Prediction of High Capabilities in the Development of Kindergarten Children
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Kindergarten Children Data
2.2. Data Mining Algorithms
3. Data Preprocessing
3.1. Fundamentals of Rough Set Theory
3.2. Proposed Preprocessing Technique
3.2.1. Parallel Computation of Relevant Features and Instances
 (a)
 $\forall {x}_{j}\in U\left[{x}_{i}\in cs\wedge \left(\begin{array}{c}\underset{\begin{array}{c}{x}_{k}\in U\\ {x}_{k}\ne {x}_{i}\end{array}}{\mathrm{max}}\left\{sim\left({x}_{i},{x}_{k}\right)\right\}=sim\left({x}_{i},{x}_{j}\right)\\ \vee \underset{\begin{array}{c}{x}_{k}\in U\\ {x}_{k}\ne {x}_{i}\end{array}}{\mathrm{max}}\left\{sim\left({x}_{k},{x}_{i}\right)\right\}=sim\left({x}_{j},{x}_{i}\right)\end{array}\right)\right]\Rightarrow {x}_{j}\in cs$
 (b)
 $\forall {x}_{i},{x}_{j}\in cs,\exists {x}_{{i}_{1}},\cdots ,{x}_{{i}_{q}}\in cs\left[\begin{array}{c}{x}_{i}={x}_{{i}_{1}}\wedge {x}_{j}={x}_{{i}_{q}}\wedge \forall p\left\{1,\cdots ,q1\right\}\\ \left[\begin{array}{c}\underset{\begin{array}{c}{x}_{t}\in U\\ {x}_{t}\ne {x}_{{i}_{p}}\end{array}}{\mathrm{max}}\left\{sim\left({x}_{{i}_{p}},{x}_{t}\right)\right\}=sim\left({x}_{{i}_{p}},{x}_{{i}_{p+1}}\right)\\ \vee \underset{\begin{array}{c}{x}_{t}\in U\\ {x}_{t}\ne {x}_{{i}_{p}}\end{array}}{\mathrm{max}}\left\{sim\left({x}_{{i}_{p+1}},{x}_{t}\right)\right\}=sim\left({x}_{{i}_{p+1}},{x}_{{i}_{p}}\right)\end{array}\right]\end{array}\right]$
 (c)
 Every isolated instance is a degenerated compact set.
Algorithm 1. Pseudocode of the proposed algorithm. 
Algorithm to compute the representative instance set 
Inputs: training set X 
Output: representative set C 
Steps:

3.2.2. Computation of Candidate Training Sets
3.2.3. Merging of Candidate Training Sets
Algorithm 2. Pseudocode of the proposed merging strategy. 
Merging of candidate training sets 
Inputs: Φ: correlation measure, T: set of candidate training sets, O: original training set Output: preprocessed training set $tbest$ 
Steps:

4. Results and Discussion
4.1. Results for Educational Data
4.2. Results for Repository Data
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Group  No.  Name  Description 

1  1  age  Age, in months, of the child (from 56 to 68 months) 
2  sex  Gender of the child (Male/Female)  
3  family  Whether the family encourages the child’s development (Yes/No)  
4  antecedents  Whether there exists a history of high potential in the family (Yes/No)  
5  prior education  Did the child receive previous educational attention? (Yes/No)  
6  performance  Quality of the teacher’s performance (Very good/Good/Average)  
2  7  nutrition  The nutritional status of the child (Well nurtured/Poorly nurtured) 
8  environment  How is the environment, neighborhood or place where the child is growing up (Socially challenging/Average/ Favorable)  
9  house  Condition of the dwelling where the child lives (Good/Average/Bad)  
10  hygiene  Hygiene conditions of the dwelling (Good/Poor)  
11  lifestyle  Lifestyle of the family (Healthy/Unhealthy)  
3  12  originality  Does the child like to be different or nonrepetitive? (Yes/No) 
13  help  Does the child like to help other children with their tasks, in addition to its own? (Yes/No)  
14  quality  The quality of the child’s schoolwork (Very good/Good/Average/Poor)  
15  speed  The speed with which the child works (Fast/Average/Slow)  
4  16  activity  Is the child active and energetic? (Yes/No) 
17  relationships  Does the child enjoy the company of its peers or does it prefer to be alone? (Socializes well/Usually alone)  
18  adult  Whether the child prefers the company of an adult over being with other children (Yes/No)  
19  play  Interest and participation of the child in collective play (High/Low)  
5  20  curiosity  Whether the child is curious and likes to learn new things (Yes/No) 
21  interest  Whether the child shows interest in its surroundings (Yes/No)  
22  boredom  Is the child easily bored when faced with easy tasks? (Yes/No)  
23  selfesteem  The degree of selfesteem that the child has (High/Low)  
24  superiority  Does the child feel superior to his peers? (Yes/No) 
Quick  Average  Slow  

Quick  0  0.5  1 
Average  0.5  0  0.5 
Slow  1  0.5  0 
Very Good  Good  Regular  Bad  

Very Good  0  0.1  0.4  1 
Good  0.1  0  0.2  0.7 
Regular  0.4  0.2  0  0.6 
Bad  1  0.7  0.6  0 
Very Good  Good  Average  

Very Good  0  0.4  1 
Good  0.4  0  0.4 
Average  1  0.6  0 
Favorable  Average  Socially Challenging  

Favorable  0  0.5  1 
Average  0.5  0  0.5 
Socially challenging  1  0.5  0 
Good  Average  Bad  

Good  0  0.7  1 
Average  0.3  0  0.5 
Bad  1  0.6  0 
Classified as  

Examples  Positive  Negative 
Positive  True positive (tp)  False negative (fn) 
Negative  False positive (fp)  True negative (tn) 
Algorithm  Parameters 

AKHGA  Iterations: 20 Population count: 200 individuals Crossover probability: 0.7 Mutation probability: 0.1 per bit 
EISRFS  MAX_EVALUATIONS: 10,000 Population count: 50 Crossover probability: 1.0 Mutation probability: 0.005 per bit a: 0.5, b: 0.75 MaxGamma: 1.0 UpdateFS: 100 
INGA  Iterations: 500 Population count: 50 individuals Crossover probability: 1.0 Mutation probability for features: 0.01 per bit Mutation probability for instances: $p\left(1\to 0\right)=0.1$ and $p\left(0\to 1\right)=0.01$ 
KJGA  Iterations: 100 Population count: 10 individuals Crossover probability: 1.0 Mutation probability: 0.1 per bit 
TCCS  No userdefined parameter 
Algorithm  ONN  TCCS  EISRFS  AKHGA  INGA  KJGA  FISSM 

AUC  0.94  0.94  0.93  0.87  0.64  0.76  0.95 
Instance Reduction  0.00  0.70  0.44  0.45  0.21  0.68  0.93 
Feature Reduction  0.00  0.52  0.00  0.71  0.52  0.43  0.73 
Datasets  Nominal Attributes  Numeric Attributes  Instances  Classes  Missing Values  Imbalance Ratio 

breastw  0  9  699  2  1.90  
credita  9  6  690  2  x  1.25 
diabetes  0  8  768  2  1.87  
heartc  7  6  303  5  x  1.20 
hepatitis  13  6  155  2  x  3.87 
labor  6  8  57  2  1.86  
wine  0  13  178  3  x  1.47 
zoo  16  1  101  7  10.46 
Datasets  ONN  TCCS  EISRFS  AKHGA  INGA  KJGA  FISSM 

breastw  0.94  0.94  0.95  0.94  0.91  0.91  0.96 
credita  0.81  0.78  0.78  0.79  0.64  0.63  0.85 
diabetes  0.68  0.58  0.65  0.64  0.63  0.60  0.69 
heartc  0.70  0.69  0.77  0.64  0.63  0.60  0.71 
hepatitis  0.63  0.71  0.63  0.79  0.73  0.76  0.76 
tictactoe  0.76  0.73  0.53  0.75  0.70  0.84  0.79 
wine  0.96  0.41  0.96  0.81  0.82  0.83  0.96 
zoo  0.97  0.90  0.97  0.80  0.71  0.81  0.95 
Datasets  TCCS  EISRFS  AKHGA  INGA  KJGA  FISSM 

breastw  0.32  0.02  0.50  0.47  0.46  0.25 
credita  0.51  0.01  0.49  0.49  0.48  0.32 
diabetes  0.58  0.01  0.49  0.47  0.48  0.28 
heartc  0.59  0.01  0.49  0.47  0.48  0.30 
hepatitis  0.56  0.03  0.51  0.43  0.46  0.30 
labor  0.75  0.07  0.52  0.51  0.48  0.39 
wine  0.95  0.04  0.51  0.45  0.45  0.37 
zoo  0.52  0.05  0.49  0.49  0.47  0.12 
Datasets  TCCS  EISRFS  AKHGA  INGA  KJGA  FISSM 

breastw  1.00  1.00  0.62  0.40  0.49  1.00 
credita  0.87  1.00  0.58  0.39  0.45  0.87 
diabetes  1.00  1.00  0.63  0.31  0.40  1.00 
heartc  0.81  1.00  0.63  0.31  0.40  0.83 
hepatitis  0.67  1.00  0.60  0.43  0.54  0.73 
labor  0.53  0.49  0.41  0.44  0.49  0.53 
wine  0.73  0.88  0.52  0.44  0.45  0.73 
zoo  0.43  0.12  0.44  0.43  0.54  0.43 
Pair  Avg_Acc  Instance Retention  Feature Retention  

w–l–t  Probability  w–l–t  Probability  w–l–t  Probability  
FISSM vs. ONN  611  0.075  800  0.012  620  0.270 
FISSM vs. TCCS  620  0.012  800  0.012  026  0.180 
FISSM vs. EISRFS  521  0.176  080  0.012  422  0.463 
FISSM vs. AKHGA  710  0.025  800  0.012  170  0.017 
FISSM vs. INGA  710  0.012  800  0.012  071  0.018 
FISSM vs. KJGA  620  0.034  800  0.012  170  0.025 
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VilluendasRey, Y.; ReyBenguría, C.F.; CamachoNieto, O.; YáñezMárquez, C. Prediction of High Capabilities in the Development of Kindergarten Children. Appl. Sci. 2020, 10, 2710. https://doi.org/10.3390/app10082710
VilluendasRey Y, ReyBenguría CF, CamachoNieto O, YáñezMárquez C. Prediction of High Capabilities in the Development of Kindergarten Children. Applied Sciences. 2020; 10(8):2710. https://doi.org/10.3390/app10082710
Chicago/Turabian StyleVilluendasRey, Yenny, Carmen F. ReyBenguría, Oscar CamachoNieto, and Cornelio YáñezMárquez. 2020. "Prediction of High Capabilities in the Development of Kindergarten Children" Applied Sciences 10, no. 8: 2710. https://doi.org/10.3390/app10082710