Record linkage, also known as entity resolution, data matching or duplicate detection [6, 12], is the process of identifying and linking records about the same real-world entity from one or several databases. This process is widely used in the data preparation phase of data mining projects that require data from various sources to be integrated before they can be analyzed. Traditionally, record linkage has been employed in the health sector and for national censuses, while more recently it has seen application in a wide range of areas including e-commerce, the social sciences, crime and fraud detection, and national security [6, 12, 15].
Much research in record linkage is based on bibliographic data (with the aim to identify which publications have been written by the same authors) due to the easy availability of large bibliographic databases when compared to personal data about people (such as health or government records) that are often sensitive or confidential .
Bibliographic data also have the advantage of containing several types of entities (like authors, publications, and venues). These provide a complex information space  that allows graph-based and clustering techniques to exploit both attribute similarities (such as similar publication titles) as well as relationships (for example two authors have co-written several publications). Several advanced graph and collective linkage techniques have been developed for bibliographic data in recent years [2, 9]
The question of how to employ such advanced linkage techniques on personal data (such as names, addresses, dates of birth, etc.) has however so far only seen very limited research [10, 11]. A major reason for this is the lack of available real-world databases about people. Most approaches used to link personal data are still based on traditional techniques that only consider pair-wise record comparisons 
. These techniques classify each record pair individually as either amatch (assumed to refer to the same entity) or a non-match (assumed to refer to different entities) without considering relationships between records.
Recent years have seen a significant increase in interest on how to efficiently and effectively link large databases about people, with the aim to reconstruct populations for social science and health research, or for use as a valuable resource for governments and businesses [1, 3]. The emerging field of population informatics  is aimed at the linkage and analysis of large and dynamic databases that contain information about people, such as the health, education, financial, census, location, shopping, employment, and social networking records of a large proportion of individuals in a population.
Compared to bibliographic data with their different types of entities, population databases contain records about people where the role of an individual can change over time, and where different databases contain different types of information about the same individual. Furthermore, the different roles of individuals lead to various types of relationships and diverse constraints (with regard to roles, time, and number of individuals involved in a link).
This is illustrated in Fig. 1, which shows the roles and relationships in the data sets we use in our evaluation in Sect. 5. For each of the pairs of roles shown (for example Baby–Bride), different attributes (fields) are available for calculating the similarities between records, different temporal constraints are possible (for example, a Baby can only become a Bride after a certain age), and different 1-to-1 or 1-to-many linkage restrictions need to be considered (a Baby can be a Bride in one or more marriages, but each Bride can only have been a Baby once).
The linkage of such data is challenging due to people moving around (address changes), changing their names (either in the form of small spelling variations or errors, or full name changes due to marriage), and other data quality issues such as transcription or scanning errors when these certificates were converted from their original handwritten into digital form (as illustrated in Fig. 2). People in the 19th century also did not always know their exact date of birth or even their true age, leading to inaccurate age values in certificates. Additionally, the variety of personal names was much more limited (as Table 1 shows for our data sets), and often only a few common names covered a large proportion of a population. This means that, compared to many modern databases, the use of attribute similarities does not provide enough information to distinguish between individuals.
On the other hand, the various types of relationships can help improve linkage quality. For example, a Baby and her parents occurring in a census certificate (as a child and her parents) that have a high similarity to a Bride and her parents in a marriage certificate, will provide supportive evidence that the Baby and Bride refer to the same person.
The outcomes of linking such population databases are linked records for each individual that can then be visualized into life segments (as shown in Fig. 3) or converted into family trees, and used for example in health  and genealogical research studies .
While most techniques for reconstructing populations [1, 3, 10, 11], including those in the present paper, focus on historical data (due to their easier availability compared to contemporary data) they are also applicable to modern data that have similar structure and content.
Contributions: While graph and collective linkage techniques [2, 9] use both attribute and relational similarities between entities of different types (such as papers, authors and venues in publications), we study the problem of linking records about entities (such as people) that are of the same type but can have different roles in different records, where these roles can change over time, and where there are constraints both for the roles and relationships of an entity.
We specifically investigate how advanced record linkage techniques can be successfully applied for the reconstruction of complex populations such as those collected by governments and health organizations. We develop a novel linkage approach that combines pair-wise attribute and group similarities, incorporates temporal as well as 1-to-1 and 1-to-many linkage constraints, and considers relationship information between individuals and groups of people as for example occur on certificates such as those shown in Fig. 1. We show that even state-of-the-art advanced linkage techniques have difficulty to achieve high linkage quality in an experimental evaluation on a real collection of Scottish data sets that span over five decades of the nineteenth century.
2 Related Work
The challenges of how to link records about the same entities within and across databases have been investigated in various research domains since the 1950s. Several recent books provide an overview of the topic [6, 12, 17]. In the following we describe related work specifically aimed at linking complex data. These approaches include group, graph and collective techniques that consider data that contain temporal aspects, or that are specific to linking (historical) census and similar types of personal data.
Traditional record linkage techniques only consider the similarities between record attributes mainly using approximate string comparison functions [6, 12], followed by the individual classification of each compared record pair as a match or a non-match. On et al.  were the first to investigate how to link groups of records in the context of bibliographic data (such as groups of papers written by the same author) using a weighted bipartite matching approach. While this approach still classifies each pair of groups of records independently from all others, recently developed collective techniques [2, 9] additionally also consider the relationships between entities. They build a graph of all compared records that is clustered such that each cluster refers to one entity. For bibliographic data, the available relationships include authors who have co-authored together, or who work at the same institution.
These group and graph-based techniques have been developed in the context of bibliographic data, where several types of entities are available. Fu et al.  were the first to investigate how group linkage techniques can be employed in the context of (historical) census data by using household information to group records with the aim of linking individuals by first linking similar households. Experimental results showed that this approach can lead to a significant reduction of ambiguous links between individuals.
While most record linkage techniques do not consider temporal aspects, Li et al.  and Chiang et al.  investigated temporal information in the context of bibliographic data where authors can change their affiliations over time. Their approach adjusts similarity weights depending upon the temporal differences between two records. Christen and Gayler  developed a similar approach for personal data where temporal likelihood values, such as how likely it is that somebody moves address over a certain period of time, are learned from a large population database. In our approach we also consider temporal relationships between records, for example that a birth has to occur before any other records of the same person, or that a marriage or birth of a child can only occur once a person has reached a certain age.
To improve linkage quality, various supervised learning techniques have been developed specifically aimed at linking (historical) census data. Fu et al. investigated multiple instance learning by first linking individuals with high confidence, and then using those to link households over time. More recently, the same authors  exploited information in households that does not change over time (such as the age differences between a husband and wife) within a graph-matching approach to improve the quality of linking census data over time. Antoine et al. 
used a support vector machine classifier to successfully link two large Canadian census data sets from 1871 and 1881.
The main drawback of supervised approaches is their reliance on training data, which generally have to be manually prepared by domain experts in an expensive and time consuming process. Our approach, on the other hand, is unsupervised and aims to exploit the relationships between individuals and their changing roles over time to achieve high linkage quality.
3 Problem Definition
We now define the problem we aim to tackle using the following notation. We assume a collection of data sets that contain details about entities (in our case people), where each data set contains certificates of different types. We assume birth (), death (), marriage (), and census () data sets. These four types are common both in historical as well as contemporary data as collected for example by government registries and census agencies . We denote certificates as , , , and . We drop the superscript (, , etc.) if a data set or certificate can be of any type. Each certificate contains the details of one or several individuals, as shown in Fig. 1. Each certificate also has an event year, , such as the year of a birth, a marriage, or a death, or the year a census was conducted, as illustrated in Fig. 3.
A record for an individual in a certificate is denoted as , where is the set of all individual records from all data sets, i.e. . A record contains a set of attributes , where is the value of attribute for record . Each record represents an entity (person), and we use to denote the entity identifier for that record. Two records that have the same value in their entity identifiers are a match, i.e. they are assumed to correspond to the same person. It is important to note that all individual records in a certificate are about different people, i.e. . We denote with the set of all entities (individuals) that occur in all records in , i.e. .
We assume a set of role types , such as those shown in Fig. 1, where different data sets contain records of individuals with different roles. For example, . Each individual record has one such role type, denoted as . From these roles, we are interested in pairs of roles that correspond to the roles a person can have in the different pairs of certificates. As an example, the pair corresponds to a baby in a birth certificate who becomes the bride in a marriage certificate. We denote the set of all valid role pair types as . Note that not all possible pairs that could be generated from roles in are in . For example as this is not a valid pair of roles for the same individual. Limiting role pairs to those in ensures that we do not link pairs of records with invalid role pairs. This helps both to reduce the number of records to compare, as well as to improve linkage quality, as we discuss in the following section.
Finally, we define a life segment as a sequence of one or more individual records , with , ordered according to the event years of their corresponding certificates, i.e. , where the role types of all pairs of records in a life segment are valid role pairs, i.e. . These life segments can be converted into family trees as used in genealogical studies  (this process is outside of the topic of this paper). We now formally define the problem we aim to address in this paper:
Definition 1 [Linkage-based complex population reconstruction]: Given data sets , , , and with different types of certificates, where each certificate contains one or more records about individual entities , the aim of linkage-based complex population reconstruction is to link certificates and individual records to generate a set of life segments such that for each entity there will be one life segment that only contains records about entity , and no other life segment in contains any records of entity , i.e. .
The following questions now arise: how can we (1) calculate similarities between pairs and groups of records and certificates; (2) take relationships, roles, and temporal aspects into account during this linkage process; and (3) conduct the linkage efficiently and effectively to generate life segments from potentially very large population databases.
4 Complex Population Linkage
In this section we discuss all steps involved in our approach to linking complex population databases, as illustrated in Fig. 4. We first discuss the three steps involved in the traditional pair-wise linkage of individuals, then describe the use of temporal, and 1-to-1 and 1-to-many constraints, then provide details of the advanced relational and group linkage approaches, and finally discuss the result fusion step.
4.1 Pair-wise Linkage of Individuals
The input to the pair-wise linkage steps are the data sets , , , and , which contain different types of certificates as described above. We first extract and clean the attribute values required for linkage for all individuals from the different certificates . We then use a mapping schema which maps each individual record into a single table with a common set of attributes (such as first and last name, gender, address, role, occupation, and so on), together with a reference to its source certificate and its event year .
In the second step we apply blocking with the aim to extract sets of records that likely correspond to the same entity. Blocking is commonly used in record linkage to reduce the number of record pairs that are to be compared from the full quadratic comparison space [6, 12]. We use a blocking criteria that consists of a set of blocking key definitions to split the data sets into blocks, such that all records with the same blocking key value are inserted into the same block. Each blocking key is a tuple , where is a set of role types and are one or more attributes.
We apply phonetic encoding on name and address attribute values to group variations of similar sounding values into the same block. In our application we use Double-Metaphone which overcomes some of the drawbacks of the commonly used Soundex method, such as sensitivity to different first letters . All records with that have the same value in their concatenated phonetically encoded attribute values are inserted into the same block. We only insert records into the same block if pairs of their role types are in the set of valid role pair types to prevent comparing records with invalid roles (for example, records with types and are never inserted into the same block).
Records in the same block are compared pair-wise in the third step using a set of similarity functions, such as edit distance or Jaro-Winker  for string attributes, and an approximate year difference function  to allow for variations in year values. For each compared record pair, the similarity is then normalized into , where a similarity of means two records are totally different, means they have exactly the same values in the compared attributes, and values in-between and mean records are somewhat similar. Only pairs with a similarity , where is a minimum similarity threshold, are kept in the set of linked pairs along with their similarities, as pairs with lower similarities likely correspond to different entities. As with traditional record linkage , this pair-wise linkage step does not take any group or relationship aspects into account but only calculates attribute based similarities . We however enforce temporal constraints to prevent definite non-matching pairs from being compared ( records are not compared to records with later event years).
The set of calculated individual pair-wise similarities, , is the input to the two advanced linkage approaches used in step 4. Each of these two approaches is conducted individually and incorporates information from linked individuals, role type pairs, the relationships between individuals, and temporal constraints, with the aim to identify links of high quality and high confidence between certificates. The minimum similarity , used in the pair-wise similarity calculation (step 3), is kept at a low value to ensure all links between matching individuals are included in . We aim for a high recall of true links in at the cost of low precision. The aim of the relational and group-based linkage steps is to improve precision by identifying the set of true links from the potentially very large set of linked individuals.
4.2 Temporal Linkage Constraints
Temporal linkage constraints can be considered both at the level of linking records of individuals, as well as at the level of linking certificates. At the individual level, for each role type pair in the set we define a time interval which determines if two individual records are to be compared or not in the pair-wise attribute similarity calculation step. For two individual records and from two certificates and with event years and , respectively, the pair will be compared if the following equation evaluates to true:
assuming . For example, for the role type pair , and , indicating a death record for an individual can only occur after the person’s birth. In our experiments, we however set for this and related role pairs because due to data quality issues it is possible that some birth and death certificates have wrongly recorded event years. As a second example, for the role type pair , we set and assuming a woman can only become a bride’s mother once she is old enough (again providing several years tolerance to account for wrong event years).
While such temporal constraints limit which pairs of individuals are compared or not, similar constraints can also be applied at the level of linking pairs of certificates in the relational and group linkage steps. At this level, temporal constraints ensure that certificate links are limited to valid time periods. For example, a marriage and a census certificate can be linked in different ways. One is to link the bride and her parents to an earlier census certificate of this family, while another way is to link the bride and groom to a later census certificate as a new family.
Our temporal linkage constraints consist of a list of role type pairs and certificate pairs and their corresponding time intervals . Not all role type pairs and not all certificate pairs have temporal constraints. For example, a women can have the roles across multiple birth certificates spread over several years.
4.3 1-to-1 and 1-to-Many Linkage Constraints
Similar to temporal constraints, 1-to-1 and 1-to-many (and many-to-1) constraints are applicable both at the level of pairs of individual records, as well as at the level of pairs of certificates. An example of a 1-to-1 constraint is that a in a birth record can be a true match to only one individual in a death record, and vice versa; while a 1-to-many constraint is where a can be a true match to a in one or more marriage certificate (assuming a women re-marries), while each can only be a true match to a in one birth certificate.
Such 1-to-1 and 1-to-many linkage constraints are often applied in general record linkage applications where a record in one database can match to a maximum of one record in a second database . The best-matching pairs of records are generally selected based on their calculated pair-wise similarities, assuming that the record pair with the highest similarity is the true match. 1-to-1 and 1-to-many linkage constraints can be implemented in either a greedy fashion or using an optimal assignment procedure .
We do not apply such linkage constraints in the pair-wise attribute similarity step because this might lead to reduced similarities between certificates in the relational and group linkage steps if links between individuals are being removed due to 1-to-1 and 1-to-many linkage constraints. For example, if an individual has a low similarity due to a name variation or wrongly recorded age value it might not be linked if a 1-to-1 constraint is applied, thereby lowering the number of individuals that are linked between two certificates in the group linkage step (as we describe below).
We instead apply 1-to-1 and 1-to-many constraints after the relational and group linkage steps to reduce the number of linked certificates further. Our hypothesis is that linked certificates contain a larger set of evidence (in the group linkage step from several individuals and in the relational linkage step from the relationships between individuals) that leads to true matching certificate pairs with higher similarities compared to non-matching pairs. Our linkage constraints consist of a list of certificate type pairs and how they are to be linked, their corresponding ‘1-to-1’, ‘1-to-m’, ‘m-to-1’ constraints (or ‘m-to-m’ for no constraint), that are applied after the relational and group linkage steps.
4.4 Relational Similarity Linkage
Based on ideas from graph-based and collective entity resolution techniques [2, 9], in this step of our approach we calculate a relational similarity for each pair of certificates that is based on its neighborhood of certificates. To do so, we first generate a graph where nodes are certificates and edges between certificates are pairs of individuals from the set that were linked in the pair-wise linkage step and that had a similarity above the minimum threshold . Formally, with the sets of vertices and edges .
For each pair of certificate types (birth to census, birth to death, etc.) there are generally several ways of how two certificates can be linked. For example, a birth and marriage certificate can be linked in the following three ways: (1) a baby girl is linked to her marriage, (2) a baby boy is linked to his marriage, and (3) a baby’s parents are linked to their marriage. For each such linkage type, we define the possible relationships with other types of certificates.
An example is shown in Fig. 5 for the linkage of a baby girl to her marriage (), where individual links to neighboring census and death records in are used to calculate the relational similarity. In this example, if this birth certificate has several linked individuals with high similarity to the same death and census certificates as the marriage certificate, then this provides evidence that they refer to the same group of individuals and should be linked. On the other hand, if there are no individuals linked to the same neighboring death and census certificates then this pair of birth and marriage certificates should not be linked.
We investigate seven relational similarity functions : (1) Jaccard, which is the size of the intersection of neighboring certificates divided by the size of the union of neighbors; (2) multi-Jaccard, which also takes the number of individuals linked between certificates into account; (3) the average individual similarity between common neighboring certificates without taking the number of linked individuals into account; (4) multi-average, which is the same as (3) but takes the number of individuals linked between certificates into account; (5) the maximum individual similarity between common neighboring certificates; (6) the Adar/Adamic similarity  which considers the number of neighbors of common neighbors (i.e. neighbors of neighbors), where a smaller number of other neighboring certificates means a common neighbor is more relevant because it is less connected (less ambiguous) ; and (7) the multi-Adar/Adamic similarity which also takes the number of individuals linked between certificates into account.
Optional 1-to-1 and 1-to-many linkage constraints can be applied after the relational similarities between certificates have been calculated to further reduce the number of links between certificates, and to ensure no invalid links are being produced (for example, the death of an individual is not linked to the birth of more than one baby).
4.5 Group Linkage
Using group similarities has previously been used in the linkage of both bibliographic and historical census data [11, 19]. The basic idea is to consider all the calculated links between individuals in a pair of certificates, and based on those to calculate a group similarity measure between certificates. As with the relational similarity approach, the input to the group linkage step is the set of all pair-wise linked individuals that have a similarity of at least .
We investigate five group similarity functions: (1) maximum, which takes as the group similarity the maximum of the individual pair-wise similarities for a pair of certificates: , where ; (2) average, where we calculate the average similarity between all pairs of individuals for a pair of certificates: ; (3) group size, which is the ratio of the number of linked individuals divided by the larger size of the two certificates, calculated as ; and (4) group bipartite, which follows the approach of On et al.  and calculates the similarity between two certificates as: . Finally, our last group similarity function combines the previous four similarities by calculating their average as , with the hypothesis being that each of these four similarities provides some evidence towards an overall group similarity for two certificates.
As with the relational similarity approach, optional 1-to-1 and 1-to-many linkage constraints can be applied after the group similarities between certificates have been calculated to reduce the number of invalid links.
4.6 Result Fusion
The final step (step 5 in Fig. 4) of our complex population record linkage approach is to combine the linkage results obtained from the relational and group linkage steps with the aim to find true matching certificates. Our assumption is that true matches should have both a high group similarity (i.e. have several individuals linked between them each with a high similarity) as well as a high relational similarity (i.e. be linked to a similar set of neighboring certificates).
The input to the fusion step are two sets of linked certificates, (relational matches) and (group matches), respectively. Our fusion approach is to calculate a (weighted) sum of the two similarities for each pair of certificates in the intersection of both match sets, and to then only classify certificate pairs as final matches that have an overall similarity above a minimum similarity threshold :
Note that the overall minimum similarity threshold can be different from the similarity threshold used in the pair-wise linkage of individuals described in Sect. 4.1. While needs to be set to a lower value to ensure as many matches as possible are included into the set of linked individuals (i.e. high recall), can be set higher to ensure the final set of matched certificates has a high precision as well.
In the following section, using real historical data from Scotland, we will experimentally evaluate how the different steps of our approach, and the different ways of how to calculate relational and group similarities, influence the quality of the final set of matched certificates.
|Data set||Number of||Number of unique values in selected attributes|
|records / individuals||First name||Last name||Relationship||Address||Occupation|
|Birth||17,614 / 70,456||2,055||547||150||1,257||820|
|Marriage||2,668 / 16,008||427||343||n/a||903||589|
|Death||12,285 / 61,425||837||639||243||988||983|
|Census 1861||19,605 / 19,605||653||507||222||1,908||1,318|
|Census 1871||18,102 / 18,102||611||459||146||1,924||1,559|
|Census 1881||17,684 / 17,684||748||441||114||1,232||1,309|
|Census 1891||16,476 / 16,476||884||507||135||1,556||1,483|
|Census 1901||14,609 / 14,609||932||440||191||1,405||1,354|
5 Experiments and Discussion
We evaluate our proposed approach using a collection of real Scottish data sets that cover the population of the Isle of Skye over the period from 1861 to 1901. These data sets have been extensively curated and linked semi-manually (using database queries to extract tables of possible links) by demographers who are experts in the domain of linking such historical data [18, 21].
The linkage approach taken by the demographers followed long established rules for family reconstruction , leading to set of linked certificates that are heavily biased towards certain types of links (as we discuss further below). As an example, a first step in family reconstruction is often to link babies who had died very shortly after birth (as these do not exhibit much variation or changes in the names and addresses of their parents), followed by the linking of birth certificates to their next census certificate (less than ten years in the future for our data sets).
We thus have a set of manually generated links that allow us to compare the quality and coverage of our automatically identified links to those identified by the domain experts. We like to emphasize that we do not have a gold standard of all true links in these data sets (neither do the demographers ). All results presented here therefore only indicate the overlap between manual and automatically generated links between certificates.
, they have a very small number of unique name values. The frequency distributions of names are also very skewed. Across all data sets, the five most common first and last name values occur in betweenand of all records. Many records have missing values in address or occupation attributes, and Informants are mostly missing (we therefore do not include any records with this role).
While we do have a set of manually generated links available (biased as described above), we only use them for evaluation purpose because our overall aim is to develop fully unsupervised techniques that are applicable even when no training data are available, as is often the case in practical record linkage projects . The set of manually linked certificates contains life segments, where consist of a single certificate and the maximum number of certificates in a life segment is , leading to manually linked certificate pairs. The median number of certificates per life segment is and the average is .
|Certificate pair types||Number of links||Percentage|
As Table 2 shows, the number of different types of manually linked certificate pairs is highly skewed, with the majority of true matches being between pairs of census (35.8%), birth to census (28.3%), and census to death (18.1%) certificates. There are less than a few hundred links between birth and marriage and death and marriage certificates, and an even smaller number of marriage to marriage links. Understandably, there are no true matching pairs of certificates of types birth to birth and death to death in the set of manually linked certificates.
To compare the quality of our automatic linkage approach with the manually identified links, we use precision, and recall, as commonly used in record linkage evaluations . We set as true positives, , the set of certificate pairs linked both manually and automatically; as false positives, , those pairs linked only automatically by our approach but not manually by the domain experts; and as false negatives, , those pairs linked manually by the domain experts but not by our approach.
Record linkage is often a very imbalanced problem . In our case the ratio of the number of manually linked certificate pairs over the number of compared certificates is . This makes identifying linked certificates highly challenging. To provide summary information for our automatic versus manual linkage approaches, we report the area under the precision-recall curve (AUC-PR) which is more meaningful for such an imbalanced problem compared to the area under the ROC curve . We use the Scikit-learn (http://scikit-learn.org
) machine learning package for calculating AUC-PR.
We implemented our approach in Python 2.7 using the functionalities of the Febrl  record linkage system. We conducted all experiments on a server with 64-bit Intel Xeon 2.4 GHz CPUs, 128 GBytes of memory, and running Ubuntu 14.04. To facilitate repeatability we will make our programs available, while for the Isle of Skye data sets the interested reader is encouraged to contact the owners .
We applied basic cleaning of attribute values in our data by removing unwanted characters, standardizing age and gender values, and imputing birth years calculated from age values. In the blocking step we usedblocking keys (different combinations of role types, selected attributes, and phonetic encodings). We set the minimum individual similarity threshold as , resulting in a total of compared pairs of individual records in the attribute similarity calculation step (step 3).
We also investigated the following four options of how to calculate pair-wise similarities and constraint comparisons:
Given the large number of missing values in certain attributes (notably in addresses and occupations), when calculating individual similarities we either included (with a similarity of ) or excluded attributes when at least one value in an attribute pair was missing.
Also in the pair-wise similarity step, we either assigned each attribute a weight of towards its contribution to the individual record pair similarity (as described in Sect. 4.1), or we calculated attribute specific weights as is commonly done in traditional record linkage  using the manual linked certificates (with higher weights given to attributes that are more similar in manually linked certificate pairs compared to randomly selected pairs that do not correspond to the same individuals).
We either allowed links to census certificates without temporal constraints, or we limited such links to only one decade before/after a census, with the aim of limiting links to only the temporal closest census certificates. For example, a birth certificate from 1868 would only be linked to census certificates in 1861 and 1871. The hypothesis is that such links should be of higher quality because households and families are changing over time and thereby become more difficult to link over longer time periods.
Finally, we investigated how the 1-to-1 and 1-to-many linkage constraints described in Sect. 4.3 (when enforced or not enforced) affect the quality of the obtained set of linked certificates.
for individual certificate type pairs. We show average and standard deviations of AUC-PR results as run over the different settings of the options described above.
As all result figures show, the pair-wise linkage of individuals alone does not lead to acceptable linkage quality at all. In fact, the highest AUC-PR values obtained with pair-wise linkage only is around for census to census certificate pairs, indicating that manual links are mainly based on more than just attribute similarities.
Similarly, applying a relational or group linkage approach individually only improves linkage quality to a certain degree. Fusion of the linked certificate pairs obtained by both relational and group linkage provides the best results for all types of pairs. With regard to relational similarities, somewhat surprisingly the Jaccard similarity achieved the best results overall, outperforming more advanced relational similarity methods. For group linkage, no clear winner can be found for the different group similarities.
With regard to the different linkage options we investigated, including missing attribute values seems to lead to slightly better results than excluding them; using attribute weights in the individual similarity calculation does surprisingly not lead to any improvement; and limiting census links to the closest temporal census certificates can improve linkage quality. Finally, applying 1-to-1 and 1-to-many constraints does significantly improve the quality of group linkage, however it does not lead to improvements for relational linkage methods.
Overall, as the results show, the overlap between the links obtained with our automatic approach compared to the links manually identified by domain experts is below what we expected with state-of-the-art advanced linkage techniques that have been able to achieve very high linkage quality on bibliographic databases [2, 9]. We did not expect to achieve very high AUC-PR of or above in the first place, given the challenging nature of the data used in the experiments and the extensive manual linkage conducted by experienced domain experts [18, 21]. However, it seems advanced linkage techniques developed for bibliographic data cannot be directly used for linking complex personal data, such as the ones we aim to link in our work. More development of new linkage techniques that better exploit the contents, roles, temporal aspects, and relationships between individuals and groups, is therefore required.
6 Conclusions and Future Work
We have presented a novel approach to link complex personal data from (historical) birth, death, marriage, and census certificates. Our approach combines individual, group, and relational linkage methods, and incorporates temporal, as well as 1-to-1 and 1-to-many linkage constraints. An experimental evaluation on real Scottish data highlighted the challenges of linking such complex data, where no approach achieved high linkage quality compared to a careful manual linkage as conducted by domain experts . For these specific data sets, we see the main reason for this to be the large number of intrinsically difficult to link cases that were manually linked by the domain experts despite not having high attribute, relational, or group similarities; or having highly ambiguous name or address values.
As future work we aim to improve each step of our automatic linkage approach, starting with pair-wise similarity calculations that are suitable for the highly skewed frequency distributions of attribute values. We plan to explore different blocking techniques, such as the sorted neighborhood method , to improve the scalability of our approach, and we aim to incorporate a fully relational collective entity resolution approach  and evaluate how this can improve linkage quality.
While currently the role pair types used to limit pair-wise individual comparisons are set manually based on domain expertise, we plan to investigate if association or pattern mining algorithms  can help to automatically identify role pairs that are likely to correspond to true changes of people’s roles over time. Finally, we plan to refine the temporal linkage constraints by calculating fine-tuned temporal similarity adjustments [7, 16]. Our overall goal is to develop highly accurate, scalable, and automatic techniques for linking large-scale complex population databases.
This work was partially supported by a grant from the Simons Foundation, and partially funded by the Australian Research Council under Discovery Project DP160101934, the Administrative Data Research Centre Scotland (ADRC-Scotland), and the Digitising Scotland project. The author would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Data Linkage and Anonymisation where parts of this work was conducted (EPSRC grant EP/K032208/1).
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