Journal of Electronic Science and Technology  2019, Vol.17 Issue (3): 231-241   DOI: 10.11989/JEST.1674-862X.71018117   PDF    
http://dx.doi.org/10.11989/JEST.1674-862X.71018117
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Article

Ching-Kan Lo, Hsing-Chung Chen, Pei-Yuan Lee, Ming-Chou Ku, Lidia Ogiela, Cheng-Hung Chuang
Smart Dynamic Resource Allocation Model for Patient-Driven Mobile Medical Information System Using C4.5 Algorithm
Journal of Electronic Science and Technology, 2019, 17(3): 231-241
http://dx.doi.org/10.11989/JEST.1674-862X.71018117

Article History

Manuscript received January. 13, 2017
revised May. 31, 2017
Smart Dynamic Resource Allocation Model for Patient-Driven Mobile Medical Information System Using C4.5 Algorithm
Ching-Kan Lo, Hsing-Chung Chen, Pei-Yuan Lee, Ming-Chou Ku, Lidia Ogiela, Cheng-Hung Chuang    
C.-K. Lo is with the Department of Orthopedics and the Department of Information, Show-Chwan Health Care System, Changhua 50008 (e-mail: drsimonlo@gmail.com);
H.-C. Chen and C.-H. Chuang are with the Department of Computer Science and Information Engineering and the Department of Bioinformatics and Medical Engineering, Asia University, Taichung 41354 (e-mail: cdma2000@asia.edu.tw; chchuang@asia.edu.tw);
P.-Y. Lee and M.-C. Ku are with the Department of Orthopedics, Show-Chwan Health Care System, Changhua 50008 (e-mail: b1208@ms26.hinet.net; showjoeku@gmail.com);
L. Ogiela is with the Department of Applied Informatics, Akademia Górniczo-Hutnicza University of Science and Technology, Krakow 30-059 (e-mail: logiela@agh.edu.pl)
Manuscript received 2017-01-13; revised 2017-05-31
Ching-Kan Lo received his medical degree (M.D.) from National Taiwan University, Taipei in 1995 and completed his postgraduate medical degree at Royal National Orthopedic Hospital, London in 2005, and received the master degree in public health (M.P.H.) from Tulane University, New Orlean in 2006. Also, he received the Ph.D. degree in computer science and information engineering from Asia University, Taichung in 2017. He was the Director of the Department of Information, Show-Chwan Health Care System, Changhua. Currently, he is the senior consultant at the Department of Information, Show-Chwan Health Care System. Besides, he is currently employed as the Director at the Department of Orthopedics, Show-Chwan Health Care System. His current research interests include clinical medicine, health care, medical information, computer science, and project management.
Hsing-Chung Chen received the Ph.D. degree in electronic engineering from National Chung Cheng University, Chiayi in 2007. From February 2008 to July 2018, he had successively been the assistant professor and associate professor with the Department of Computer Science and Information Engineering and the Department of Bioinformatics and Medical Engineering, Asia University. From August 2018 to July 2019, he was a full professor with Asia University. Since August 2019, he has been a distinguished full professor with the Department of Computer Science and Information Engineering, Asia University, and also the Director of the same department. Since May 2014, he has been a research consultant with the Departemnt of Medical Research, China Medical University Hospital, China Medical University, Taichung. He served as the Program Committee Chair of APNIC44 (2017). He is the IEEE Senior Member. He is also the Member of TFSA, ICCIT, CCISA, and IET. He had been awarded the Best Paper Awards by BWCCA2018, MobiSec2017, and BWCCA2016, respectively. He was awarded the Best Journal Paper Award by AACT. Currently, his research interests include information and communications security, cyberspace security, blockchain network security, Internet of things applications and security, mobile and wireless networks protocols, medical and bio-information signal and image processing, artificial intelligence and soft computing, and applied cryptography.
Pei-Yuan Lee received his medical degree (M.D.) from National Yang Ming University, Taipei in 1985 and received his master degree in public health (M.P.H.) from Tulane University in 2010. He is currently the Director of the Department of Orthopedics and the Vice Superintendent of Show-Chwan Health Care System. His interests include sporting injuries, trauma, and reconstructive and fracture surgery.
Ming-Chou Ku received his medical degree (M.D.) from Taipei Medical University, Taipei in 1979 and received his M.S. degree from the Royal National Orthopedic Hospital and the master degree in public health (M.P.H.) from Tulane University, in 2005. He was the Director of the Department of Orthopedics from 1994 to 2002 and the Superintendent from 2003 to 2008, Show-Chwan Health Care System. He is currently the Vice President of Show-Chwan Health Care System. His interests include joint disorders, joint degeneration, joint replacements, and arthroscopic surgeries.
Lidia Ogiela received her M.S. degree in mathematics from Pedagogical University, Krakow, and the master of business administration in management and marketing from Akademia Górniczo-Hutnicza (AGH) University of Science and Technology, Krakow, both in 2000. In 2005 she was awarded the title of doctor in computer science and engineering at the Faculty of Electrical, Automatic Control, Computer Science and Electronic Engineering, AGH University of Science and Technology, for her thesis and research on cognitive analysis techniques and its application in intelligent information systems. She is the author of a several dozens of scientific international publications on information systems, cognitive analysis techniques, biomedical engineering, and computational intelligence methods. She is the Member of a few prestigious international scientific societies, such as SIAM, SPIE, and CSS. Currently, she is working as an associate professor with the Department of Applied Informatics, AGH University of Science and Technology. Her research interests include information systems, cognitive analysis techniques, cognitive economy and cognitive management, biomedical engineering, and computational intelligence methods.
Cheng-Hung Chuang received his M.S. and Ph.D. degrees in electrical engineering from National Chung Cheng University in 1996 and 2003, respectively. From 2003 to 2007, he was a postdoctoral fellow with the Institute of Statistical Science, Taipei. In 2007, he entered the Department of Computer Science and Information Engineering, Asia University as an assistant professor. Since 2013, he has been employed as an associate professor with the Department of Computer Science and Information Engineering, Asia University. He is also a research consultant with the Department of Medical Research, China Medical University Hospital, China Medical University. His research interests include image/video processing, optical and biomedical signal processing, computer vision, and pattern recognition
Abstract: A mobile medical information system (MMIS) is an integrated application (app) of traditional hospital information systems (HIS) which comprise a picture archiving and communications system (PACS), laboratory information system (LIS), pharmaceutical management information system (PMIS), radiology information system (RIS), and nursing information system (NIS). A dynamic resource allocation table is critical for optimizing the performance to the mobile system, including the doctors, nurses, or other relevant health workers. We have designed a smart dynamic resource allocation model by using the C4.5 algorithm and cumulative distribution for optimizing the weight of resource allocated for the five major attributes in a cooperation communications system. Weka is used in this study. The class of concept is the performance of the app, optimal or suboptimal. Three generations of optimization of the weight in accordance with the optimizing rate are shown.
Key words: Dynamic resource allocation    electronic health record    hospital information system    mobile medical information system   
1. Introduction

With increasing number of autonomous heterogeneous devices in the mobile networks, an efficient resource allocation scheme is required to maximize network throughput[1], memory, and energy optimization[2], so as to achieve higher efficient and better performance. Mobile health (mHealth), which is the usages of mobile computing together with communications technologies in health care and public health, is a rapidly expanding e-health[3] area, such as the usages of applications (apps) for post-operative follow-up in orthopedic surgery patients[4],[5]. There are huge potential demands for mHealth interventions to obtain the beneficial effects of health, the delivery processes of health service as well as the improvement of the working time and satisfaction of the nurses[6]. In a wireless sensor network (WSN), the usages of resources are usually highly related to the execution of tasks which consume a certain amount of computing and communications bandwidth[7]. Due to the limitations of resource availability and communications medium, these existing algorithms cannot be directly addressed for the requirements of the mHealth system.

In addition, decision tree methodology has become more popular in medical researches. Some examples may include a predictive computer-assisted decision-making system for traumatic injury using machine learning algorithms[8] and diagnosis of coronary artery stenosis. The decision tree method is a powerful statistical tool for classification, prediction, interpretation, and data manipulation, which has several potential applications in medical research[9],[10]. The Waikato Environment for Knowledge Analysis (Weka) is a popular suite of machine learning software written in Java, developed at the University of Waikato, New Zealand[11]. It is a workbench that contains a collection of visualization tools and algorithms for data analyses and predictive modeling together with graphical user interfaces for easily accessing to these functions[11].

C4.5 is an algorithm used to generate a decision tree developed by Quinlan[12]. C4.5 is an extension of Quinlan’s earlier ID3 algorithm. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a statistical classifier. Weka supports several standard data mining tasks, more specifically, data preprocessing, clustering, classification, regression, visualization, and feature selection. All of Weka’s techniques are predicated on the assumption that the data are available as a single flat file or a relation, where each data point is described by a fixed number of attributes (normally, numeric or nominal attributes, but some other attribute types are also supported)[11].

The rest of this paper is organized as follows: In Section 2, the related works are reviewed. Section 3 introduces the proposed algorithm model in detail. In Section 4, the simulation results of the proposed are presented and the algorithm’s performance is discussed. Finally, in Section 5, conclusions are made.

The goal of this paper is to create a smart and dynamic resource-mapping management table for the medical management information systems (MMISs) to optimize the weights of each server.

2. Related Works

In general, network resources, storages, and energy allocation are a fundamental challenge in the mHealth system due to their unique features. Most of those traditional solutions do not consider resource consumption during communications and task execution. Therefore, they cannot be implemented efficiently. Furthermore, the allocation becomes a topic that remains largely unexplored for the mHealth system.

Several algorithms[13]-[15] have been proposed for the task allocation and scheduling problem. Giannecchini et al.[13] proposed an online task scheduling mechanism called CoRAl to allocate the network resources, between the tasks of periodic applications in WSNs[16],[17]. Xie and Qin[14] proposed another allocation strategy called balanced energy-aware task allocation (BEATA) for collaborative applications running on heterogeneous networked embedded systems. Their strategies aimed at making the best trade-offs between energy savings and schedule lengths[14],[16],[17]. Lee and Jeong[15] proposed a fuzzy relevance-based cluster head selection algorithm (FRCA) to solve problems, such as energy consumption, transmission rate reduction, decrease in throughput, and incorrect cluster head election.

However, there is little literature discussed a decision tree algorithm model to allocate multiple, heterogeneous resources in the mHealth system. This paper proposes to construct a decision tree more efficiently by reducing the incorrectness and ambiguity in the selection of service’s resources.

3. Resource Allocation Using Modified C4.5 Algorithm

In this section, there are three subsections consisting of the machine learning analysis (MLA) using the C4.5 algorithm, the definition of symbols and formula, and the smart allocation algorithm using the modified C4.5 algorithm.

3.1 MLA Using Modified C4.5 Algorithm

The C4.5 algorithm is applied to MLA in our algorithm as shown in subsection 3.1, which is one of the best decision tree algorithms[12]. It builds decision trees using the concept of information entropy from a set of training data in the same way as iterative Dichotomiser 3 (ID3). The training data are a set of already classified samples. At each node of the tree, C4.5[12] chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized information gain (difference in entropy). The attribute with the highest normalized information gain (νγ) is chosen to make the decision. The algorithm then recurs on a smaller sub list.

Weka freeware with the J48 classifier[12] selected for the C4.5 algorithm is used in this study. It does not require the discretization of numeric attributes, in contrast to the ID3 algorithm from which C4.5[12] has evolved Microsoft Excel 2010 for statistical computation of the formula in comparing with the Weka. The entropy, split entropy, normalized information gain (NIG), and visualization of tree structure will be evaluated and shown.

3.2 Definition of Symbols and Formulas

Some symbols and formulas applied in this paper are defined below.

1) g is the generation of algorithm, where g $= $ 0 represents the root generation.

2) n is the collection of resources or attributes to allocate.

3) m is the collection of the node, where m $= $ 0 is the root node.

4) i is the attribute index, and its value is from 1 to n.

5) j is the attribute value index from 1 to its final value that depends on its attribute (refer to Table 1).

Table 1 Information of five major resources (abbreviation)
Attribute Attribute value
1. Picture archiving and communications system (PACS) 1. Magnetic resonance image (MR)
2. Computed tomography (CT)
3. X-ray (XR)
4. Echography (Ec)
2. Laboratory information system (LIS) 1. Culture (Cu)
2. Biochemistry/serology (Bc)
3. Hemogram (Hm)
3. Nursing information system (NIS) 1. Vital sign chart (VS)
2. Nursing education (NE)
3. Nursing record (NR)
4. Pharmaceutical management information system (PMIS) 1. Inpatient stat order (IS)
2. Inpatient regular order (IR)
3. Outpatient stat order (OS)
5. Report information system (RIS) 1. Consultation sheet (CS)
2. Inpatient note (IN)
3. Image report (IR)

6) $W_i^g$ is the weight of each resource allocated in the gth generation and $W_i^0\!=\!\left({{1 / n}}\right)\!\times \!100 $ %.

7) Xg,m is the total instance in the gth generation at the node m, where m $= $ 0 represents the root node. Xi is the total instance in the attribute i. Xi,j is the total instance in the attribute i and the attribute value j.

8) A is a number represented as the total counts of optimal performance for Xg,m, similarly, Ai is that for Xi, and Ai,j is that for Xi,j.

9) B is a number represented as the total counts of suboptimal performance for Xg,m, similarly, Bi is that for Xi, and Bi,j is that for Xi,j.

10) αg $= $ A/Xg is the optimal performance rate in the gth generation.

11) βg $= $ 1−αg $= $ B/Xg is the suboptimal performance rate in the gth generation.

12) Set g and ${}_i^g$ respectively as the entropy of the parent node, and that of the child node of the attribute i, and ${}_i^g$ $= $ −( $\sum $ Ai/X g,m)log2( $\sum $ Ai/X g,m)−( $\sum $ Bi/X g,m)log2( $\sum $ Bi/X g,m).

13) Set ${}_{i\!,j}^{g,m}$ as the entropy of the attribute i and the attribute value j, and ${}_{i\!,j}^{g,m}$ $= $ (Xi,j /Xi)[−(Ai,j/Xi)log2(Ai,j/Xi)−(Bi,j /Xi)log2(Bi,j/Xi)].

14) Set ${}_i^{g,m}$ as the total entropy in atribute i and the gth generation at the node m, and ${}_i^{g,m} = \sum\limits_j$ ${}_{i\!,j}^{g,m} $ .

15) Set ${\tilde {\hat e}}_i^{g,m}$ as the split entropy of attribute i, and ${\tilde {\hat e}}_i^{g,m}$ $= $ $\mathop\sum \limits_j $ −(Xi,j/Xi)log2(Xi,j/Xi).

16) Set ${\text{γ}} _i^{g,m}$ as the information gain, and ${\text{γ}} _i^{g,m} =$ ( ${}^{g,m} $ ${}_i^{g,m} $ ) in the gth generation at the node m.

17) Set ${\text{ν}} {\text{γ}} _i^{g,m}$ is the normalized information gain, which is ${\text{γ}} _i^{g,m}\!\text{/}{{{\tilde {\hat e}}}^{g,m}_i} $ in the gth generation at the node m.

18) κ is the node or relevant attribute with $\mathop {\max}\limits_i ({\rm{v{\text{γ}} }}_i^{g,m})$ , where κ $\subseteq $ i, and i $= $ {1, 2, $\cdots $ , n}.

19) Set ${\text{θ}} _{\text{κ}}$ as the cumulative suboptimal Bi from the bottommost of all the child nodes for the node κ.

20) Set ${\small\sum} {\text{θ}}$ as the sum of all cumulative suboptimal Bi in all nodes.

21) ${\textit{Ƃ}}_{\text{κ}} ^g = W_i^g\left( {{{\text{α}} ^g}} \right)$ is the base weight of the attribute i for the node κ.

22) ${\text{λ}} _{\text{κ}^g} = {\text{β} ^g}({{{\text{θ}} ^{\text{κ}} }}\!{\text{/}}\!{{\small\sum} {\text{θ}}}) $ is the weight gain for the node κ.

23) $W_i^{g + }$ $={\textit{Ƃ}}_{\text{κ}}^g+{\text{λ}} _{\text{κ}} ^g$ is the updated weight allocated for the attribute i.

3.3 Smart Allocation Algorithm and Creation of New Generation

The purpose of this study is to tune the weight for resource allocation in accordance to βg, θκ, and the cumulative of Bi from the bottommost node resource to its parent node and substantially to the uppermost root node. The updated weight is the sum of ${\textit{Ƃ}}_{\text{κ}} ^g$ and ${\text{λ}} _{\text{κ}} ^g$ . Ƃg is calculated as the product of $W_i^g$ and αg. The ${\small\sum} {\text{θ}} $ is the sum of θ of all nodes or relevant resources. The weight gain ${\text{λ}} _{\text{κ}} ^g$ of a relevant resource is the product of the suboptimal rate with its initial weight and the rate of cumulating $R = W_i^g {{{\text{β}} ^g}}\!\left( {{{\text{θ}} ^{\text{κ}} }\!\text{/}\!{\small\sum} {\text{θ}} } \right)$ .

Using the new weight for resource allocation, another iterative of generation g+1 will restart the above algorithm to tune the weight, so as to minimize βg. And βg<0.05 is set as a significant optimization or stop criteria of the algorithm in this paper.

4. Experimental Results and Analyses

In MMIS, the five major resources of HIS will be the attributes of the modified C4.5 algorithm in a cooperation communications system, including PACS, LIS, NIS, PMIS, and RIS, where i equals to 1 to 5 as its ID, individually. The class of concepts is scored as A if the performance of MMIS is optimal or B if the performance is suboptimal. The details of the attributes and attribute values are shown in Table 1.

Moreover, the modified C4.5 algorithm is processed by three phases consisting of the root generation phase, child nodes and decision tree generation phase, and weight updating for resource allocation phase. The details are described below.

4.1 Root Generation Phase

The follows are the processed steps by using the modified C4.5 algorithm. The details are listed below.

1. γ $\,=\, $ 0, m $\,=\, $ 0, n $\,=\, $ 5;

2. $W_1^{0,0} = W_2^{0,0} = W_3^{0,0} = W_4^{0,0} = W_5^{0,0} = 20$ %;

3. X0,0 $\,=\, $ 100, total instances in node 0;

4. A $\,=\, $ 50, B $\,=\, $ 50, α0 $\,=\, $ β0 $\,=\, $ 50/100 $\,=\, $ 50%;

5. Entropy of parent node:

0 $\,=\, $ −(50/100) $\times $ log20.50−(50/100) $\times $ log20.50 $\,=\, $ 1.00;

6. Entropy of MR:

${}_{1,1}^{0,0}$ $\,=\, $ (X1,1/X1)[−(A1,1/X1,1)log2(A1,2/X1,1)−(B1,1/X1,2)log2(B1,1/X1,1)] $\,=\, $ 0.25 $\times $ [−(0/25) $\times $ 0−(25/25) $\times $ 0] $\,=\, $ 0;

7. Entropy of CT:

${}_{1,2}^{0,0}$ $\,=\, $ (X1,2/X1)[−(A1,2/X1,2)log2(A1,2/X1,2)−(B1,2/X1,2)log2(B1,2/X1,2)] $\,=\, $ 0.25 $\times $ [−(10/25) $\times $ log2(0.4)−(15/25) $\times $ log2(0.6)] $\,=\, $ 0.24;

8. Entropy of XR:

${}_{1,3}^{0,0}$ $\,=\, $ (X1,3/X1)[−(A1,3/X1,3)log2(A1,3/X1,3)−(B1,3/X1,3)log2(B1,3/X1,3)] $\,=\, $ 0.25 $\times $ [−(21/25) $\times $ log2(0.84)−(4/25) $\times $ log2(0.16)] $\,=\, $ 0.16;

9. Entropy of Ec:

${}_{1,4}^{0,0}$ $=$ (X1,4/X1)[−(A1,4/X1,4)log2(A1,4/X1,4)−(B1,4/X1,4)log2(B1,4/X1,4)] $=$ 0.25 $\times $ [−(19/25) $\times $ log2(0.76)−(6/25) $\times $ log2(0.24)] $= $ 0.20;

10. Total entropy of PACS:

${}_1^{g,m}=$ ${}_{1,1}^{0,0} +$ ${}_{1,2}^{0,0} + $ ${}_{1,3}^{0,0} +$ ${}_{1,4}^{0,0}$ $\,=\, $ 0+0.24+0.16+0.20 $\,=\,$ 0.60;

11. Information gain of PACS:

${\text{γ}} _1^{0,0} = $ ${}^{0,0} - $ ${}_1^{0,0}=1.00 - 0.60=0.40 $ ;

12. Split entropy of PACS:

${\tilde {\hat e}}_1^{0,0}=\,$ ${\textstyle\mathop \sum\limits_j} $ −(X1,j/X1)log2(X1,j/X1) $\,=\, $ −(25/100) $\times $ log2(25/100)−(25/100) $\times $ log2(25/100)−(25/100) $\times $ log2(25/100)−(25/100) $\times $ log2(25/100) $\,=\, $ 2.00;

13. Normalized information gain of PACS:

${\text{ν}} {\text{γ}} _1^{0,0}={\text{γ}} _1^{0,0}/{{{\tilde {\hat e}}}_1^{0,0}} = 0.60/2.00 = 0.30$ ;

14. The ${}_{i,j}^{0,0},$ ${}_i^{0,0},\;{\tilde {\hat e}}_i^{0,0},\;{\text{γ}} _i^{0,0} $ , and ${\text{ν}} {\text{γ}} _i^{0,0}$ of the other attribute i $\,=\, $ 2, 3, 4, 5 and value $\,j\!\!=\!\!1, 2, \cdots\!,5 $ are listed in Table 2;

Table 2 Normalized information gain of all resources in root note
Attribute Value A B ${}_{i,j}^0$ ${}_{i}^0$ 0 ${{\tilde {\hat e}}}$ γ νγ
PACS (i=1) MR 0 25 0 0.60 1.00 2.00 0.40 0.20
CT 10 15 0.24 - - - - -
XR 21 4 0.16 - - - - -
Ec 19 6 0.20 - - - - -
LIS (i=2) Cu 10 23 0.29 0.94 - 1.58 0.06 0.04
Bc 19 16 0.35 - - - - -
Hm 21 11 0.30 - - - - -
NIS (i=3) VS 14 31 0.40 0.91 - 1.54 0.09 0.06
NE 21 10 0.28 - - - - -
NR 15 9 0.23 - - - - -
PMIS (i=4) IS 14 13 0.27 1.00 - 1.57 0 0
IR 16 17 0.33 - - - - -
OS 20 20 0.40 - - - - -
RIS (i=5) CS 19 15 0.34 - - - - -
IN 17 13 0.30 0.98 - 1.58 0.02 0.01
IR 14 22 0.35 - - - - -

15. The maximum of ${\text{ν}} {\text{γ}} _i^{0,0}$ ( $i=1, 2, \cdots\!,5$ ) is obtained when i $\;=\; $ 1. Thus, κ $\;= \;$ 1 and the root node is PACS.

4.2 Child Nodes and Decision Tree Generation Phase

The algorithm then recurred in the smaller sub lists of PACS. As all samples of MR were B, the other 3 attribute values of CT, XR, and Ec were used separately to find the maximum ${\text{ν}} {\text{γ}}_i^{0,1} $ or the child node of PACS.

In the attribute value of CT, there were 25 instances of training samples,

1. X0.1 $\,=\, $ 25, A0.1 $\,=\, $ 10, B0.1 $\,=\, $ 15.

2. ${}_{{\rm{CT}}}^0$ $\,=\, $ −(10/25) $\times $ log2(0.4)−(15/25) $\times $ log2(0.6) $\,=\, $ 0.97.

3. Entropy of Cu of LIS is $_{2,1}^{0,1}$ $\,=\, $ (9/25) $\times $ [−(2/9) $\times $ log2(2/9)−(7/9) $\times $ log2(2/9) $\,=\, $ 0.28 and ${}_{2,2}^{0,1}$ $\,=\, $ ${}_{2,3}^{0,1}$ $\,=\, $ 0.31.

4. The maximum ${\text{ν}} {\text{γ}}_i^{0,0}$ was on the attribute NIS. Thus, NIS was chosen as the child node of PACS on the attribute value of CT.

5. The rest of the child node is shown in Fig. 1.

Fig. 1 Decision tree drawn by Weka, showing the hierarchy relationship of the resources allocation and the suboptimal performance.
4.3 Weight Updating for Resource Allocation Phase

The cumulative suboptimal performance B from the bottommost child nodes of LIS and NIS to the uppermost root node of PACS is 13, 25, and 50. So,

$ \begin{array}{l} {\small\sum}{\text{θ}} = 14 + 26 + 51 = 91.\\ {{\text{α}} ^0} = A/{X_0} = 49/100 = 49\text{%}. \end{array} $

The suboptimal performance rate is

$ {{\text{β}} ^0} = 1 - {{\text{α}} ^0} = 51\text{%} . $

The base weight of all resources is

$ {\textit{Ƃ}}_i^0 = {W_i}\left( {{{\text{α}} ^0}} \right) = 10\text{%}\quad \left( {i = 1,2, \cdots\!,5} \right) $

There are three resources on the nodes of the decision tree. The weight gain of the root node PACS is

$ {\text{λ}} _1^0 = {{\text{β}} ^0}({{\text{θ}} _1}/{\small\sum}{\text{θ}} ) = 50\text{%} \times 51/91 = 28.6\text{%}. $

The weight gain of the child node NIS is

$ {\text{λ}} _3^0 = 50\text{%} \times 26/91 = 14.6\text{%}. $

The weight gain of the second child node LIS is

$ {\text{λ}} _2^0 = 50\text{%} \times 14/91 = 7.8\text{%} . $

The weight gain of both RIS and PMIS, that is, the resources that are not on the decision tree, is

$ {\text{λ}} _4^0 = 50\text{%} \times 0/91 = 0. $

The updated weight for the root generation is shown in Table 3.

Table 3 Updated weight for the root generation
Resources PACS NIS LIS PMIS RIS
θκ 51 26 14 0 0
θκ/Σθ 56.0% 28.6% 15.4% 0 0
$W_i^0$ 20.0% 20.0% 20.0% 20.0% 20.0%
${\text{Ƃ}}_{\text{κ}} ^0$ 9.8% 9.8% 9.8% 9.8% 9.8%
${\text{λ}} _{\text{κ}} ^0$ 28.6% 14.6% 7.8% 0 0
$W_i^{0+}$ 38.4% 24.4% 17.6% 9.8% 9.8%

After the updated weight allocation table is assigned to the resources, a new testing sample of 100 instances is recurred and shows a different class of concept. The optimal performance rate is improved to 78%, α1=A/X1=78/100=78%. Owing to β1=1–α1>0.05, the loop is going on to do the algorithm above.

The new decision trees of the first and second generations are drawn and shown in Fig. 2 and Fig. 3, respectively. In Fig. 2, the root node is RIS, and PMIS, NIS, and LIS are as child roots, respectively. After applying the updated resource allocation table, the second generation decision tree is shown with a root node of LIS, and NIS and RIS as its child nodes.

Fig. 2 Decision tree of the first generation with a new hierarchy relationship of the resources allocation with RIS as the root node.

Fig. 3 Decision tree of the second generation with LIS as the root node, and RIS and NIS as its child nodes.

The resource allocation tables of the first and second generations are shown in Tables 4 and 5. The new resource allocation table in the first generation improved the optimal performance rate A and α2 $= $ 91%. But β2 $= $ 0.91 $= $ 0.09>0.05, thus the second generation will continue the loop of the algorithm.

Table 4 First generation weight updating table
Resources RIS PMIS LIS NIS PACS
θκ 22 22 2 7 0
θκθ 41.5% 41.5% 3.8% 13.2% 0
$W_i^0$ 9.8% 9.8% 17.6% 24.4% 38.4%
Ƃ0κ 7.6% 7.6% 13.8% 19.0% 29.9%
${\text{λ}} _{\text{κ}} ^0$ 9.1% 9.1% 0.8% 2.9% 0
$W_i^{0+}$ 16.8% 16.8% 14.6% 21.9% 29.9%

Table 5 Weight allocation table of second generation
Resources LIS NIS RIS PMIS PACS
θκ 9 9 9 0 0
θκθ 33.3% 33.3% 33.3% 0 0
$W_i^0$ 14.6% 21.9% 16.8% 16.8% 29.9%
Ƃ0κ 13.3% 19.9% 15.3% 15.3% 27.2%
${\text{λ}} _{\text{κ}} ^0$ 3.0% 3.0% 3.0% 0 0
$W_i^{0+}$ 16.3% 22.9% 18.3% 15.3% 27.2%

After the new weight allocation table of the second generation is assigned to the resources, the new different classes of concepts show that the optimal performance rate improved to 95%, α3 $= $ 95/100 $= $ 95%. Owing to β3 $= $ 1−0.95 $= $ 0.05 $\leq$ 0.05, the loop stops.

5. Conclusions and Future Work

In this study, a method of smart and dynamic resource allocation management algorithm is designed by the combination of the C4.5 algorithm and cumulative distribution function. The cumulative function accumulates the suboptimal classes of concepts in hierarchy tree nodes from the bottommost child nodes to the uppermost root nodes. The initial allocation is assigned with an evenly distributed weight. The optimal performance rate is improved from 49% to 78%, 91%, and 95% in the first, second, and third generations after the algorithm run. This algorithm could be applied in the mHealth system with different resources. Future work should be done for the services with more resources to allocate.

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