# Ability Grouping of Elderly Individuals Based on an Improved K-Prototypes Algorithm

Authors: Yanfang Gao; Yanxue Hu; Yuying Chu
Journal: Mathematical Problems in Engineering
 (2023)

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## Abstract

Elderly individuals with similar abilities are likely to have similar care needs. Abilities are the basis for analysing the need patterns of elderly individuals. Abilities of elderly individuals are both numerical and categorical; therefore, an improved K-prototypes cluster algorithm for mixed attributes was proposed to group elderly individuals based on abilities. In this algorithm, the dissimilarity measure of categorical attributes is designed to consider not only the difference between the object to be allocated and the prototype of the cluster but also the differ6ence between the object to be allocated and other objects in the cluster and can measure the difference in sequential values of ordinal categorical attributes. Experimental results show that the improved K-prototypes algorithm performs well for clustering datasets containing mixed attributes. Taking the CHARLS dataset as an example, distinct groups of elderly individuals based on the improved K-prototypes algorithm showed significant ability differences.


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## Body

## 1. Introduction

Ageing is an irreversible worldwide trend in the 21st century. Taking China as an example, 264 million people were over 60 years old by the end of 2020, accounting for 18.7% of the total population [1]. The rapid development of the ageing population, accompanied by an increase with disabilities and oldest-old people, leads to a large increase in the demand for care services, which places tremendous pressure on society and on families. At the same time, due to limited care service resources, it is necessary to improve their utilization rate through precision care services to achieve sustainable care services for elderly individuals. Therefore, precision care services for elderly individuals have become a hot research issue [2–4]. Precision care services are mainly studied from two approaches. One approach is to recommend services for elderly individuals based on the idea of precision service of e-commerce. The other approach is to assess the care needs of elderly individuals based on their abilities to access precision care services according to their personalized needs.Recommended care services for elderly individuals driven by big data are the focus of researchers’ attention in the field of smart elderly care. Wongpun and Guha studied case-based reasoning for care services’ recommendation [5]. Kitamura et al. broke through the limitations of traditional services’ recommendation technology, such as the lack or limited consideration of lifestyle, health status, physical ability, and elderly individuals’ expected experience of services, and studied the social activity recommendation system for elderly individuals [6]. Kim and Chung studied food and exercise service recommendations based on an ontology-based healthcare context information model [7]. Hu studied the diet recommendation system for elderly individuals based on situational awareness [8]. Li et al. studied the recommendation method of exercise prescription for elderly individuals with hypertension based on deep learning [9]. In these studies, the methods used included k-nearest neighbour, support vector machine, Bayesian classifier, and other machine learning methods and traditional statistical methods.It is also the focus of this study to assess the care service needs based on the abilities of elderly individuals. In 1987, the United States developed the international Resident Assessment Instrument (interRAI), on the basis of which researchers, physicians, and public health administrators in dozens of countries developed the interRAI Home Care Assessment Scale [10, 11]. This tool mainly analyses the care needs of elderly individuals from their functional state, clinical health, cognitive and mental state, social function, and other indicators. In addition, the International Standardization Organization has proposed standard guidelines to assess the needs of older persons and persons with disabilities, including the needs arising from abilities loss and providing tools to identify their needs [12]. Muszalik et al. used a questionnaire based on the Care Dependency Scale and an activity of daily living (ADL) questionnaire based on the Katz Scale to obtain the physical function, cognitive ability, and depression degree of elderly individuals and then analysed their care needs [13].Ability grouping of elderly individuals can provide support for care needs assessment of elderly individuals. Therefore, this article studies the ability grouping of the elderly individuals based on clustering algorithm. Tobis et al. selected the indicators of the Mini-Mental State Examination (MMSE), Barthel Index, and Geriatric Depression Scale as the variables of k-means clustering analysis to analyse ability differences and demand pattern differences among different groups [14]. K-means is a clustering algorithm created to solve problems where all of the attributes in the dataset are numerical. However, the abilities of elderly individuals are both numerical and categorical, which is very common in practice [15]. The K-prototypes algorithm [16] was proposed to deal with mixed attributes’ dataset clustering and shows excellent performance in clustering of mixed attributes’ dataset. Therefore, this article adopts K-prototypes algorithm to group the abilities of the elderly individuals.Due to the excellent performance of K-prototypes in mixed attributes’ dataset clustering, some researchers have studied and improved the existing limitations of the K-prototypes clustering algorithm. The research of dissimilarity measure is the main direction to improve K-prototypes algorithm. Chatzis provides a novel FCM-type algorithm employing a fully probabilistic dissimilarity function for handling data with mixed attributes [17]. Ji et al. propose a new measure to calculate the dissimilarity between data objects and prototypes of clusters, which takes into account the significance of different attributes towards the clustering process [18]. Sangam and Om studied the limitations of the dissimilarity measure in the K-prototypes algorithm based on examples and proposed a dissimilarity measure for datasets with numerical, categorical, and mixed attributes [19]. In these research studies, on improving K-prototypes’ dissimilarity measure, the focus is mainly on the dissimilarity of categorical attributes.It is unreasonable to define the abilities dissimilarity of elderly individuals as 0 or 1, most of which are categorical and ordinal. Taking the ability of elderly individuals, that is, instrumental activities of daily living, as an example, the ability level of elderly individuals includes complete self-care, mild disabled, moderate disabled, severe disabled, and complete disabled. Obviously, the difference between complete self-care and mild disabled is not equal to the difference between complete self-care and moderate disabled. Therefore, it is necessary to extend the dissimilarity measure to better calculate the dissimilarity of categorical attributes and ordinal attributes.For this reason, the dissimilarity measure was further extended and improved based on the data distribution of clusters in this article so that it can better cluster elderly individuals with categorical and ordinal attributes. Then, the improved K-prototypes was used to group elderly individuals by their abilities, taking the CHARLS [20] dataset as an example. Based on the differences in abilities, the needs of different groups of elderly individuals can be found, and precision services can be achieved accordingly.


## 2. K-Prototypes Algorithm

K-prototypes is a combination of the K-means and K-mode algorithms. K-prototypes adopts weight to adjust the influence degree of numerical and categorical attributes on clustering results. Similar to the K-means and K-modes, K denotes the number of clusters, and dissimilarity measure is the main part of the algorithm. Therefore, only the dissimilarity measure of the algorithm is described below.LetX=X1,X2,…Xn be a dataset with n objects and m attributes, Xi=xi1,xi2,…,xil,…,xim, where 1≤i≤n and 1≤l≤m. Let Al be an attribute; Al is a numerical attribute when 1≤l≤q and is a categorical attribute when q+1≤l≤m. Objects in cluster Cj is represented as Xcj=X1cj,X2cj,…,Xtcj, and an object in cluster Cj is represented as Xscj=xs1cj,xs2cj,…,xsmcj. In the algorithm, the centre of cluster Cj named prototype is represented as Vj=vj1,vj2,…,vjm, where j∈1,k, j is an integer number, and k is number of clusters.When the attribute is numerical, the distance betweenXi and Vj is defined as follows:(1)d1Xi,Vj=∑l=1qxil−vjl2.When the attribute is categorical, the distance betweenXi and Vj is defined as follows:(2)d2Xi,Vj=∑l=q+1mδxil,vjl,where(3)δxil,vjl=1,xil≠vjl,0,xil=vjl,In summary, the distance betweenXi and Vj is defined as the weighted sum of d1Xi,Vj and d2Xi,Vj:(4)dXi,Vj=d1Xi,Vj+θd2Xi,Vj,where θ is a weight to adjust the influence of categorical attributes and numerical attributes on the clustering results.


## 3. Improved K-Prototypes Algorithm

K-prototypes is a simple and efficient algorithm that is easily understood and implemented, but its shortcomings are evident. The dissimilarity measure of K-prototypes does not consider the difference between the object to be allocated and the existing objects in the cluster, and it does not distinguish the ordinal and nonordinal categorical attributes. In fact, the dissimilarity between the object to be allocated and the cluster can be reflected by two factors: one is the dissimilarity between the object to be allocated and the prototype of the cluster, and the other is the dissimilarity between the object to be allocated and other objects in the cluster. The dissimilarity measure proposed in this paper combines these two factors. Clustering performance of the improved K-prototypes based on the dissimilarity measure proposed in this article was validated using UCI datasets [21].


### 3.1. Dissimilarity Measure

In order to better measure the dissimilarity between the object to be allocated and the cluster, we should not only consider the dissimilarity between the object to be allocated and the prototype but also considers the difference between it and other objects in the cluster. According to this idea, the improved dissimilarity of categorical attributes is shown in the following equation:(5)d3Xi,Vj=∑l=q+1mμxil,vjl,where(6)μxil,vjl=1+d¯Nlv,xil≠vjl,1−Nfxild¯Cj,xil=vjl,where xil is the value of attribute Al of Xi, vjl is the value of attribute Al of prototype Vj, Nlv represents the number of distinct values on categorical attribute Al in cluster Cj, Nfxil represents the frequency of xil on categorical attribute Al in cluster Cj, Cj represents the total number of objects in cluster Cj, and d¯ represents the average of the dissimilarity between the value xil and the corresponding attribute value xslcj of objects in cluster Cj. When d¯ is the denominator, μxil,vjl=0 if d¯=0 or Nfxil>d¯Cj. d¯ can be expressed as the following equation:(7)d¯=∑s=1tdxil,xslcjt,where dxil,xslcj=0 if xil=xslcj. dxil,xslcj=1 if xil≠xslcj and Al is a nonordinal categorical attribute. dxil,xslcj=xil−xslcj, if xil≠xslcj and Al is an ordinal attribute. In this article, the values of ordinal Al are set as increasing integer sequences with adjacent difference of 1.The difference betweenμxil,vjl in equation (6) and δxil,vil in equation (3) is as follows.Whenxil≠vjl, the value of δxil,vjl is 1. However, the dissimilarity d¯ between the attribute value of the object to be allocated and the corresponding attribute value of objects in cluster Cj is taken as the penalty value for μxil,vjl on the basis of δxil,vjl=1. The larger d¯ is, the larger μxil,vjl will be. At the same time, Nlv is also an influence factor of μxil,vjl. The larger Nlv is, the lower the aggregation degree of attribute values in cluster Cj is, and the lower the reliability of the prototype value is. Therefore, increased value of Nlv can be used to reduce the corresponding punishment.Whenxil=vjl, the value of δxil,vjl is 0. In order to better reflect the dissimilarity between the object to be allocated and other objects in the cluster, the dissimilarity is extended on the basis of δxil,vjl=1. Therefore, the ratio Nfxil/Cj between the frequency of xil on categorical attribute Al in cluster Cj and the total number of objects in cluster Cj is introduced as the excitation factor based on the basis of δxil,vjl=1. The higher Nfxil/Cj is, the smaller μxil,vjl is. In addition, the dissimilarity d¯ between the attribute value of the object to be allocated and the corresponding attribute value in cluster Cj is also considered. If d¯ increases, the excitation value will be reduced.The nonordinal attributes and ordinal attributes are further distinguished. The dissimilarity of nonordinal attributes is represented byd31Xi,Vj, and the dissimilarity of ordinal attributes is represented by d32Xi,Vj. To reflect the difference between distinct values of an ordinal attribute, the values of the ordinal attribute are set to different numbers when calculating dissimilarity. For example, the hearing ability of elderly individuals includes four levels, which are excellent, good, average, and poor, and these four values are assigned as 1, 2, 3, and 4, respectively. In this case, the difference between excellent and good is 1, and the difference between excellent and average is 2. For nonordinal attributes, the difference between different values is set to 1 and difference between the same values is set to 0.Using the improved dissimilarity measure of nonordinal attributes and ordinal attributes, combined with the dissimilarity measure of numerical attributes in equation (1), the dissimilarity measure of objects Xi and Vj is defined as follows:(8)dXi,Vj=d1Xi,Vj+λ1d31Xi,Vj+λ2d32Xi,Vj,where λ1 and λ2 are weights to adjust the influence of nonordinal attributes and ordinal attributes on the clustering results.


### 3.2. Performance Evaluation of the Improved K-Prototypes

Our proposed improved K-prototypes with the dissimilarity measures in equation (8) is compared with other typical clustering algorithms with different dissimilarity measures based on various evaluation criteria of clustering algorithms.Rivera-Ríos [22] summarized a variety of dissimilarity measures. The dissimilarity measures that can be used to measure the mixed attributes, such as Euclidean distance of K-means++, the dissimilarity measure of K-prototypes, and the dissimilarity measure of equi-biased K-prototypes in [19], are selected to compare with our proposed dissimilarity measure.The performance of the clustering algorithm can be evaluated by external evaluation criteria and internal evaluation criteria [22–24]. The internal evaluation criteria are calculated based on the dissimilarity of objects in clusters, and the dissimilarity measure of several algorithms is different, and accordingly, the internal evaluation results of different algorithms will not be on the same scale. Therefore, the internal evaluation criteria are not used for algorithm evaluation. External evaluation criteria are used to evaluate the clustering performance by classification labels contained in the dataset. In this article, external evaluation criteria, such as F-measure, RAND index, adjusted RAND index, and accuracy [22, 23], are used to evaluate the clustering performance. The value range of the F-measure, RAND index, and accuracy is [0, 1], and value range of the adjusted RAND index is [−1, 1]. The closer the value is to 1, the better the clustering effect is. The closer it is to 0 or −1, the worse the clustering effect is.Five mixed UCI datasets containing mixed attributes were selected to evaluate the performance of our improved K-prototypes algorithm. The experimental results of the five UCI datasets are shown in Tables1–5. The average of F-measure, Rand index, adjusted Rand index, and accuracy had been obtained over 30 runs of the cluster algorithm. While running K-prototypes and our proposed improved K-prototypes, the weight θ of K-prototypes and the weights λ1 and λ2 of our proposed improved K-prototypes were set to three different values. Since the numerical attributes of all datasets are normalized, and the average of the standard deviation of numerical attributes is less than 1, so the weights are taken in the range of 0 to 1. In addition, the cluster results of these K-prototypes algorithms are unstable due to the influence of the random initial prototype. Therefore, average accuracy of the top 5 in 30 runs results is also used to evaluate the stability of these cluster algorithms.Table 1
Clustering performance on the credit approval dataset.
Cluster algorithmF-measureRand indexAdjusted Rand indexAccuracyAverage accuracy of the top 5 in 30 runs resultsK-means++0.51860.51070.02130.58190.5819K-prototypesθ = 0.10.58500.52820.05470.75720.7887K-prototypesθ = 0.20.56720.51900.03650.73240.7841K-prototypesθ = 0.30.55790.52100.04080.69750.7856K-prototypes in [19]0.58420.56320.12570.70650.8273Our improved K-prototypesλ1 = λ2 = 0.10.69010.68720.37440.80630.8101Our improved K-prototypesλ1 = λ2 = 0.20.67150.66690.33370.78860.8070Our improved K-prototypesλ1 = λ2 = 0.30.66480.65780.31530.78070.7994Table 2
Clustering performance on the heart disease dataset.
Cluster algorithmF-measureRand indexAdjusted Rand indexAccuracyAverage accuracy of the top 5 in 30 runs resultsk-means++0.64070.63700.27380.76300.7630K-prototypesθ = 0.10.64990.63520.26990.76110.7704K-prototypesθ = 0.20.67890.67280.23750.79490.7963K-prototypesθ = 0.30.66350.66020.32020.78410.7889K-prototypes in [19]0.60750.59970.19910.71200.8185Our improved K-prototypesλ1 = λ2 = 0.10.72690.72120.44220.83330.8333Our improved K-prototypesλ1 = λ2 = 0.20.70460.69850.39690.81590.8185Our improved K-prototypesλ1 = λ2 = 0.30.68690.68330.36650.80370.8037Table 3
Clustering performance on the acute dataset.
Cluster algorithmF-measureRand indexAdjusted Rand indexAccuracyAverage accuracy of the top 5 in 30 runs resultsk-means++0.51550.51270.02560.59170.5917K-prototypesθ = 0.10.74990.74630.49250.85220.8633K-prototypesθ = 0.20.76210.75350.50650.83330.9333K-prototypesθ = 0.30.74200.72920.45750.82440.9333K-prototypes in [19]0.67560.65400.30630.77940.9650Our improved K-prototypesλ1 = λ2 = 0.10.73260.72690.45350.81360.9333Our improved K-prototypesλ1 = λ2 = 0.20.81670.80190.60260.88390.9333Our improved K-prototypesλ1 = λ2 = 0.30.78860.77110.54090.86240.9333Table 4
Clustering performance on the liver disorders dataset.
Cluster algorithmF-measureRand indexAdjusted Rand indexAccuracyAverage accuracy of the top 5 in 30 runs resultsk-means++0.54270.50310.00290.69560.6956K-prototypesθ = 0.10.58680.5011−0.00690.81230.8748K-prototypesθ = 0.20.55800.50350.00160.72080.8232K-prototypesθ = 0.30.53470.50150.00020.67130.7177K-prototypes in [19]0.56390.5017−000310.74150.9246Our improved K-prototypesλ1 = λ2 = 0.10.60240.5033−0.00460.84430.9507Our improved K-prototypesλ1 = λ2 = 0.20.60330.50600.00090.83600.9391Our improved K-prototypesλ1 = λ2 = 0.30.61560.5046−0.00400.86950.9507Table 5
Clustering performance on the contraceptive method choice dataset.
Cluster algorithmF-measureRand indexAdjusted Rand indexAccuracyAverage accuracy of the top 5 in 30 runs resultsk-means++0.36570.56400.03390.44530.4453K-prototypesθ = 0.10.36910.54900.01840.46780.5058K-prototypesθ = 0.20.36580.54610.01250.44800.4562K-prototypesθ = 0.30.36120.54440.00770.46280.4811K-prototypes in [19]0.43410.48970.00830.65080.7605Our improved K-prototypesλ1 = λ2 = 0.10.36970.55290.02340.46720.4765Our improved K-prototypesλ1 = λ2 = 0.20.36590.55030.01760.45630.4959Our improved K-prototypesλ1 = λ2 = 0.30.36650.54870.01620.45310.5040The experimental results in Tables1–5 show that F-measure, Rand index, adjusted Rand index, and accuracy of our proposed improved K-prototypes algorithm are better than those of the other three cluster algorithms in the four datasets. In these four datasets, the average accuracy of the top 5 in 30 runs results of our proposed K-prototypes is less than that of K-prototypes in [19] in two datasets, which show that our proposed dissimilarity measure can make clustering results more stable than the dissimilarity measure of K-prototypes in [19].After the performance of the improved K-prototypes was evaluated, the abilities of elderly individuals were grouped based on the improved K-prototypes, and the differences in abilities of each group were analysed (see Section4).


## 3.1. Dissimilarity Measure

In order to better measure the dissimilarity between the object to be allocated and the cluster, we should not only consider the dissimilarity between the object to be allocated and the prototype but also considers the difference between it and other objects in the cluster. According to this idea, the improved dissimilarity of categorical attributes is shown in the following equation:(5)d3Xi,Vj=∑l=q+1mμxil,vjl,where(6)μxil,vjl=1+d¯Nlv,xil≠vjl,1−Nfxild¯Cj,xil=vjl,where xil is the value of attribute Al of Xi, vjl is the value of attribute Al of prototype Vj, Nlv represents the number of distinct values on categorical attribute Al in cluster Cj, Nfxil represents the frequency of xil on categorical attribute Al in cluster Cj, Cj represents the total number of objects in cluster Cj, and d¯ represents the average of the dissimilarity between the value xil and the corresponding attribute value xslcj of objects in cluster Cj. When d¯ is the denominator, μxil,vjl=0 if d¯=0 or Nfxil>d¯Cj. d¯ can be expressed as the following equation:(7)d¯=∑s=1tdxil,xslcjt,where dxil,xslcj=0 if xil=xslcj. dxil,xslcj=1 if xil≠xslcj and Al is a nonordinal categorical attribute. dxil,xslcj=xil−xslcj, if xil≠xslcj and Al is an ordinal attribute. In this article, the values of ordinal Al are set as increasing integer sequences with adjacent difference of 1.The difference betweenμxil,vjl in equation (6) and δxil,vil in equation (3) is as follows.Whenxil≠vjl, the value of δxil,vjl is 1. However, the dissimilarity d¯ between the attribute value of the object to be allocated and the corresponding attribute value of objects in cluster Cj is taken as the penalty value for μxil,vjl on the basis of δxil,vjl=1. The larger d¯ is, the larger μxil,vjl will be. At the same time, Nlv is also an influence factor of μxil,vjl. The larger Nlv is, the lower the aggregation degree of attribute values in cluster Cj is, and the lower the reliability of the prototype value is. Therefore, increased value of Nlv can be used to reduce the corresponding punishment.Whenxil=vjl, the value of δxil,vjl is 0. In order to better reflect the dissimilarity between the object to be allocated and other objects in the cluster, the dissimilarity is extended on the basis of δxil,vjl=1. Therefore, the ratio Nfxil/Cj between the frequency of xil on categorical attribute Al in cluster Cj and the total number of objects in cluster Cj is introduced as the excitation factor based on the basis of δxil,vjl=1. The higher Nfxil/Cj is, the smaller μxil,vjl is. In addition, the dissimilarity d¯ between the attribute value of the object to be allocated and the corresponding attribute value in cluster Cj is also considered. If d¯ increases, the excitation value will be reduced.The nonordinal attributes and ordinal attributes are further distinguished. The dissimilarity of nonordinal attributes is represented byd31Xi,Vj, and the dissimilarity of ordinal attributes is represented by d32Xi,Vj. To reflect the difference between distinct values of an ordinal attribute, the values of the ordinal attribute are set to different numbers when calculating dissimilarity. For example, the hearing ability of elderly individuals includes four levels, which are excellent, good, average, and poor, and these four values are assigned as 1, 2, 3, and 4, respectively. In this case, the difference between excellent and good is 1, and the difference between excellent and average is 2. For nonordinal attributes, the difference between different values is set to 1 and difference between the same values is set to 0.Using the improved dissimilarity measure of nonordinal attributes and ordinal attributes, combined with the dissimilarity measure of numerical attributes in equation (1), the dissimilarity measure of objects Xi and Vj is defined as follows:(8)dXi,Vj=d1Xi,Vj+λ1d31Xi,Vj+λ2d32Xi,Vj,where λ1 and λ2 are weights to adjust the influence of nonordinal attributes and ordinal attributes on the clustering results.


## 3.2. Performance Evaluation of the Improved K-Prototypes

Our proposed improved K-prototypes with the dissimilarity measures in equation (8) is compared with other typical clustering algorithms with different dissimilarity measures based on various evaluation criteria of clustering algorithms.Rivera-Ríos [22] summarized a variety of dissimilarity measures. The dissimilarity measures that can be used to measure the mixed attributes, such as Euclidean distance of K-means++, the dissimilarity measure of K-prototypes, and the dissimilarity measure of equi-biased K-prototypes in [19], are selected to compare with our proposed dissimilarity measure.The performance of the clustering algorithm can be evaluated by external evaluation criteria and internal evaluation criteria [22–24]. The internal evaluation criteria are calculated based on the dissimilarity of objects in clusters, and the dissimilarity measure of several algorithms is different, and accordingly, the internal evaluation results of different algorithms will not be on the same scale. Therefore, the internal evaluation criteria are not used for algorithm evaluation. External evaluation criteria are used to evaluate the clustering performance by classification labels contained in the dataset. In this article, external evaluation criteria, such as F-measure, RAND index, adjusted RAND index, and accuracy [22, 23], are used to evaluate the clustering performance. The value range of the F-measure, RAND index, and accuracy is [0, 1], and value range of the adjusted RAND index is [−1, 1]. The closer the value is to 1, the better the clustering effect is. The closer it is to 0 or −1, the worse the clustering effect is.Five mixed UCI datasets containing mixed attributes were selected to evaluate the performance of our improved K-prototypes algorithm. The experimental results of the five UCI datasets are shown in Tables1–5. The average of F-measure, Rand index, adjusted Rand index, and accuracy had been obtained over 30 runs of the cluster algorithm. While running K-prototypes and our proposed improved K-prototypes, the weight θ of K-prototypes and the weights λ1 and λ2 of our proposed improved K-prototypes were set to three different values. Since the numerical attributes of all datasets are normalized, and the average of the standard deviation of numerical attributes is less than 1, so the weights are taken in the range of 0 to 1. In addition, the cluster results of these K-prototypes algorithms are unstable due to the influence of the random initial prototype. Therefore, average accuracy of the top 5 in 30 runs results is also used to evaluate the stability of these cluster algorithms.Table 1
Clustering performance on the credit approval dataset.
Cluster algorithmF-measureRand indexAdjusted Rand indexAccuracyAverage accuracy of the top 5 in 30 runs resultsK-means++0.51860.51070.02130.58190.5819K-prototypesθ = 0.10.58500.52820.05470.75720.7887K-prototypesθ = 0.20.56720.51900.03650.73240.7841K-prototypesθ = 0.30.55790.52100.04080.69750.7856K-prototypes in [19]0.58420.56320.12570.70650.8273Our improved K-prototypesλ1 = λ2 = 0.10.69010.68720.37440.80630.8101Our improved K-prototypesλ1 = λ2 = 0.20.67150.66690.33370.78860.8070Our improved K-prototypesλ1 = λ2 = 0.30.66480.65780.31530.78070.7994Table 2
Clustering performance on the heart disease dataset.
Cluster algorithmF-measureRand indexAdjusted Rand indexAccuracyAverage accuracy of the top 5 in 30 runs resultsk-means++0.64070.63700.27380.76300.7630K-prototypesθ = 0.10.64990.63520.26990.76110.7704K-prototypesθ = 0.20.67890.67280.23750.79490.7963K-prototypesθ = 0.30.66350.66020.32020.78410.7889K-prototypes in [19]0.60750.59970.19910.71200.8185Our improved K-prototypesλ1 = λ2 = 0.10.72690.72120.44220.83330.8333Our improved K-prototypesλ1 = λ2 = 0.20.70460.69850.39690.81590.8185Our improved K-prototypesλ1 = λ2 = 0.30.68690.68330.36650.80370.8037Table 3
Clustering performance on the acute dataset.
Cluster algorithmF-measureRand indexAdjusted Rand indexAccuracyAverage accuracy of the top 5 in 30 runs resultsk-means++0.51550.51270.02560.59170.5917K-prototypesθ = 0.10.74990.74630.49250.85220.8633K-prototypesθ = 0.20.76210.75350.50650.83330.9333K-prototypesθ = 0.30.74200.72920.45750.82440.9333K-prototypes in [19]0.67560.65400.30630.77940.9650Our improved K-prototypesλ1 = λ2 = 0.10.73260.72690.45350.81360.9333Our improved K-prototypesλ1 = λ2 = 0.20.81670.80190.60260.88390.9333Our improved K-prototypesλ1 = λ2 = 0.30.78860.77110.54090.86240.9333Table 4
Clustering performance on the liver disorders dataset.
Cluster algorithmF-measureRand indexAdjusted Rand indexAccuracyAverage accuracy of the top 5 in 30 runs resultsk-means++0.54270.50310.00290.69560.6956K-prototypesθ = 0.10.58680.5011−0.00690.81230.8748K-prototypesθ = 0.20.55800.50350.00160.72080.8232K-prototypesθ = 0.30.53470.50150.00020.67130.7177K-prototypes in [19]0.56390.5017−000310.74150.9246Our improved K-prototypesλ1 = λ2 = 0.10.60240.5033−0.00460.84430.9507Our improved K-prototypesλ1 = λ2 = 0.20.60330.50600.00090.83600.9391Our improved K-prototypesλ1 = λ2 = 0.30.61560.5046−0.00400.86950.9507Table 5
Clustering performance on the contraceptive method choice dataset.
Cluster algorithmF-measureRand indexAdjusted Rand indexAccuracyAverage accuracy of the top 5 in 30 runs resultsk-means++0.36570.56400.03390.44530.4453K-prototypesθ = 0.10.36910.54900.01840.46780.5058K-prototypesθ = 0.20.36580.54610.01250.44800.4562K-prototypesθ = 0.30.36120.54440.00770.46280.4811K-prototypes in [19]0.43410.48970.00830.65080.7605Our improved K-prototypesλ1 = λ2 = 0.10.36970.55290.02340.46720.4765Our improved K-prototypesλ1 = λ2 = 0.20.36590.55030.01760.45630.4959Our improved K-prototypesλ1 = λ2 = 0.30.36650.54870.01620.45310.5040The experimental results in Tables1–5 show that F-measure, Rand index, adjusted Rand index, and accuracy of our proposed improved K-prototypes algorithm are better than those of the other three cluster algorithms in the four datasets. In these four datasets, the average accuracy of the top 5 in 30 runs results of our proposed K-prototypes is less than that of K-prototypes in [19] in two datasets, which show that our proposed dissimilarity measure can make clustering results more stable than the dissimilarity measure of K-prototypes in [19].After the performance of the improved K-prototypes was evaluated, the abilities of elderly individuals were grouped based on the improved K-prototypes, and the differences in abilities of each group were analysed (see Section4).


## 4. Data Source and Data Preprocessing

The data source and data preprocessing are explained in the following sections.


### 4.1. Data Source

The data about the abilities of elderly individuals used in this study were selected from the CHARLS2018 dataset. CHARLS is a large-scale and long-term tracking survey project hosted by the National Development Institute of Peking University and implemented by the China Social Science Research Centre of Peking University. It collects high-quality microdata on middle-aged and older households and individuals over 45 years old in China to analyse the ageing issue in China and to promote interdisciplinary research on ageing. The CHARLS dataset covers personal information, health status, physical status, health service utilization, health insurance, income, pension, assets, consumption, household status, and community status of older people. The national baseline survey was conducted in 2011, covering 150 district-level units, 450 village-level units, and 17,000 people in approximately 10,000 households [20]. These samples are tracked every two or three years, and the latest 2018 CHARLS data were chosen for this study.A portion of the CHARLS2018 data was selected for this study. There were three criteria for data selection: one criterion was that the age of older people had to be over 60 years old, the second was that the older people had to live in urban areas, and the third was that the samples should have few or no missing values. Using the above data selection criteria, 2965 samples were selected.


### 4.2. Data Preprocessing

The abilities of elderly individuals in the CHARLS2018 dataset were determined through several questions answered by themselves. Therefore, it is necessary to extract, integrate, and process the survey data contained in the CHARLS dataset according to some criteria to obtain the ability indicators. In addition, missing data were imputed, and the numerical data were normalized.


#### 4.2.1. Grading Criteria of Self-Reported Depression Level

According to the 10-item depression scale of the Centers for Epidemiological Studies (CES-D10) [25], self-reported depression levels are divided into three grades: normal, mild, and severe, based on the total scores of the questions. A question was scored 0 points if the answer was few or none (<1 day), 1 point if the answer was not too many (1-2 days), 2 points if the answer was sometimes or half the time (3-4 days), and 3 points if the answer was most of the time (5–7 days) regarding negative emotions that arise during a week. A question was scored 0 points if the answer was most of the time (5–7 days), 1 point if the answer was sometimes or half the time (3-4 days), 2 points if the answer was not too often (1-2 days), and 3 points if the answer was rarely or not at all (<1 day) regarding positive emotions that arise during a week. The specific assessment questions, score ranges, and corresponding levels are shown in Table 6.Table 6
Grading criteria of self-reported depression level.
QuestionsScoreLevelI was bothered by things that do not usually bother me0–9NormalI had trouble keeping my mind on what I was doingI felt depressedI felt that everything I did was an effortI felt hopeful about the future10–16MildI felt fearfulMy sleep was restless≥17SevereI was happyI felt lonelyI could not get “going”


#### 4.2.2. Grading Criteria of Cognitive Ability Level

According to the MMSE [26], cognitive ability is graded into four levels: normal, mild cognitive disorder, moderate cognitive disorder, and severe cognitive disorder, based on the total scores of the questions. There are 30 test questions related to cognitive ability. A question with a correct answer was scored 1 point and was scored 0 point with a false answer. The specific assessment questions, score ranges, and corresponding levels are shown in Table 7.Table 7
Grading criteria of cognitive ability level.
QuestionsScoreLevel10 questions on orientation skills27–30Normal3 questions on memory5 questions on attention and numeracy21–26Mild3 questions on recall ability2 questions on naming ability1 question on retelling skills10–20Moderate1 question on reading skills3 questions of three-step command1 question on writing0–9Severe1 question on structural competence


#### 4.2.3. Grading Criteria of Basic Activities of Daily Living

The assessment of basic activities of daily living includes six items according to the basic activity of daily living (BADL) scale [27]. Each item is assessed, and the number of items that the older people are able to do by themselves is recorded. Based on the total score, the basic activities of daily living are divided into five levels, including complete self-care, mild disabled, moderate disabled, severe disabled, and complete disabled. The specific assessment questions, score ranges, and corresponding levels are shown in Table 8.Table 8
Grading criteria of basic activities of daily living.
QuestionsScoreLevelDressingBathingEatingGetting up and out of bedToiletingControl of defecation6Complete self-care4 or 5Mild disabled2 or 3Moderate disabled1Severe disabled0Complete disabled


#### 4.2.4. Grading Criteria of Instrumental Activities of Daily Living

The assessment of instrumental activities of daily living includes six items according to the instrumental activity of daily living (IADL) scale [27]. Each item is assessed, and the number of items that the older people are able to do is recorded. Based on the total score, the instrumental activities of daily living are divided into five levels, including complete self-care, mild disabled, moderate disabled, severe disabled, and complete disabled. The specific assessment questions, score ranges, and corresponding levels are shown in Table 9.Table 9
Grading criteria of instrumental activities of daily living.
QuestionsScoreLevelDoing houseworkCookingShoppingPhoningTaking medicineManaging money6Complete self-care4 or 5Mild disabled2 or 3Moderate disabled1Severe disabled0Complete disabled


#### 4.2.5. Missing Data and Abnormal Data Processing

For numeric attributes, the missing data are imputed with the median. For categorical attributes, the missing data are imputed with the mode. In view of the outliers, the value is directly deleted and then imputed according to the missing data processing methods.


#### 4.2.6. Data Normalization

In order to improve the rationality of the dissimilarity calculation, the numerical attributes in datasets are normalized. The original data were normalized by the min-max method to ensure the value of each numerical attribute was mapped to [0, 1].


## 4.1. Data Source

The data about the abilities of elderly individuals used in this study were selected from the CHARLS2018 dataset. CHARLS is a large-scale and long-term tracking survey project hosted by the National Development Institute of Peking University and implemented by the China Social Science Research Centre of Peking University. It collects high-quality microdata on middle-aged and older households and individuals over 45 years old in China to analyse the ageing issue in China and to promote interdisciplinary research on ageing. The CHARLS dataset covers personal information, health status, physical status, health service utilization, health insurance, income, pension, assets, consumption, household status, and community status of older people. The national baseline survey was conducted in 2011, covering 150 district-level units, 450 village-level units, and 17,000 people in approximately 10,000 households [20]. These samples are tracked every two or three years, and the latest 2018 CHARLS data were chosen for this study.A portion of the CHARLS2018 data was selected for this study. There were three criteria for data selection: one criterion was that the age of older people had to be over 60 years old, the second was that the older people had to live in urban areas, and the third was that the samples should have few or no missing values. Using the above data selection criteria, 2965 samples were selected.


## 4.2. Data Preprocessing

The abilities of elderly individuals in the CHARLS2018 dataset were determined through several questions answered by themselves. Therefore, it is necessary to extract, integrate, and process the survey data contained in the CHARLS dataset according to some criteria to obtain the ability indicators. In addition, missing data were imputed, and the numerical data were normalized.


### 4.2.1. Grading Criteria of Self-Reported Depression Level

According to the 10-item depression scale of the Centers for Epidemiological Studies (CES-D10) [25], self-reported depression levels are divided into three grades: normal, mild, and severe, based on the total scores of the questions. A question was scored 0 points if the answer was few or none (<1 day), 1 point if the answer was not too many (1-2 days), 2 points if the answer was sometimes or half the time (3-4 days), and 3 points if the answer was most of the time (5–7 days) regarding negative emotions that arise during a week. A question was scored 0 points if the answer was most of the time (5–7 days), 1 point if the answer was sometimes or half the time (3-4 days), 2 points if the answer was not too often (1-2 days), and 3 points if the answer was rarely or not at all (<1 day) regarding positive emotions that arise during a week. The specific assessment questions, score ranges, and corresponding levels are shown in Table 6.Table 6
Grading criteria of self-reported depression level.
QuestionsScoreLevelI was bothered by things that do not usually bother me0–9NormalI had trouble keeping my mind on what I was doingI felt depressedI felt that everything I did was an effortI felt hopeful about the future10–16MildI felt fearfulMy sleep was restless≥17SevereI was happyI felt lonelyI could not get “going”


### 4.2.2. Grading Criteria of Cognitive Ability Level

According to the MMSE [26], cognitive ability is graded into four levels: normal, mild cognitive disorder, moderate cognitive disorder, and severe cognitive disorder, based on the total scores of the questions. There are 30 test questions related to cognitive ability. A question with a correct answer was scored 1 point and was scored 0 point with a false answer. The specific assessment questions, score ranges, and corresponding levels are shown in Table 7.Table 7
Grading criteria of cognitive ability level.
QuestionsScoreLevel10 questions on orientation skills27–30Normal3 questions on memory5 questions on attention and numeracy21–26Mild3 questions on recall ability2 questions on naming ability1 question on retelling skills10–20Moderate1 question on reading skills3 questions of three-step command1 question on writing0–9Severe1 question on structural competence


### 4.2.3. Grading Criteria of Basic Activities of Daily Living

The assessment of basic activities of daily living includes six items according to the basic activity of daily living (BADL) scale [27]. Each item is assessed, and the number of items that the older people are able to do by themselves is recorded. Based on the total score, the basic activities of daily living are divided into five levels, including complete self-care, mild disabled, moderate disabled, severe disabled, and complete disabled. The specific assessment questions, score ranges, and corresponding levels are shown in Table 8.Table 8
Grading criteria of basic activities of daily living.
QuestionsScoreLevelDressingBathingEatingGetting up and out of bedToiletingControl of defecation6Complete self-care4 or 5Mild disabled2 or 3Moderate disabled1Severe disabled0Complete disabled


### 4.2.4. Grading Criteria of Instrumental Activities of Daily Living

The assessment of instrumental activities of daily living includes six items according to the instrumental activity of daily living (IADL) scale [27]. Each item is assessed, and the number of items that the older people are able to do is recorded. Based on the total score, the instrumental activities of daily living are divided into five levels, including complete self-care, mild disabled, moderate disabled, severe disabled, and complete disabled. The specific assessment questions, score ranges, and corresponding levels are shown in Table 9.Table 9
Grading criteria of instrumental activities of daily living.
QuestionsScoreLevelDoing houseworkCookingShoppingPhoningTaking medicineManaging money6Complete self-care4 or 5Mild disabled2 or 3Moderate disabled1Severe disabled0Complete disabled


### 4.2.5. Missing Data and Abnormal Data Processing

For numeric attributes, the missing data are imputed with the median. For categorical attributes, the missing data are imputed with the mode. In view of the outliers, the value is directly deleted and then imputed according to the missing data processing methods.


### 4.2.6. Data Normalization

In order to improve the rationality of the dissimilarity calculation, the numerical attributes in datasets are normalized. The original data were normalized by the min-max method to ensure the value of each numerical attribute was mapped to [0, 1].


## 4.2.1. Grading Criteria of Self-Reported Depression Level

According to the 10-item depression scale of the Centers for Epidemiological Studies (CES-D10) [25], self-reported depression levels are divided into three grades: normal, mild, and severe, based on the total scores of the questions. A question was scored 0 points if the answer was few or none (<1 day), 1 point if the answer was not too many (1-2 days), 2 points if the answer was sometimes or half the time (3-4 days), and 3 points if the answer was most of the time (5–7 days) regarding negative emotions that arise during a week. A question was scored 0 points if the answer was most of the time (5–7 days), 1 point if the answer was sometimes or half the time (3-4 days), 2 points if the answer was not too often (1-2 days), and 3 points if the answer was rarely or not at all (<1 day) regarding positive emotions that arise during a week. The specific assessment questions, score ranges, and corresponding levels are shown in Table 6.Table 6
Grading criteria of self-reported depression level.
QuestionsScoreLevelI was bothered by things that do not usually bother me0–9NormalI had trouble keeping my mind on what I was doingI felt depressedI felt that everything I did was an effortI felt hopeful about the future10–16MildI felt fearfulMy sleep was restless≥17SevereI was happyI felt lonelyI could not get “going”


## 4.2.2. Grading Criteria of Cognitive Ability Level

According to the MMSE [26], cognitive ability is graded into four levels: normal, mild cognitive disorder, moderate cognitive disorder, and severe cognitive disorder, based on the total scores of the questions. There are 30 test questions related to cognitive ability. A question with a correct answer was scored 1 point and was scored 0 point with a false answer. The specific assessment questions, score ranges, and corresponding levels are shown in Table 7.Table 7
Grading criteria of cognitive ability level.
QuestionsScoreLevel10 questions on orientation skills27–30Normal3 questions on memory5 questions on attention and numeracy21–26Mild3 questions on recall ability2 questions on naming ability1 question on retelling skills10–20Moderate1 question on reading skills3 questions of three-step command1 question on writing0–9Severe1 question on structural competence


## 4.2.3. Grading Criteria of Basic Activities of Daily Living

The assessment of basic activities of daily living includes six items according to the basic activity of daily living (BADL) scale [27]. Each item is assessed, and the number of items that the older people are able to do by themselves is recorded. Based on the total score, the basic activities of daily living are divided into five levels, including complete self-care, mild disabled, moderate disabled, severe disabled, and complete disabled. The specific assessment questions, score ranges, and corresponding levels are shown in Table 8.Table 8
Grading criteria of basic activities of daily living.
QuestionsScoreLevelDressingBathingEatingGetting up and out of bedToiletingControl of defecation6Complete self-care4 or 5Mild disabled2 or 3Moderate disabled1Severe disabled0Complete disabled


## 4.2.4. Grading Criteria of Instrumental Activities of Daily Living

The assessment of instrumental activities of daily living includes six items according to the instrumental activity of daily living (IADL) scale [27]. Each item is assessed, and the number of items that the older people are able to do is recorded. Based on the total score, the instrumental activities of daily living are divided into five levels, including complete self-care, mild disabled, moderate disabled, severe disabled, and complete disabled. The specific assessment questions, score ranges, and corresponding levels are shown in Table 9.Table 9
Grading criteria of instrumental activities of daily living.
QuestionsScoreLevelDoing houseworkCookingShoppingPhoningTaking medicineManaging money6Complete self-care4 or 5Mild disabled2 or 3Moderate disabled1Severe disabled0Complete disabled


## 4.2.5. Missing Data and Abnormal Data Processing

For numeric attributes, the missing data are imputed with the median. For categorical attributes, the missing data are imputed with the mode. In view of the outliers, the value is directly deleted and then imputed according to the missing data processing methods.


## 4.2.6. Data Normalization

In order to improve the rationality of the dissimilarity calculation, the numerical attributes in datasets are normalized. The original data were normalized by the min-max method to ensure the value of each numerical attribute was mapped to [0, 1].


## 5. Ability Characteristics Groups’ Analysis of Elderly Individuals Based on the Improved K-Prototypes Algorithm

### 5.1. Clustering Feature Selection and Parameter Selection

#### 5.1.1. Clustering Feature Selection

Ability indicators and basic information of elderly individuals included in the CHARLS dataset, such as age, self-reported depression, cognitive ability, basic activities of daily living ability, instrumental activities of daily living ability, seeing far, self-reported hearing, physical function ability, number of social activities in a month, daily sleep time, and paying ability, were selected as clustering features.


#### 5.1.2. Clustering Parameter Selection

Only determining the appropriate number of clusters and the categorical attribute weight can achieve a better clustering effect, so the improved K-prototypes algorithm needs to specify the number of clustersK, weight λ1, and weight λ2 in advance. In the preprocessed CHARLS data, all the older people’s ability attributes were ordinal. Therefore, it was only necessary to determine the weight λ2 in advance (the following is called λ).The number of clustersK and weight λ were determined experimentally, and the silhouette coefficient was used as the measurement standard to determine the number of clusters and weight. The silhouette coefficients, which were calculated by changing the number of clusters K and weight λ, are shown in Figure 1.Figure 1
Comparison of silhouette coefficients with differentK and λ.Figure1shows, when λ equals to 0.4, 0.5, and 0.6, the trend of the silhouette coefficient is basically the same. The value of the silhouette coefficient reaches the maximum when the number of clusters K=5. However, when λ=0.6, the value of the silhouette coefficient is always the highest when K < 7. Therefore, the number of clusters K=5 and the weight of ordinal attributes λ=0.6 were determined.


### 5.2. Clustering Results’ Analysis

Cluster numberK=5 and ordinal attribute weight λ=0.6 were used for clustering, and 5 groups of elderly individuals were obtained. The ability distribution of each group is shown in Table 10.Table 10
The ability distribution of each elderly group.
AbilitiesValuesProportion before clustering (%)Group 1 (%)Group 2 (%)Group 3 (%)Group 4 (%)Group 5 (%)Age60–6960.2059.9258.6350.4753.0268.7770–7928.3026.9829.5537.3830.2026.3880–8910.4911.6811.3510.2815.444.8590+1.011.420.471.871.340.00Self-reported depressionSevere7.757.6510.1710.7510.743.88Mild15.1814.8015.6013.0819.4614.40Normal77.0777.5574.2376.1769.8081.72Cognitive abilitySevere and moderate1.920.000.472.340.008.09Mild76.66100.0089.6085.98100.000.00Normal21.420.009.9311.680.0091.91Basic activities of daily living abilityComplete self-care90.8997.9598.5851.4068.7993.85Mild disabled6.412.051.4230.8420.814.36Moderate disabled1.150.000.007.484.700.65Severe disabled0.840.000.005.143.690.49Complete disabled0.710.000.005.142.010.65Instrumental activities of daily living abilityComplete self-care80.47100.0095.5118.220.0085.92Mild disabled12.680.003.0742.9971.489.39Moderate disabled3.550.000.9517.7616.782.10Severe disabled1.650.000.479.815.031.78Complete disabled1.650.000.0011.226.710.81Seeing farExcellent1.851.134.490.470.352.91Good14.643.5468.794.217.729.87Average64.3579.8914.8916.8277.5272.82Poor19.1615.4411.8378.5014.4314.40Self-reported hearingExcellent14.0315.1515.604.679.0616.02Good18.047.4468.095.6111.0715.70Average54.0367.2810.1617.7669.8058.74Poor13.9010.136.1571.9610.079.54Physical function abilityGood10.4611.8311.825.148.399.22Mild76.6984.3585.1120.0959.4081.39Moderate9.783.612.8455.6121.816.96Severe2.530.210.2315.428.721.94Complete0.540.000.003.741.680.49Number of social activities (a month)041.0847.5932.8645.7948.9926.38130.7529.3934.9929.4431.8830.91215.0313.8117.2613.558.7219.9037.354.7510.407.485.3712.1443.272.482.832.342.016.3151.651.270.470.931.683.5660.570.420.950.471.350.3270.100.140.000.000.000.1680.100.150.000.000.000.0090.100.000.240.000.000.32Daily sleep time[0, 6]38.8537.3943.2641.5941.2837.06[6, 10]57.1057.5852.0152.8054.7062.13>104.055.034.735.614.020.81Paying ability (a month)≤50028.0632.3729.3136.9231.2112.78(500, 1000]6.246.376.388.887.384.37(1000, 2000]15.9218.4813.0011.6820.4711.33(2000, 4000]34.5331.0934.9933.1829.1945.15(4000, 7000]12.9210.3413.247.0110.7421.68(7000, 10000]1.520.782.131.400.673.23>100000.810.570.950.930.341.46Table10 shows the five groups have obvious characteristics in their abilities. Taking instrumental activities of daily living ability and self-reported hearing as examples, the comparison results of the 5 groups are shown in Figures 2 and 3.Figure 2
Distribution of instrumental activities of daily living of each group.Figure 3
Distribution of self-reported hearing in each group.Figure2 shows groups 1, 2, and 5 have good clustering effects in terms of instrumental activities of daily living ability. In group 1, all elderly individuals could take care of themselves completely. In group 2, more than 95% of elderly individuals could take care of themselves completely. In group 5, more than 85% of elderly individuals could take care of themselves completely. There were more elderly individuals with disabilities in groups 3 and 4, which mainly included mild and moderate disabled elderly individuals. The disabilities of elderly individuals in group 3 were most serious, and nearly, 40% of elderly individuals in group 3 were moderate or worse disabled.Figure3 shows the self-reported hearing of elderly individuals in groups 2 and 3 are obvious different. More than 80% of elderly individuals in group 2 had good hearing ability, while more than 70% of elderly individuals in group 3 had poor hearing ability. The hearing ability distribution of elderly individuals in groups 1, 4, and 5 is similar, and most of elderly individuals have average hearing ability.To more clearly show the ability differences of the five groups of elderly individuals, the abilities of each group were presented in a radar chart in Figure4, where the closer the line is to the edge, the more severe the disability is.Figure 4
Radar chart of the ability distribution of each elderly group.Figure4 shows each group has distinct degrees of disability. The distribution of disability degree in group 1 and group 5 is similar. The elderly individuals of group 2 were mainly disabled in self-reported depression, cognitive ability, social activities (the number of social activities participated in a month), and paying ability. Group 4 had a more severe disability level in physical function, self-reported depression, paying ability, social activities, and instrumental activities of daily living. In group 3, the disability level of elderly individuals was the most serious.


## 5.1. Clustering Feature Selection and Parameter Selection

### 5.1.1. Clustering Feature Selection

Ability indicators and basic information of elderly individuals included in the CHARLS dataset, such as age, self-reported depression, cognitive ability, basic activities of daily living ability, instrumental activities of daily living ability, seeing far, self-reported hearing, physical function ability, number of social activities in a month, daily sleep time, and paying ability, were selected as clustering features.


### 5.1.2. Clustering Parameter Selection

Only determining the appropriate number of clusters and the categorical attribute weight can achieve a better clustering effect, so the improved K-prototypes algorithm needs to specify the number of clustersK, weight λ1, and weight λ2 in advance. In the preprocessed CHARLS data, all the older people’s ability attributes were ordinal. Therefore, it was only necessary to determine the weight λ2 in advance (the following is called λ).The number of clustersK and weight λ were determined experimentally, and the silhouette coefficient was used as the measurement standard to determine the number of clusters and weight. The silhouette coefficients, which were calculated by changing the number of clusters K and weight λ, are shown in Figure 1.Figure 1
Comparison of silhouette coefficients with differentK and λ.Figure1shows, when λ equals to 0.4, 0.5, and 0.6, the trend of the silhouette coefficient is basically the same. The value of the silhouette coefficient reaches the maximum when the number of clusters K=5. However, when λ=0.6, the value of the silhouette coefficient is always the highest when K < 7. Therefore, the number of clusters K=5 and the weight of ordinal attributes λ=0.6 were determined.


## 5.1.1. Clustering Feature Selection

Ability indicators and basic information of elderly individuals included in the CHARLS dataset, such as age, self-reported depression, cognitive ability, basic activities of daily living ability, instrumental activities of daily living ability, seeing far, self-reported hearing, physical function ability, number of social activities in a month, daily sleep time, and paying ability, were selected as clustering features.


## 5.1.2. Clustering Parameter Selection

Only determining the appropriate number of clusters and the categorical attribute weight can achieve a better clustering effect, so the improved K-prototypes algorithm needs to specify the number of clustersK, weight λ1, and weight λ2 in advance. In the preprocessed CHARLS data, all the older people’s ability attributes were ordinal. Therefore, it was only necessary to determine the weight λ2 in advance (the following is called λ).The number of clustersK and weight λ were determined experimentally, and the silhouette coefficient was used as the measurement standard to determine the number of clusters and weight. The silhouette coefficients, which were calculated by changing the number of clusters K and weight λ, are shown in Figure 1.Figure 1
Comparison of silhouette coefficients with differentK and λ.Figure1shows, when λ equals to 0.4, 0.5, and 0.6, the trend of the silhouette coefficient is basically the same. The value of the silhouette coefficient reaches the maximum when the number of clusters K=5. However, when λ=0.6, the value of the silhouette coefficient is always the highest when K < 7. Therefore, the number of clusters K=5 and the weight of ordinal attributes λ=0.6 were determined.


## 5.2. Clustering Results’ Analysis

Cluster numberK=5 and ordinal attribute weight λ=0.6 were used for clustering, and 5 groups of elderly individuals were obtained. The ability distribution of each group is shown in Table 10.Table 10
The ability distribution of each elderly group.
AbilitiesValuesProportion before clustering (%)Group 1 (%)Group 2 (%)Group 3 (%)Group 4 (%)Group 5 (%)Age60–6960.2059.9258.6350.4753.0268.7770–7928.3026.9829.5537.3830.2026.3880–8910.4911.6811.3510.2815.444.8590+1.011.420.471.871.340.00Self-reported depressionSevere7.757.6510.1710.7510.743.88Mild15.1814.8015.6013.0819.4614.40Normal77.0777.5574.2376.1769.8081.72Cognitive abilitySevere and moderate1.920.000.472.340.008.09Mild76.66100.0089.6085.98100.000.00Normal21.420.009.9311.680.0091.91Basic activities of daily living abilityComplete self-care90.8997.9598.5851.4068.7993.85Mild disabled6.412.051.4230.8420.814.36Moderate disabled1.150.000.007.484.700.65Severe disabled0.840.000.005.143.690.49Complete disabled0.710.000.005.142.010.65Instrumental activities of daily living abilityComplete self-care80.47100.0095.5118.220.0085.92Mild disabled12.680.003.0742.9971.489.39Moderate disabled3.550.000.9517.7616.782.10Severe disabled1.650.000.479.815.031.78Complete disabled1.650.000.0011.226.710.81Seeing farExcellent1.851.134.490.470.352.91Good14.643.5468.794.217.729.87Average64.3579.8914.8916.8277.5272.82Poor19.1615.4411.8378.5014.4314.40Self-reported hearingExcellent14.0315.1515.604.679.0616.02Good18.047.4468.095.6111.0715.70Average54.0367.2810.1617.7669.8058.74Poor13.9010.136.1571.9610.079.54Physical function abilityGood10.4611.8311.825.148.399.22Mild76.6984.3585.1120.0959.4081.39Moderate9.783.612.8455.6121.816.96Severe2.530.210.2315.428.721.94Complete0.540.000.003.741.680.49Number of social activities (a month)041.0847.5932.8645.7948.9926.38130.7529.3934.9929.4431.8830.91215.0313.8117.2613.558.7219.9037.354.7510.407.485.3712.1443.272.482.832.342.016.3151.651.270.470.931.683.5660.570.420.950.471.350.3270.100.140.000.000.000.1680.100.150.000.000.000.0090.100.000.240.000.000.32Daily sleep time[0, 6]38.8537.3943.2641.5941.2837.06[6, 10]57.1057.5852.0152.8054.7062.13>104.055.034.735.614.020.81Paying ability (a month)≤50028.0632.3729.3136.9231.2112.78(500, 1000]6.246.376.388.887.384.37(1000, 2000]15.9218.4813.0011.6820.4711.33(2000, 4000]34.5331.0934.9933.1829.1945.15(4000, 7000]12.9210.3413.247.0110.7421.68(7000, 10000]1.520.782.131.400.673.23>100000.810.570.950.930.341.46Table10 shows the five groups have obvious characteristics in their abilities. Taking instrumental activities of daily living ability and self-reported hearing as examples, the comparison results of the 5 groups are shown in Figures 2 and 3.Figure 2
Distribution of instrumental activities of daily living of each group.Figure 3
Distribution of self-reported hearing in each group.Figure2 shows groups 1, 2, and 5 have good clustering effects in terms of instrumental activities of daily living ability. In group 1, all elderly individuals could take care of themselves completely. In group 2, more than 95% of elderly individuals could take care of themselves completely. In group 5, more than 85% of elderly individuals could take care of themselves completely. There were more elderly individuals with disabilities in groups 3 and 4, which mainly included mild and moderate disabled elderly individuals. The disabilities of elderly individuals in group 3 were most serious, and nearly, 40% of elderly individuals in group 3 were moderate or worse disabled.Figure3 shows the self-reported hearing of elderly individuals in groups 2 and 3 are obvious different. More than 80% of elderly individuals in group 2 had good hearing ability, while more than 70% of elderly individuals in group 3 had poor hearing ability. The hearing ability distribution of elderly individuals in groups 1, 4, and 5 is similar, and most of elderly individuals have average hearing ability.To more clearly show the ability differences of the five groups of elderly individuals, the abilities of each group were presented in a radar chart in Figure4, where the closer the line is to the edge, the more severe the disability is.Figure 4
Radar chart of the ability distribution of each elderly group.Figure4 shows each group has distinct degrees of disability. The distribution of disability degree in group 1 and group 5 is similar. The elderly individuals of group 2 were mainly disabled in self-reported depression, cognitive ability, social activities (the number of social activities participated in a month), and paying ability. Group 4 had a more severe disability level in physical function, self-reported depression, paying ability, social activities, and instrumental activities of daily living. In group 3, the disability level of elderly individuals was the most serious.


## 6. Conclusions

The K-prototypes are an effective algorithm for clustering mixed attributes datasets. The improved K-prototypes took into account not only the differences between the objects to be allocated and the prototypes in the cluster but also the differences between the objects to be allocated and other objects in the cluster when calculating the dissimilarity of attributes. The performance of the improved K-prototypes algorithm is evaluated using five UCI datasets with mixed attributes. The experimental results showed that mixed attributes data clustering can be better solved based on the improved K-prototypes by adjusting the weight of categorical attributes in the dissimilarity measure.The improved K-prototypes in this article have two limitations. First, when determining the weights of ordinal and nonordinal attributes, we cannot quantitatively determine the optimal weights but can only find the better weights through enumeration. Second, the cluster results of the improved K-prototypes and other K-prototypes algorithms are not stable due to the random selection of initial prototypes. Therefore, the optimal weights and the initial prototypes selection can be further studied to improve the stability of the algorithm.The improved K-prototypes were used to cluster elderly individuals based on their abilities. In the future, there will be many problems worthy of further study, including cluster features selection from abilities of elderly individuals, grading criteria of elderly individuals’ abilities, and the precision care service recommendation based on the common characteristics of an elderly individuals’ group. In addition, the mining and explanation of the clustering results of elderly individuals based on mining techniques [28] will be more conducive to analyse the abilities characteristics of different elderly individuals’ groups. We will also pay more attention to mine unknown patterns contained in the clustering results of elderly individuals based on mining techniques in the future research.



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*Source: 7114343-2023-02-03.xml*