Sebuah Kajian Pustaka:


IT Journal Research and Development (ITJRD) 

Vol.6, No.1, August 2021, E-ISSN : 2528-4053 | P-ISSN : 2528-4061 

DOI : 10.25299/itjrd.2021.6872      60 
  

Journal homepage: http://journal.uir.ac.id/index/php/ITJRD 

Implementation of Agglomerative Hierarchical 

Clustering Based on The Classification of Food 

Ingredients Content of Nutritional Substances 
 

Syabdan Dalimunthe1, Anggi Hanafiah2 

Departement of Computer Engineering, Politeknik Caltex Riau1 

Departement of Informatic Engineering, Universitas Islam Riau2 

syabdan@mahasiswa.pcr.ac.id1, anggihanafiah@eng.uir.ac.id2 
 

Article Info  ABSTRACT  

Article history: 

Received May 14, 2021 

Revised May 25, 2021 

Accepted August 4, 2021 

 

 Health is something very precious. Maintaining health can be done in 

many ways, one of them by keeping your diet. The correct diet will 

keep your immune system so that it can avoid various diseases. The 

proper diet will also put the body in a balanced nutrition state, which 

all need to be nourished. Nutrient requirements include calories, 

protein, fat, carbohydrates, calcium, phosphorus, iron, vitamin A, 

vitamin B, and vitamin C with a mass of 100 grams each. To 

facilitate the search for nutrients needed, then build a system that can 

categorize food based on its nutritional status and calculate the 

average value of nutrients in agglomerative hierarchical clustering 

using average linkage. Calculation of intermediate linkage methods 

produces data that has some similarities to the data sought nutrients 

that can be seen from its index, so precise data are in each group. Of 

the 6 categories of foodstuffs and 10 nutrient contents obtained, the 

cluster results were selected in the staple food category for testing in 

cluster 5, obtaining an SI value of 1, in the animal side dish category, 

in cluster 3, obtaining an SI value of 1, in the test vegetable side dish 

category. in cluster 4 obtained an SI of 0.846. In the vegetable 

category, the test in cluster 8 obtained an SI value of 9, in the fruit 

category, the test in cluster 3 obtained an SI value of 1, and in the 

egg, fruit and test categories in cluster 4 obtained an SI value of 1. 

Keyword: 

Agglomerative hierarchical 

Clustering  

Average Linkage  

Nutrients  

Silhouette Index  

 

© This work is licensed under a Creative Commons Attribution-

ShareAlike 4.0 International License. 

Corresponding Author: 

Syabdan Dalimunthe 

Applied Master of Computer Engineering Program 

Politeknik Caltex Riau 

Jl. Umban Sari (Patin) No. 1 Rumbai, Pekanbaru, Riau 

Email: pcr@pcr.ac.id 

 

 

1. INTRODUCTION 
A well-chosen daily diet will provide all the nutrients needed for the normal functioning of 

the body. Conversely, if the food is not appropriately chosen, the body will experience a deficiency 

of certain essential nutrients. 

Nutrients in food can be divided into two parts based on the amount contained therein, 

namely micronutrients (micronutrients) and macronutrients (macronutrients). Macronutrients are 

nutrients that contribute a lot of energy to the body. The term macronutrient describes chemicals 

that provide calories for energy, including carbohydrates, protein, and fat. The body requires these 



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 Syabdan Dalimunthe, Implementation Agglomerative Hierarchical Clustering Based on The Classification 

of Food Ingredients Content of Nutritional Substances 

61 

nutrients in large quantities. Meanwhile, micronutrients are substances such as vitamins and 

minerals that are essential for healthy growth and development. Although micronutrients are only 

needed in small amounts, micronutrient deficiencies can also cause serious problems. Examples of 

micronutrients include vitamin A, folic acid, iodine, iron, and zinc. Deficiencies in these nutrients 

can have severe consequences for children, pregnant women, and women of childbearing age. 

The human body needs macronutrients and micronutrients. However, the food contained in 

the surrounding environment has different types and nutritional content. People only know the 

nutrients in the food. For example, rice contains carbohydrates. Even though the ones that contain 

carbohydrates are not only rice, there are sweet potatoes, wheat, sago, and others. People find it 

challenging to find foods that have similar nutritional content in large quantities. Besides, people 

affected by certain diseases, people who are undergoing a diet program, and particular sports 

require the consumption of special nutrients. Most of them find it difficult to choose foods with the 

similarity of the nutrients they need. 

Based on this, data mining and clustering techniques can help provide solutions to these 

problems. Clustering is a method that can be used to make it easier to find data in the database. 

Clustering is a technique in data mining for grouping data. The agglomerative hierarchical 

clustering method is used to group data. In this method, food ingredients will be grouped based on 

nutritional attributes. The process of grouping foodstuffs is done by calculating the distance matrix 

using the euclidean distance. Where each data item is a cluster. After getting the distance between 

the data, the next step is to find each distance matrix's average value using the average linkage 

clustering method. Where is the average value of the comparison between the two distance 

matrices that will be taken to find the next iteration to obtain the desired number of clusters.  

 

 

2. RESEARCH METHOD 
2.1.  Related research 

 The literature study in this study is a literature study, where the literature referred to 

according to previous researchers is as follows: 

Based on research conducted by [1] regarding the grouping of food and beverages at PT. 

Indomarco Palembang. PT. Indomarco Palembang is a company engaged in the distribution of food 

and beverages. Not only PT. Indomarco Palembang, there are still quite a lot of other companies 

engaged in similar fields. This, of course, creates business competition between companies.From 

these problems, the solution obtained is to apply data mining to make decisions in the business 

world to develop business and to see the sales that consumers are most interested in, especially 

food and beverage sales. Based on this research, it can be concluded that one of the methods 

contained in data mining used in this study is the clustering method. The result of this research is 

that the application built can help the company as an illustration in making decisions in order to get 

product sales patterns.Originality in this study with this research is the problem under study. 

Namely, this study examines the problem of grouping food ingredients based on the nutrients 

contained therein, while the method used is different from this research, namely Agglomerative 
Hierarchical Clustering with the Average Linkage method. 

Based on research conducted by [2] regarding the grouping of types of food based on the 
nutrients contained therein.From these problems, the solution obtained is to classify the types of 

food into the number of micronutrients (carbohydrates and calcium) and macronutrients (protein 

and fat). The method used is the Discriminant Analysis method. Data taken from the List of Food 

Ingredients Composition (DKBM) of Indonesia includes 50 types of food and 4 variables of types 

of nutrients. The 4 types of nutrition are Protein, and Fat, carbohydrates, Calcium.Based on this 

problem, it can be concluded that dividing 4 variables into 2 groups, namely micronutrients and 

macronutrients in food. The results of the data analysis will show that the type of food is the type of 

food that contains a lot of micronutrients or contains more macronutrients. The originality of this 

study compared to that of the study is the method used. This study, using the Agglomerative 

Hierarchical Clustering algorithm with the Average Linkage method. 



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Syabdan Dalimunthe, Implementation Agglomerative Hierarchical Clustering Based on The Classification of 

Food Ingredients Content of Nutritional Substances 

62 

Based on research conducted by [3] about classifying food ingredients based on nutrient 

content in food. Based on these problems, the solution taken is to classify the food material data 

consisting of food ingredients with nutritional content as a source of combustion substances, a 

source of regulatory substances, and a source of building substances. From these problems, it can 

be concluded that each foodstuff group is grouped into three groups using the fuzzy c-means 

method. Information regarding foodstuff groups can be used as a reference for selecting food 

ingredients according to the required nutritional content. The originality of this study compared to 

that of the study is the problem under study. In this study, the types of foodstuffs were classified 

into 4 groupings, namely high-micronutrient high macronutrient, high-micronutrient high 

macronutrient, low macronutrient high-micronutrient, low macronutrient low-micronutrient. In 

addition, this study also differs in methods, namely using the Agglomerative Hierarchical 

Clustering algorithm with the Average Linkage method. 

 

2.3. Average Linkage Clustering 

Average linkage clustering is a method in which the similarity rules between clusters are 
based on the average distance of all objects in a cluster with all other objects in other clusters [12]. 

In the average linkage method, the distance between two clusters is defined as the average distance 

between all object pairs, where one of the pair members comes from each cluster. 

The following is the formula for calculating distance using the euclidean distance method 

in the following equation: 

 

 𝑑𝐴𝐵 = √∑ |𝑥𝑖 − 𝑦𝑖 |
2𝑛

𝑖=1  (1) 

 

Measurement of the distance between two clusters in the average linkage uses the average 

proximity formula as in equation as follows: 

 

 𝑑(𝑈, 𝑉) =  
1

𝑛𝑢× 𝑛𝑣 
 ∑ 𝑑(𝑈, 𝑉); 𝑑(𝑈, 𝑉) ∈ 𝐷 (2) 

 
Note: Nu and NV, respectively, is the amount of data in clusters U and V. 

For all the distances that have been obtained, if the clusters U and V are candidates for the 

two clusters to be combined while W is the other clusters that are not candidates, then for all the 

distances that have been calculated in equation (2.2), the smallest of them is chosen. . The 

formulation can be seen in the equation as follows: 

 

 𝑈 ∩ (𝑉, 𝑊) = min{𝑑(𝑈, 𝑉), 𝑑(𝑈, 𝑊)}; 𝑑(𝑈, 𝑉), 𝐷(𝑈, 𝑊)  ∈ 𝐷  (3)  
  

2.4. Silhoutte Index  

The silhouette index (SI) can be used to validate either a single data cluster (one cluster out 

of a number of clusters) or even an entire cluster. This method is most widely used to validate 

clusters that combine cohesion and separation values. To calculate the SI value of an ith data, there 

are 2 components, namely ai and bi. ai is the average distance of the I data to all other data in one 

cluster, while bi is obtained by calculating the average distance of the I data to all data from other 

clusters not in one cluster with the ith data, then take the smallest [12]. 

Here's a formula for calculating cohesion: 

 

 𝑐𝑜ℎ𝑒𝑠𝑖𝑜𝑛(𝐶𝑖) =  ∑ 𝑝𝑟𝑜𝑥𝑖𝑚𝑖𝑡𝑦(𝑥, 𝐶𝑖 )𝑥 ∈ 𝐶𝑖   (4) 

 
The following is the formula for separation between two clusters: 

 

 𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑖𝑜𝑛(𝐶𝑖, 𝐶𝑗 ) = 𝑝𝑟𝑜𝑥𝑖𝑚𝑖𝑡𝑦(𝐶𝑖 , 𝐶𝑗 )  (5) 

 



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 Syabdan Dalimunthe, Implementation Agglomerative Hierarchical Clustering Based on The Classification 

of Food Ingredients Content of Nutritional Substances 

63 

Here's the formula for calculating 𝑎𝑖
𝑗
: 

 𝑎𝑖
𝑗

=
1

𝑚𝑗−1
 ∑ 𝑑(𝑥𝑖

𝑗
, 𝑥𝑟

𝑗
),   𝑖 = 1,2, … , 𝑚𝑗

𝑚𝑗
𝑟=1
𝑟≠1

   (6) 

𝑑(𝑥𝑖
𝑗
, 𝑥𝑟

𝑗
) is the distance between the ith data and the r-the data in one cluster j, while 𝑚𝑗  

is the amount of data in the jth cluster. 

 

Here's a formula for calculating 𝑏𝑖
𝑗
: 

 𝑏𝑖
𝑗

=  min
𝑛=1,…,𝑘

𝑛≠𝑗

 {
1

𝑚𝑛
 ∑ 𝑑(𝑥𝑖

𝑗
 , 𝑥𝑟

𝑛 )
𝑚𝑛
𝑟=1
𝑟≠𝑖

} , i = 1,2, … 𝑚𝑛   (7) 

 
To get the ith Silhouette Index (SI) data, use the following equation: 

   

 𝑆𝐼 =
𝑏

𝑖
𝑗

−𝑎
𝑖
𝑗

max{𝑎
𝑖
𝑗

,𝑏
𝑖
𝑗

}
    (8) 

 
The value of ai measures how dissimilar a data is to the cluster it follows. The smaller the 

value, the more precisely the data is in the cluster. A large bi value indicates how bad the data is 

against other clusters. The SI values obtained are in the range [-1, +1]. The SI value that is close to 

1 indicates that the data is increasingly right in the cluster. A negative SI value (ai> bi) indicates 

that the data is not right in the cluster (because it is closer to another cluster). SI value 0 (or close to 

0) means that the data is positioned on the border between the two clusters. 

The SI value of a cluster is obtained by calculating the average SI value of all data that 

joins the cluster, as in the following equation: 

 

 𝑆𝐼 =
1

𝑚𝑗
∑ 𝑆𝐼𝑖

𝑗𝑚𝑗
𝑖=1

    (9) 

While the global SI value is obtained by calculating the average SI value of all clusters as 

in the following equation: 

 𝑆𝐼 =
1

𝑘
∑ 𝑆𝐼𝑗

𝑘
𝑗=1    (10) 

 

3. RESULTS AND ANALYSIS 
3.1. System Analysis 

 In this stage, a grouping application will be designed and built using existing techniques in 

data mining. This application will classify food material data based on the content of certain 

nutrients. Grouping to find information in food ingredients based on these nutrients uses clustering 

techniques in data mining using agglomerative hierarchical clustering algorithms. 

 This grouping of information in foodstuff data will help make it easier for people to find 

information related to nutrient content and food ingredients as needed. This application is used to 

find out information on the relationship between existing food material data with food material data 

or nutrient content and find out information on existing food data groups based on certain criteria. 

An overview of the data mining process can be seen as follows: 

 



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Syabdan Dalimunthe, Implementation Agglomerative Hierarchical Clustering Based on The Classification of 

Food Ingredients Content of Nutritional Substances 

64 

User Interface

Pattern Evaluation

Data Collecting, cleaning, 

Transformation, dan selection

Data Mining Engine

Knoledge Base

Data lagu DataLogSiar

User

 
Fig 1. Process Flow in Data Mining 

 

3.2. Implementation  

1. System Implementation in Society 

The implementation of the system is by making a questionnaire with 4 (four) questions 

and 10 (ten) correspondents from various circles of society. The fourth question in question 

is as follows: 

a. What do you think about the appearance of this system design? 
b. Are the input and output display easy to understand? 
c. Is the system easy to use? 
d. Does this system make it easier for you to find substitute food ingredients 

similar to what you want? 

From these questions, the results of the answers or responses from correspondents to 

the performance of the system based on the questions posed are as follows: 



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 Syabdan Dalimunthe, Implementation Agglomerative Hierarchical Clustering Based on The Classification 

of Food Ingredients Content of Nutritional Substances 

65 

 
Fig 2. Graph of The Results of The Questionnaire From The Community 

 

2. Implementation of Systems in the Health Sector 

Implementation of the system is by making a questionnaire with 5 (five) questions and 

10 (ten) correspondents, 5 of which are medical students and the other 5 are doctors. The 

five questions in question are as follows: 

a. What do you think about the appearance of this system design? 
b. Are the input and output display easy to understand? 
c. Is the system easy to use? 
d. Does this system make it easier for you to find food ingredients similar to what 

you want? 

e. Does the system provide the correct information on the group of foodstuffs and 
their nutritional content? 

From these questions, the results of the answers or responses from correspondents to 

the performance of the system based on the questions posed are as follows: 

 

 
Fig 3. Graph of The Results of The Questionnaire From The Nutrition Sector 

 

 

 

 

 

0

2

4

6

8

10

1 2 3 4

C
O

R
R

E
SP

O
N

D
E

N
T

QUESTIONS

COMMUNITY QUESTIONNAIRE GRAPHICS

YES/GOOD

MEDIUM/ENOUGH

NOT/ORDINARY

0

2

4

6

8

10

1 2 3 4 5

C
O

R
R

E
S
P

O
N

D
E

N
T

QUESTIONS

HEALTH QUESTIONNAIRE GRAPHICS

YES/GOOD

MEDIUM/ENOUGH

NOT/ORDINARY



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Syabdan Dalimunthe, Implementation Agglomerative Hierarchical Clustering Based on The Classification of 

Food Ingredients Content of Nutritional Substances 

66 

3.3.  Test Result  

 

  In this study, there are 6 categories of food ingredients and 10 nutritional content. The 

testing is carried out by inputting the number of clusters you want to test, which will later calculate 

the validity of the clusters using the Silhouette Index (SI) method. The results of the calculation of 

the foodstuff clustering system can be seen in the table 1. 

 

Table 1. Table of Silhouette Index Value Result 
Foodstuff Category Cluster Testing Silhouette Index 

Staple food 2 

3 

4 

5 

6 

7 

8 

0.620 

0.547 

0.455 

1 

1 

1 

1 

Animal side dishes 2 

3 

4 

5 

6 

7 

8 

0.989 

1 

1 

1 

1 

1 

1 

Vegetable side dishes 2 

3 

4 

5 

6 

7 

8 

0.563 

0.502 

0.846 

0.846 

0.846 

0.846 

0.846 

Vegetables 2 

3 

4 

5 

6 

7 

8 

0.817 

0.259 

0.707 

0.792 

0.792 

0.783 

1 

Fruits 2 

3 

4 

5 

6 

7 

8 

0.964 

1 

1 

1 

1 

1 

1 

Eggs, milk, and milk products 2 

3 

4 

5 

6 

0.705 

0.980 

1 

1 

1 



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 Syabdan Dalimunthe, Implementation Agglomerative Hierarchical Clustering Based on The Classification 

of Food Ingredients Content of Nutritional Substances 

67 

7 

8 

1 

1 

 

 In this test, the number of clusters was tested as many as 2 clusters to 8 clusters. From the test 

results, the number of clusters in the staple food category, the highest silhouette index value 1 was 

found in clusters 5, 6, 7, and 8, while the lowest silhouette index value was 0.455 exist in 4 total 

clusters. For the category of animal side dishes, the highest silhouette index value was 1 in clusters 

3, 4, 5, 6, 7, and 8, while the lowest silhouette index value in the category of animal side dishes was 

0.989 in 2 clusters. Then for the category of vegetable side dishes, the highest silhouette index 

value was 0.846, while the lowest silhouette index value was 0.502, which was located in 3 total 

clusters. In the vegetable foodstuff category, the highest silhouette index value is 1, located in 8 

total clusters, while the lowest silhouette index value is 0.259, located in 3 total clusters. In the fruit 

foodstuff category, the highest silhouette index value is 1, which is located in 3, 4, 5, 6, 7, and 8 of 

the number of clusters, while the lowest value of the silhouette index lies in 2 total clusters in that 

category. Furthermore, for the category of eggs, milk, and milk, the highest silhouette index value 

is 1, which is located at 4, 5, 6, 7, and 8 in the number of clusters, while the lowest silhouette index 

value is 0.705, which is located in 2 total clusters in the category of eggs, milk. and milk yields. 

The results of the calculation of the validity of this cluster will later select the number of clusters 

with the highest SI value, which is 1 or close to 1. The number of selected clusters is the highest SI 

value which can be seen in table 2. 

 

Table 2. Table of Number of Clusters 
Foodstuff Category Cluster Testing Silhouette Index 

Staple food 5 1 

Animal side dishes 3 1 

Vegetable side dishes 4 0.846 

Vegetables 8 1 

Fruits 3 1 

Eggs, milk, and milk products 4 1 

 

 

From the results of testing using a black box, the system that has been done, the following 

conclusions are obtained: 

1. Food material data can be grouped based on similarity in nutritional content. 

2. The best silhouette index (SI) value is close to 1 (one) or 1 (one), meaning that the data 

for the food being sought have similar nutrients in the cluster. In the category of staple food, the 

best SI value was in 5 clusters, in the category of animal side dishes the best SI value was in 3 

clusters, in the category of vegetable side dishes the best SI value was in 4 clusters, in the vegetable 

category the best SI value was in 8 clusters. Whereas in the fruit category, the best SI value was in 

3 clusters, and in the category of eggs, milk, and milk, the best SI value was in 4 clusters. 

From table 2, we can see the silhouette index value and the number of selected clusters 

which will later become the cluster values that will be studied in foodstuff data. The selected 

silhouette index value is the highest value of the silhouette index value from all clusters in one 

category. If the largest silhouette index value in one category is the same, for example, the staple 

food category, the largest silhouette index values are 5, 6, 7, and 8, Then the smallest number of 

clusters is chosen, namely, the number of clusters 5 (five) because the greater the number of 

clusters, the less data there is even one data in one cluster, Therefore, the smallest number of 

clusters was chosen with the largest silhouette index value. 

 

 



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Syabdan Dalimunthe, Implementation Agglomerative Hierarchical Clustering Based on The Classification of 

Food Ingredients Content of Nutritional Substances 

68 

4. CONCLUSION 
From the design and manufacture of food clustering systems based on their nutritional 

content, it can be concluded that The implementation of the Agglomerative Hierarchical Clustering 

Average Linkage algorithm for grouping food ingredients has been successfully designed and 

implemented in the form of a web application that can provide detailed information on food 

ingredients needed based on nutritional content.The best silhouette index (SI) value is close to 1 

(one) or 1 (one), meaning that the data for the food being sought have similar nutrients in the 

cluster. In the category of staple food, the best SI value was in 5 clusters, in the category of animal 

side dishes, the best SI value was in 3 clusters, in the category of vegetable side dishes, the best SI 

value was in 4 clusters, in the vegetable category the best SI value was in 8 clusters. Whereas in the 

fruit category, the best SI value was in 3 clusters, and in the category of eggs, milk, and milk, the 

best SI value was in 4 clusters. 

 

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BIOGRAPHY OF AUTHORS 

 

 

 

Syabdan Dalimunthe obtained a Bachelor of Informatics from Riau Islamic University in 2016. 

He has served as Assistant Lecturer in the Riau Islamic University Informatics Department since 

2013. His current research interests include machine learning, Data Science, and the Internet of 

Things. 

 

 

 

 

 

 

  

 

 

 

Anggi Hanafiah is a Lecturer of Department of Informatics Engineering, Islamic University of 

Riau.Obtained Bachelor Degree in Informatics Engineeringfrom STMIK-AMIK Riau , obtained 

Master Degree in Information Engineeringfrom UPI-YPTK Padang.His current research interests 

include Data Mining, Artificial Inteligent, Networking, and Multiplatform Programming. 

 

 

 

 

 

 

  

 

http://kamuskesehatan.com/arti/