## 3 The Mutual Algorithm
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & C1 & C2 & C3 \\ \hline
**P1** & **0.7/07106781** & **2.397915762** & **2.236067977** \\
**P2** & **0.7/07106781** & **1.322875656** & **1.732050808** \\
**P3** & **1.58113883** & **2.179449472** & **3** \\
**P4** & **1.224744871** & **2.397915762** & **1.732050808** \\
**P5** & **1.870828693** & **0.866025404** & **2.236067977** \\
**P6** & **1.224744871** & **2.598076211** & **1** \\
**P7** & **2.121320344** & **2.598076211** & **1** \\
**P8** & **1.58113883** & **2.179449472** & **3.16227766** \\
**P9** & **1.870828693** & **2.598076211** & **0** \\
**P10** & **1.22474871** & **1.322875656** & **2** \\
**P11** & **2.121320344** & **0.866025404** & **3.16227766** \\
**P12** & **2.549509757** & **2.598076211** & **2.236067977** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Similarity of Temporary Groups for Older People. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **P1** & **P2** & **P3** & **P4** & **P8** & **P10** \\
**P2** & **0.7/07106781** & **1.322875656** & **1.732050808** \\
**P3** & **1.58113883** & **2.179449472** & **3** \\
**P4** & **1.224744871** & **2.397915762** & **1.732050808** \\
**P5** & **1.870828693** & **0.866025404** & **2.236067977** \\
**P6** & **1.870828693** & **0.866025404** & **2.236067977** \\
**P6** & **1.224744871** & **2.598076211** & **1** \\
**P7** & **2.121320344** & **2.598076211**respectively (Table 8). The LCDA dataset shows a total of 66 observations calculated in Equation (5):

\[\sum_{i=1,j=1,i\
eq j}^{12}\textit{Combination }(i,j)=\text{C}_{2}^{12}=\frac{12!}{2!*10!}=66 \tag{5}\]

The accuracies are 86.36%, 96.97%, 98.48%, and 98.48% using SVMs, logistic, and MLP, random forest, respectively. The MLP and random forests achieve the highest level of accuracy (Figure 6). The collaboration is built randomly 66 times, and the highest accuracy is 56.06% from SVMs. The mean difference is \(-30.3\) (\(p<0.01\)), which is significant. Therefore, the second hypothesis is also supported. ## 7 Discussion

Based on the literature review, currently, the design of long-term care intends to use centralized architecture, which means agencies assign caretakers to older people based on their manpower policies without taking the appropriate characteristics of older people into consideration. The study proposed methods including MMC and LCDA to overcome some important issues based on the existing architecture that could lead to shortages of manpower and inappropriate cooperation between caretakers and older people. After \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**RL1** & **Phy1** & **MR1** & **Dem1** & **RL2** & **Phy2** & **MR2** & **Dem2** & **LCDA** \\ \hline
2 & 2 & 1 & 3 & 1 & 3 & 1 & 3 & Y \\
2 & 1 & 1 & 2 & 1 & 2 & 3 & 1 & N \\
2 & 2 & 1 & 3 & 3 & 3 & 3 & Y \\
2 & 1 & 1 & 2 & 2 & 3 & 1 & 3 & N \\
2 & 3 & 1 & 3 & 3 & 3 & 3 & Y \\
2 & 1 & 1 & 2 & 2 & 2 & 1 & 3 & N \\
2 & 3 & 1 & 3 & 3 & 3 & 3 & Y \\
2 & 2 & 2 & 2 & 2 & 3 & 2 & 1 & N \\ \hline \hline \end{tabular}
\end{table} 
Table 8: LCDA Dataset of Older People. Figure 6: Accuracy of Classification Algorithms. being systematically evaluated in the experiment, the hypotheses are all supported, those issues can be confirmed to be solved by using the proposed mapping mutual clustering method and long-term care decentralized architecture. Older people sense the suitable caretakers around them, cognitively group caretakers by some characteristics generated from MMC, form long-term corporation relationships with LCDA, and generate records in order to adjust groups dynamically. With the proposed methods, older people can involve and generate a corporate process when realistic circumstances are acted out in the long-term care systems in order to better understand the outcome of caretakers no matter they are coming from.