Single Linkage Method Research Articles

Implementation of K-Means and Single Linkage on Types of Disabilities in East Java Province

The high number of people with disabilities is one of the problems faced by the Indonesian government, especially in Java Province. After West Java Province, East Java Province is in second place as the province with the highest rate of people with disabilities in Indonesia. Disabled people are people with physical disabilities such as not being able to walk, not being able to talk, not being able to see, and so on. The aim of this research is to group districts in East Java Province based on types of disabilities with the hope of facilitating activities in fulfilling the rights of people with disabilities in East Java Province. The grouping was carried out in order to determine the characteristics of each cluster using so that the optimal k-means method was used for clustering using the Euclidean distance method with cluster 1 in 29 districts and cluster 2 in 9 districts. The most optimal single linkage uses the Euclidean distance method with cluster 1 having 8 districts and cluster 2 having 30 districts. From the results of the validity index values, it was found that the single linkage method had the smallest validity value of the icdrate method compared to the k-means method.

Comparisons of Different Cluster Analysis Methods with Application to Mizoram Rainfall Data

Analysing rainfall patterns in Mizoram from 1998 to 2017 reveals diverse trends. The highest average rainfall occurred in 2004, reaching 292.8 mm, while 2014 marked the lowest at 151.77 mm. Siaha District experienced the highest average rainfall (3020.2 mm), while Champhai District had the lowest (1663 mm). In 2017, the Kendall method showed correlations between temperature and relative humidity, rainfall and relative humidity, but not between rainfall and temperature. Cluster analysis, a technique partitioning datasets into cohesive groups, was applied to Mizoram’s district-wise rainfall data using single, complete, and average linkage methods. The Single Linkage Method formed one large cluster with under 26% similarity and the shortest distances between data points. The complete linkage method divided districts into two clusters with under 26% similarity and maximal inter-cluster distance. The Average Linkage Method merged all districts into one cluster with under 26% similarity and minimised inter-cluster distances. Comparing the techniques, Single and Complete Linkage Methods proved most effective for Mizoram’s district-wise rainfall data. With only eight districts, forming additional clusters remained limited. This analysis highlights the significance of rainfall patterns in agricultural ecosystems and the utility of statistical methodologies like cluster analysis in understanding long-term trends.

Hierarchical Clustering via Single and Complete Linkage Using Fully Homomorphic Encryption.

Hierarchical clustering is a widely used data analysis technique. Typically, tools for this method operate on data in its original, readable form, raising privacy concerns when a clustering task involving sensitive data that must remain confidential is outsourced to an external server. To address this issue, we developed a method that integrates Cheon-Kim-Kim-Song homomorphic encryption (HE), allowing the clustering process to be performed without revealing the raw data. In hierarchical clustering, the two nearest clusters are repeatedly merged until the desired number of clusters is reached. The proximity of clusters is evaluated using various metrics. In this study, we considered two well-known metrics: single linkage and complete linkage. Applying HE to these methods involves sorting encrypted distances, which is a resource-intensive operation. Therefore, we propose a cooperative approach in which the data owner aids the sorting process and shares a list of data positions with a computation server. Using this list, the server can determine the clustering of the data points. The proposed approach ensures secure hierarchical clustering using single and complete linkage methods without exposing the original data.

Similarity-Based Three-Way Clustering by Using Dimensionality Reduction

Three-way clustering uses core region and fringe region to describe a cluster, which divide the dataset into three parts. The division helps identify the central core and outer sparse regions of a cluster. One of the main challenges in three-way clustering is the meaningful construction of the two sets. Aimed at handling high-dimensional data and improving the stability of clustering, this paper proposes a novel three-way clustering method. The proposed method uses dimensionality reduction techniques to reduce data dimensions and eliminate noise. Based on the reduced dataset, random sampling and feature extraction are performed multiple times to introduce randomness and diversity, enhancing the algorithm’s robustness. Ensemble strategies are applied on these subsets, and the k-means algorithm is utilized to obtain multiple clustering results. Based on these results, we obtain co-association frequency between different samples and fused clustering result using the single-linkage method of hierarchical clustering. In order to describe the core region and fringe region of each cluster, the similar class of each sample is defined by co-association frequency. The lower and upper approximations of each cluster are obtained based on similar class. The samples in the lower approximation of each cluster belong to the core region of the cluster. The differences between lower and upper approximations of each cluster are defined as fringe region. Therefore, a three-way explanation of each cluster is naturally formed. By employing various UC Irvine Machine Learning Repository (UCI) datasets and comparing different clustering metrics such as Normalized Mutual Information (NMI), Adjusted Rand Index (ARI), and Accuracy (ACC), the experimental results show that the proposed strategy is effective in improving the structure of clustering results.

Comparative Evaluation of Six Agglomerative Hierarchical Clustering Methods With a Robust Example

The agglomerative hierarchical clustering methods are the most popular type of hierarchical clustering used to group objects in clusters based on their similarity. The methods are represented by a bottom-up approach where each object starts in its cluster and pairs of clusters are merged as it moves up the hierarchy. In this paper, we present six agglomerative hierarchical clustering methods namely: the single linkage method, complete linkage method, average linkage method, centroid method, median method, and Ward’s method. We also evaluated how these methods work on a practical basis using a matrix of distance pairs of five points. It was observed that the single linkage method through its dendrogram produced the most similarity measure between x_i and x_j, while Ward’s method produced the highest distance measure between x_i and x_j.

Analisis pengelompokan jumlah tanaman kehutanan yang diusahakan menurut jenis tanaman di Indonesia

One of the problems of archipelagic countries is the lack of maximum utilization of natural resources which has resulted in some areas being left behind. Indonesia is one of those who experience the impact of the lack of utilization of natural resources in the forestry sector. The non-optimal use of forests for planting forestry plants has made most Indonesians use their land as artificial forests, namely to plant forestry plants. Cluster analysis in this case seeks to classify provinces in Indonesia based on the type of forestry plants cultivated. The method used is hierarchical and non-hierarchical. The hierarchical method uses single linkage and complete linkage methods while the non-hierarchical method uses the K-mean method. By making comparisons between methods, the results obtained are that the single linkage method with 8 clusters is the best method for grouping provinces in Indonesia according to the types of plants cultivated. Of the 34 provinces in Indonesia, cluster 1 consists of 27 provinces, while clusters 2 to 8 each consist of only 1 province.
 Keywords: Cluster analysis, single linkage, complete linkage, K-mean, forest plantsMSC2020: 62H30

Discovering smart cities' potential in Kazakhstan: A cluster analysis.

The potential for developing smart cities in Kazakhstan is evaluated using cluster analysis. Built on previous research focused on clustering the regions of Kazakhstan, this study applies the same method to the cities of the country. The analysis uses indicators related to human capital, infrastructure, education, information technology, production, and other factors to assess the potential of each city. The clustering is performed using Single Linkage, Complete Linkage, and Ward's methods. The results show that Almaty and Astana are the cities with the highest potential for becoming smart cities. Aktobe is identified as a city with distinctive features that may help or hinder its development as a smart city. The remaining cities are clustered into two groups, with one group having the potential to catch up and maintain the trend of developing smart cities, while the other group is less suitable for starting smart city projects and may require more investment per capita. The study highlights the deep regional inequality affecting the potential to successfully develop and manage smart cities in Kazakhstan. The analysis also reveals some limitations and challenges in the data and variables used, including the lack of data for some variables and the difficulties in "translating" some factors and indicators into quantitative variables for clustering. The study concludes that future research should address these challenges and consider clustering inside certain regions to focus on their unique features. The study recommends launching pilot projects in small cities, with the most successful practices then scaled and implemented in the core smart cities and possibly Aktobe, if it manages to use its advantages to compensate for risks. Overall, this study provides insights into the potential of smart city development in Kazakhstan and can inform policymakers in their efforts to support smart city projects in the country.

Strategy for improving and empowering MSMEs through grouping using the AHC method

The high number of migrants in the city of Yogyakarta has resulted in increased opportunities for Micro, Small and Medium Enterprises (MSMEs) in Culinary and Handicrafts. The large amount of data collected by the Cooperative Office, which reached thousands, caused inas to have difficulties in determining what training was needed by MSMEs and also difficulties in choosing which MSMEs would receive training held by the Cooperative Office. In addition, the Yogyakarta Cooperatives and UMKM Office had difficulties in selecting which UMKM needed to receive these trainings. Grouping can be used as a strategy in selecting MSMEs and determining training according to their individual needs. The purpose of this study was to group SMEs using the Agglomerative Hierarchical Clustering Single Linkage method and its application to provide recommendations for MSME groups to the Yogyakarta Cooperative and MSME Office. The results of the recommendations for the number of groups can be used in providing implementation, design, and evaluation of the development and empowerment of MSME data in the City of Yogyakarta. This study uses the Agglomerative Hierarchical Clustering Single Linkage method. The stages in this research are Load Data, Cleaning Data, Data Selection, Transformation Data, Clustering Process with AHC single linkage, Silhouette Coefficient, and Knowledge Representation. This research resulted in 2 group recommendations from a total of 1336 Culinary MSME data and 3 group recommendations from a total of 145 Handicraft MSME data. The results of the silhouette score test in the Culinary Sector are included in the strong structure category with a value of 0.79 and the Crafts Sector is included in the Medium Structure category with a value of 0.615. From the number of these groups, recommendations were obtained for improving a service in increasing MSMEs, especially those with a turnover of less than 10 million, marketing purposes within the Yogyakarta area, and not having financial assistance from the government. The high number of immigrants in the city of Yogyakarta has resulted in increased opportunities for Micro, Small and Medium Enterprises (MSMEs) in the Culinary and Crafts sector. The large number of MSMEs creates increasingly higher competitiveness. Apart from that, the large amount of data collected by the Department of Cooperatives and MSMEs, which reaches thousands, causes the Department to have difficulties in efforts to improve and empower these MSMEs. Grouping is one method that can be used as a strategy in mapping MSMEs, especially in efforts to improve and empower MSMEs through training conducted by the Department. The aim of this research is to group MSMEs using the Agglomerative Hierarchical Clustering (AHC) method in an effort to achieve strategies for improving and empowering MSMEs. The focus of this research is[a1] MSMEs in the craft sector and MSMEs in the culinary sector. The results of this research provide 2 group recommendations from a total of 1336 Culinary MSME data and 3 group recommendations from a total of 145 Craft MSME data. The silhouette score test results in the Culinary Sector are in the strong structure category with a value of 0.79 and in the Crafts Sector are in the Medium Structure category with a value of 0.615. From the number of groups in the two MSMEs, strategies were obtained to improve and empower MSMEs, especially those with a turnover of less than 10 million, marketing objectives within the Yogyakarta area, and not having capital assistance from the government. [a1]the result of the revision of the Abstract

Determining the Optimum Number of Clusters in Hierarchical Clustering Using Pseudo-F

Poverty refers to the condition where a person cannot meet the basic necessities based on the minimum living standards. Statistics Indonesia proxied an increase in the poverty rate in North Sumatra Province in 2021 from 8.75% to 9.01%. However, this increase is exclusive to North Sumatra Province, which has Indonesia's 3rd largest number of districts/cities. This study discussed mapping the North Sumatra Province region based on 10 poverty factor variables. The 10 variables are life expectancy, health complaints, poverty line, Gross Regional Domestic Product (GRDP), population growth rate, Expected Years of Schooling (EYS), Human Development Index (HDI), labor force participation rate, open unemployment rate, and district/city minimum wage. The Hierarchical Clustering analysis was employed to compare single, complete, and average linkage methods. The best method was determined based on the pseudo-F statistic value. 4 clusters had complete linkage methods, each of which possessed varied characteristics. Cluster 1 contains cities with the lowest poverty rate, including Medan City and Pematang Siantar City. Cluster 2 consists of cities with low poverty rates, while Cluster 3 consists of cities with high poverty rates. Cities that are included in Cluster 4 have very high poverty rates, including South Nias District and Pakpak Bharat District. The clusters present significant poverty rate gaps among North Sumatra Province regions.

Exploring the Performance and Characteristics of Single Linkage and Complete Linkage Hierarchical Clustering Methods for IoT Sensor Networks

Abstract The research explores applying hierarchical clustering methods, namely single linkage and complete linkage, in IoT Sensor Networks (ISNs). ISNs are distributed systems comprising numerous sensor nodes that collect data from the environment and communicate with each other to transmit the data to a base station. Hierarchical clustering is a technique that groups nodes into clusters based on proximity and similarity. This paper implements and compares the performance of single linkage and complete linkage methods in terms of cluster size, network lifetime, and cluster quality. The study’s findings provide guidance for ISN researchers and designers in selecting the appropriate clustering method that meets their specific requirements.

PENERAPAN ANALISIS KLASTER HIERARKI UNTUK PENGELOMPOKAN KABUPATEN/ KOTA DI PROVINSI MALUKU BERDASARKAN STATUS PENDIDIKAN

One of the main goals of education is to develop potential and to educate individuals. Education is an effort to help the souls of students both physically and mentally towards a better human civilization. This research was conducted to group districts/cities in Maluku province based on educational status using hierarchical cluster analysis with the single linkage, average linkage and ward's methods. The results showed that clustering using the single linkage and average linkage methods was almost the same, while clustering using the ward's method had quite different results. Clustering using the single linkage and average linkage methods shows that Ambon city is the only city that always has its own cluster and does not join other districts/cities. This shows that the city of Ambon has an education status that is quite different from other districts/cities in Maluku Province. Regencies/cities that are always in the same cluster, namely cluster 1, both in the single linkage method, average linkage and the ward's method are Tanimbar Islands Regency, Southeast Maluku Regency, Central Maluku Regency and Tual City

Cluster Analysis of Indonesian Provinces Based On Harvest Area And Rice Productivity Using Single Linkage Method

In this article, a cluster analysis will be conducted for provinces in Indonesia based on the harvest area (ha) and rice productivity (ku/ha) of 34 provinces in Indonesia. Clustering is done using a hierarchical method, namely single linkage. The distance used as the basis for clustering is the euclidian distance. Based on the results of clustering using single linkage, 3 large clusters were obtained. In this article, a cluster analysis will be conducted for provinces in Indonesia based on the harvest area (ha) and rice productivity (ku/ha) of 34 provinces in Indonesia. clustering is done using a hierarchical method, namely single linkage. The distance used as the basis for clustering is the euclidian distance. Based on the results of clustering using single linkage, 3 large clusters were obtained. Cluster consists of 3 provinces, cluster 2 consists of 1 province and cluster 3 consists of 30 provinces. Cluster 1 is a province with high rice production with an average total rice production of 9,628,788 tons. Cluster 2 with an average total rice production of 5,341,021 tons. While cluster 3 with an average rice production of 863,995.34 tons. Furthermore, based on cluster validation using the anova test, the significance value is 0.00>0.05, which means that there is a significant difference between clusters. Thus it can be stated that the division of 34 Indonesian provinces in terms of land area and rice productivity into 3 large clusters using the single linkage method is valid.

GENETIC DIVERSITY AND PHYLOGENETICS OF FOUR RELEASED COWPEA (Vigna unguiculata (L.) Walp) VARIETIES (FUAMPEA-1, FUAMPEA-2, FUAMPEA-3 AND FUAMPEA-4) USING SIMPLE SEQUENCE REPEATS MARKERS

Cowpea improvement has continued to play key roles in the quest for national food security. This work elucidated the molecular genetic diversity and phylogenetics among four released cowpea varieties (FUAMPEA-1, FUAMPEA-2, FUAMPEA-3 AND FUAMPEA-4). DNA was extracted from 14 day old seedlings using the CTAB method. A total of nine (9) SSR (Simple Sequence Repeats) markers were employed in DNA amplifications. Binary matrix was generated from banding profiles of gel images and uploaded into the Minitab 17.0 software for analysis. Polymorphic Information Content (PIC) was computed for the primers and cowpea varieties. Cluster analysis was carried out using the Single Linkage method measured on Euclidean Distance. Four primers (CLM1190, CLM0342, RB38 and RB7) produced maximum of two bands each resulting in 15.4% polymorphism and 0.977 Polymorphism Information Content (PIC). Varietal Polymorphic Content (VPC) varied from 15.4% in FUAMPEA-2 as the lowest to 38.5% in FUAMPEA-1 as the highest. FUAMPEA-1 had the lowest genetic similarity index (19.82). Dendrogram further showed that FUAMPEA-2 and FUAMPEA-3 were more closely related than others with about 46.55 similarity index. Therefore, FUAMPEA-1 was the most divergent and genetically diverse variety followed by FUAMPEA-4. These are potential genetic resource material that can used to develop more cultivars when their inherent agronomic traits and genes coding for the traits are identified and tapped.

ЛИЧНОСТНОЕ САМОСТАНОВЛЕНИЕ БУДУЩИХ ПСИХОЛОГОВ

Statement of the problem. The article is devoted to the study of the problem of personal self-development of future psychologists. To achieve success in their professional activities, it is very important for future psychologists to know and evaluate their personal resources, focusing on the characteristics of personal self-development, so that, gaining life experience, harmoniously approach optimal states, flexibly acquire new forms in the process of development during adolescence, where the very process of self-formation is transformed into a bright and intense action, when civic maturity sets in and social roles change. Changing social roles, as a rule, occurs heterochronously, some roles are assimilated earlier, others later, therefore, an individual’s assessment of his/her resources is often incorrect. The noted specificity of personal self-development in adolescence raises the question of the need to analyze the personal self-development of future psychologists and describe its typological features for the formation and development of professional competencies. The purpose of the article is to present the results of a study on the characteristics of the personal self-development of future psychologists. The methodology of the study is based on the materials of scientific works of Russian and foreign scientists on the problem of personal self-development. The following diagnostic tools were used: the Life Style Index (LSI) technique, Lazarus coping test, the Behavior Self-Regulation Style test (V.I. Morosanova), the Meaningful Orientation test (D.A. Leontiev) the test of motivation for achieving success by T. Ehlers. Cluster analysis (single link method) was used in the analysis of empirical materials. Research results. Significant differences in the characteristics of personal self-development among students with different levels in terms of the general indicator of life meaningfulness are highlighted. Students with a low level of life-purpose orientation (LPO) have a tendency to use the mechanism of protection, i.e., “reactive formation” and “substitution”. It was revealed that in groups of students with a high level of LPO, the overall tension of psychological defenses increases by the 4th year. It has been established that the process of personal self-development among students with an average level of LPO is characterized by a weak connection between psychological defenses and coping strategies. It is noted that in all courses, future psychologists with different levels of LPO rarely use the “denial” defense mechanism. Conclusion. It is concluded that the results of the study indicate the need to develop technologies for working with psychological defenses in the educational process of future psychologists.

Evaluation of Different Clustering Techniques in Classifying the Vegetable Growing Panchayats of Ernakulam District, Kerala

The goal of this study was to evaluate different clustering techniques in classifying the vegetable growing locations of Ernakulam (EKM) district of Kerala so that same nutrient recommendation can be prescribed for panchayats coming under the same cluster. Hierarchical clustering (HC) and K –means clustering were performed to group the panchayats based on soil fertility status and thereafter comparison of various clustering procedures was done using Davies – Bouldin (DB) index. Different dissimilarity measures- Euclidean, squared Euclidean, Chebychev distance and Mahalanobis D2 were determined and single linkage, complete linkage and average linkage methods were adopted under these measures. The results revealed that Mahalanobis D2 was the better clustering procedure with seven clusters (DB index: 0.120) followed by average linkage method under Euclidean distance (DB index: 0.306) with seven clusters. Manjapra and Keerampara panchayats remained as individual clusters. Keerampara had strongly acidic soils (pH -5.17) with high available Mg (158 mg kg-1) while Manjapra soils had low Mg availability (19 mg kg-1) and high S content (57 mg kg-1). Kakkad, Kalady and Vengoor came under cluster I which possessed approximately same EC (0.15-0.19 dS m-1), OC (2-2.4%) and Mg (71-73 mg kg-1) content. Chengamanadu and Vengola came under cluster III while Ayyampuzha and Mudakkuzha belong to cluster IV.

Analisis Hierarchical Clustering Multiscale Bootstrap (Kasus: Indikator Kemiskinan di Provinsi Sulawesi Selatan Tahun 2020)

Hierarchical cluster analysis is a statistical analysis used to group data based on their similarities. The single linkage, complete linkage and average linkage methods can be used to group data using distance techniques. There is a large difference in the number of poor people in urban and rural areas in South Sulawesi Province, so an analysis is needed to classify areas that have the same characteristics based on poverty indicators. For this reason, these three methods are used. However, the results of this analysis are only based on the similarity measure based on the distance technique used. Thus, the multiscale bootstrap method is used to obtain the validity of the resulting clusters. The results of the research using these three methods are four clusters with different characteristics. By using multiscale bootstrap, it is found that in single linkage there are four valid clusters, for complete linkage there is only one valid cluster and on average linkage there are three valid clusters. So it is found that single linkage is the best method in classifying these cases.

Dendrograms, minimum spanning trees and feature selection

Feature selection is a fundamental process to avoid overfitting and to reduce the size of databases without significant loss of information that applies to hierarchical clustering. Dendrograms are graphical representations of hierarchical clustering algorithms that for single linkage clustering can be interpreted as minimum spanning trees in the complete network defined by the database. In this work, we introduce the problem that determines jointly a set of features and a dendrogram, according to the single linkage method. We propose different formulations that include the minimum spanning tree problem constraints as well as the feature selection constraints. Different bounds on the objective function are studied. For one of the models, several families of valid inequalities are proposed and the problem of separating them is studied. For another formulation, a decomposition algorithm is designed. In an extensive computational study, the effectiveness of the different models is discussed, the model with valid inequalities is compared with the decomposition algorithm. The computational results also illustrate that the integration of feature selection to the optimization model allows to keep a satisfactory percentage of information.

Analisis Cluster Hierarki Metode Single Linkage Pada Kabupaten/Kota di Provinsi Sumatera Barat Berdasarkan Indikator Kesehatan

Health indicators are variables that are needed as a benchmark to determine conditions and changes in the health sector. Health indicators are needed by the government to plan development in the health sector in order to achieve optimal results in accordance with the conditions of each region. The purpose of this study is to group districts/cities in West Sumatra Province based on health indicators in 2020 and interpret the characteristics of each cluster that has been formed by using single linkage method hierarchical cluster analysis. The results of the grouping are divided into 2 clusters, cluster 1 consists of one district, namely the Mentawai Islands Regency, including areas with high health levels. Cluster 2 consists of 18 regencies/cities namely Pesisir Selatan Regency, Agam Regency, Solok Regency, Tanah Datar Regency, Bukittinggi City, Payakumbuh City, Sijunjung Regency, Fifty Cities Regency, Padang City, Sawahlunto City, Dharmasraya Regency, Pariaman City, Regency South Solok, Padang Pariaman Regency, West Pasaman Regency, Solok City, Pasaman Regency, and Padang Panjang City are areas with low health levels.

Comparison of Hierarchical Clustering, K-Means, K-Medoids, and Fuzzy C-Means Methods in Grouping Provinces in Indonesia according to the Special Index for Handling Stunting

Stunting has been widely known as the highest case of malnutrition suffered by toddlers in the world and has a bad impact on children's future. In 2018, Indonesia was ranked the 31st highest stunting in the world and ranked 4th in Southeast Asia. About 30.8% (roughly 3 out of 10) of children under 5 years suffer from stunting in Indonesia. To support the government policy making in handling stunting, it is undoubtedly necessary to classify the levels of stunting handling in regions in Indonesia. In this work, the hierarchical agglomerative and non-hierarchical clustering is compared and evaluated to perform clustering on stunting data. The agglomerative hierarchical cluster uses Single Linkage, Average Linkage, Complete Linkage, and Ward Method, while the non-hierarchical cluster uses K-Means, K-Medoids (PAM) Clustering, and Fuzzy C-Means. This study uses data from 12 IKPS indicators in 34 provinces in Indonesia in 2018. Based on the results of the evaluation using the Connectivity Coefficient, Dunn Index, Silhouette Coefficient, Davies Bouldin Index, Xie & Beni Index, and Calinski-Harabasz Index, the results show that the Average Linkage is the best cluster method with the optimal number of clusters is four clusters. The first cluster is a cluster with a good level of stunting management which consists of 28 provinces. The second cluster consists of only one province, DI Yogyakarta with a very good level of stunting handling. The third cluster consists of four provinces with poor stunting handling rates. Finally, the last cluster consisting of one province, Papua, has a very poor level of stunting handling.

Bespoke automated linkage to enable analysis of covid deaths by ethnicity.

In early 2020 there was intense media speculation that ethnicity and Covid-19 deaths were correlated. However, the existing method of adding ethnicity to death records resulted in low linkage rates for very recent deaths. We designed and implemented a bespoke linkage in three days enabling accurate reporting to the nation.
 We linked the 2011 England and Wales Census to death records using a range of personal identifiers. Due to time pressure, we focused on executing a single linkage method well. Deterministic linkage was chosen, using a variety of matchkeys which were tested via clerical review. To overcome the issue of addresses changing since 2011, we also linked 2020 death record residuals to the 2019 Patient Register (PR) and then made use of the 2011 PR address where it existed. This additionally provided an indication of whether unmatched death records might be attributable to migration into England and Wales post-2011.
 The prior linking method used NHS Number only. Although the overall linkage rate was approximately 90%, the rate for recent deaths (2nd March 2020 to 10th April 2020 in the first iteration of the linkage) was closer to 30% due to an administrative lag in adding NHS Numbers to death records. Our novel bespoke linkage method linked over 39,000 extra death records. Whilst this had minimal impact on the overall linkage rate, it improved the linkage rate for recent deaths to approximately 90%. This was without an impact on accuracy: clerical review demonstrated that the false positive rate was approximately 0.2%. A report was published using this data showing that the risk of death involving Covid-19 among some ethnic groups was significantly higher than others.
 Determining whether Covid-19 disproportionally affected certain ethnicities was of crucial importance in the early phase of the pandemic to enable appropriate government strategies to be developed. We delivered a bespoke linkage under an exceptional time-limit without compromising on accuracy, enabling this impactful analysis with nation-wide interest and impact.