of any length. This means that the annotation scheme can have two or three levels, and the evaluation process will function without problems. For example, Basque language EPEC-KORREF coreference corpus (Ceberio et al. Reference Ceberio, Aduriz, de Ilarraza and Garcia-Azkoaga2018) uses annotation scheme with three levels: type, subtype, and semantic relation. Not every type of coreference has a subtype or semantic relation value. In such cases, hyphen would be used for the second or third letter to indicate the lack of value. As a result, three-letter codes could be formed and used for the proposed evaluation strategy. For example, if coreference in this corpus was marked as nominal, no repetition, hyponym then, based on the first letters of the types, it could be transformed into “nnh” coreference type code. This code would then be used in exact same way as our presented codes in earlier sections.

Evaluation process would work as well with one level, for example, making distinction only between nominal and pronominal coreferences. However, authors of the paper believe that such classification would not be informative enough. More classification levels annotation scheme has more detailed evaluation process, and more valuable annotations can be to higher-level application.

4.5 Evaluation process

The aim of the experiment was to demonstrate the proposed evaluation strategy by evaluating existing coreference resolution component against Lithuanian Coreference Corpus (LCC) (Žitkus Reference Žitkus2018). These tools were chosen because they implement the annotation scheme that was presented in Section 4.1 and due to that make the evaluation process straightforward. For the experiment, the SSFLL NLP pipeline (Vileiniškis et al. Reference Vileiniškis, Šukys and Butkienė2015) was used, which includes these tools. The evaluation was made by analyzing 100 Lithuanian Internet news sites articles of politics and economy domains present in LCC. At the time, additional experiments were not carried out using other datasets due to them not providing detailed coreference type classification and (or) equivalent for dominant mentions. One of the goals for future work related to this research could be adapting existing English language datasets for this evaluation strategy.

The used coreference resolution approach (Žitkus et al. Reference Žitkus, Butkiene, Butleris, Maskeliunas, Damaševičius and Woźniak2019) attempts to solve certain pronominal and nominal coreferences. Additionally, evaluation of the same coreference resolution approach was done using ARCS, MUC, B $^3$ , and CEAFE. Full results of this evaluation are displayed in Table 2. As can be seen, results of our evaluation metric are not out of line with results achieved with other evaluation metrics. But in this section, we will highlight what advantages and opportunities our approach provides.

Table 2. Evaluation with different metrics

More detailed results, using proposed metric, are provided in Table 3. First column lists coreference classes: pronominal, generic nominal, and definitive nominal. The next six columns correspond to six classes of annotations that were detailed in Section 4.3. S^* is a sum of TP, WT, WL, WTL, and FN. Last three columns show precision, recall, and F-measure for each coreference class. Results for adverbial and ellipsis coreference classes are not provided, since the proposed approach does not attempt to solve them. Raw, not aggregated, data is available via GitHub (Žitkus Reference Žitkus2020).

Table 3. Evaluation of different coreference classes

Evaluation is made using the data from six annotation classes. As an example, calculations of P, R, and F for pronominal coreferences are presented in (49)–(51) formulas:

(49) \begin{equation} P_1 = \frac{k_1\text{TP} + k_2\text{WT}+k_3\text{WL}+k_4\text{WTL}}{\text{TP + WT + WL + WTL + FP}} = \frac{289+0.75*30+0.5*27+0.25*25}{289+30+27+25+29} = 82.8\% \end{equation}

(50) \begin{equation} R_1 = \frac{k_1\text{TP} + k_2\text{WT}+k_3\text{WL}+k_4\text{WTL}}{\text{TP + WT + WL + WTL + FN}} = \frac{289+0.75*30+0.5*27+0.25*25 }{289+30+27+25+182} = 59.9\% \end{equation}

(51) \begin{equation} F_1 = \frac{2P_1R_1}{P_1+R_1} = \frac{2*82.8*59.9}{82.8+59.9} = \frac{9919.44}{142.7} = 69.5\% \end{equation}

Main advantage of the proposed metric is that we can drill deeper and see more detailed results based not on coreference class but on coreference type (4-letter code). These data are provided in Appendix D, Tables D1–D3.

By analyzing this data for pronominal coreference resolution (Appendix D, Table D1), one can see that the coreference resolution approach resolves relative pronouns (peas) very well, but that it misses many (M column) personal pronouns (ppas). Additionally, reflexive pronouns that function as cataphora (prps), group, and ambiguous coreferences are not resolved at all. Such detailed information helps with error analysis and allows us to see which parts of the coreference resolution approach are sufficient enough (relative pronouns) and which need additional work (personal pronouns) or a new approach entirely (cataphoric reflexive pronouns, group, and ambiguous references).

For macro average calculations, we use coreference class value—pronominal, generic nominal, definitive nominal, adverbial, or ellipsis. But as we can see (Appendix D, Table D1), we could use full 4-letter code instead and get more specific results. This is potential direction for future researches.

Generic nominal coreference resolution gets a rather low score (38.7%) and at first glance evaluated coreference resolution approach is not very useful for resolving such coreferences. But looking closer at the data (Appendix D, Table D2), we can see that it struggles with most of these coreferences but performs much better when the discourse-world entity is referred to by its feature (gfas). For example, if a politician is being referenced by using his occupation (minister, president, and parliamentarian) or another feature (veteran, firebrand politician, man, and women), then this coreference resolution approach might be suitable for annotating texts that heavily use such type of coreferences. Therefore, coreference type identification can help in selecting the right coreference resolution approach for narrow and specific tasks. With other evaluation metrics, such information might be either lost entirely or difficult to determine.

Evaluated coreference resolution approach solves definitive nominal coreferences rather well, but as can be seen in the detailed data (Appendix D, Table D3) it missed all metonyms (dmis). This is a rather important detail if the coreference resolution approach would be used in the annotation of foreign policy texts where metonym relationship is rather common. For example, Russia, Moscow, and Kremlin are often used in such texts to refer to the same discourse-world entity (Russian government), and our coreference resolution approach is likely to miss all of them. Due to that, this coreference resolution approach might not be suitable for texts focusing on international politics. Knowing this is very valuable when selecting tools for NLP pipeline, but without coreference type identification we would not have such information.

As we can see from these results, doing a separate evaluation for each coreference class gives more clarity to the overall performance of the coreference resolution approach and helps in identifying with what specific types of coreferences it struggles with. Next, we calculate macro precision, (52) formula, recall, (53) formula, and their F-measure, (54) formula. And we do the same for micro averages in (55)–(57) formulas:

(52) \begin{equation} P_{\text{macro}} = \frac{\sum _{i}^{n_a}P_i}{n_a} = \frac{82.8+77.1+97.6}{3} = 85.8\% \end{equation}

(53) \begin{equation} R_{\text{macro}} = \frac{\sum _{i}^{n_a}R_i}{n_a} = \frac{59.9+25.8+91.5}{3} = 59.1\% \end{equation}

(54) \begin{equation} F_{\text{macro}} = \frac{2P_{\text{macro}}R_{\text{macro}}}{P_{\text{macro}}+R_{\text{macro}}} = \frac{2*85.8*59.1}{85.8+59.1} = 70\% \end{equation}

(55) \begin{equation} P_{\text{micro}} = \frac{\stackrel{(289+0.75*30+0.5*27+0.25*25)+}{(123+0.75*4+0.5*21+0.25*9)+(973+0.5*14)}}{\stackrel{(289+30+27+25+29)+}{(123+4+21+9+23)+ (973+14+17)}} = 91.5\% \end{equation}

(56) \begin{equation} R_{\text{micro}} = \frac{\stackrel{(289+0.75*30+0.5*27+0.25*25)+}{(123+0.75*4+0.5*21+0.25*9)+(973+0.5*14)}}{\stackrel{(289+30+27+25+182)+}{(123+4+21+9+380)+(973+14+84)}} = 67.1\% \end{equation}

(57) \begin{equation} F_{\text{micro}} = \frac{2P_{\text{micro}}R_{\text{micro}}}{P_{\text{micro}}+R_{\text{micro}}} = \frac{2*91.5*67.1}{91.5+67.1} = 77.4\% \end{equation}

It can be seen that the micro F-measure has a 7.4% higher score than macro F-measure. The main reason for this disparity is the fact that definitive nominal coreferences were present in 49.5% of the analyzed cases, and our evaluated coreference resolution approach solves them very well (94.5% F-measure). Therefore, definitive nominal coreference class skews micro average results in its favor.

Since these scores show how well coreference resolution approach is solving coreferences that it attempts to resolve, the following scores, (58)–(60) formulas, have been calculated to show how well it covers the used annotation scheme:

(58) \begin{equation} P_{\text{scheme}} = \frac{\sum _{i}^{n_a}P_i}{n} = \frac{82.8+77.1+97.6}{5} = 51.5\% \end{equation}

(59) \begin{equation} R_{\text{scheme}} = \frac{\sum _{i}^{n_a}R_i}{n} = \frac{59.9+25.8+91.5}{5} = 35.44\% \end{equation}

(60) \begin{equation} F_{\text{scheme}} = \frac{2P_{\text{scheme}}R_{\text{scheme}}}{P_{\text{scheme}}+R_{\text{scheme}}} = \frac{2*51.5*35.44}{51.5+35.44} = 41.99\% \end{equation}

Overall results of our proposed metric are not out of the line with what other evaluation metrics scored our coreference resolution approach. But the advantage of our proposed metric is the additional dimensions added to the inclusion of dominant mentions and coreference type tracking. This improves the quality of error analysis and provides a clearer picture for coreference resolution approach integration into higher-level applications. Coefficients for each error class also provide a fine-tuning option if certain errors are deemed to be less, or more, important than others.