J Vis
https://doi.org/10.1007/s12650-025-01052-x
R E G UL A R P A P E R
Kangqi Lu • Yi Chen
•
Zhiying Luo • Yu Dong • Cheng Lv
Visual comparison of hierarchies with inherited
attributes: application to multi-regional MRL
standards in food safety
Received: 15 October 2024 / Revised: 31 December 2024 / Accepted: 20 January 2025
The Visualization Society of Japan 2025
Abstract The Maximum Residue Limit (MRL) standard specifies the permissible pesticide residues in
various types of foods, with limit values determined by foods and inheritance rules in their classification.
Comparing both food classification trees and the values of inherited attributes across multi-regional MRL
standards is a complex, unresolved challenge. This paper introduces a visualization-based method for
comparing multiple hierarchies with inherited attribute values (HIAC) for MRL standards. First, we construct MRL trees (MRLtree) in different regions for each pesticide, recursively assigning values based on
food classification and inheritance rules. These MRLtrees are merged into a unified tree (UniMRLtree) by
visual modeling for comparative analysis. Second, we propose two visualization design solutions,
‘‘UniMRLtree for multiple regions’’ and ‘‘MRL values matrix heatmap’’ for comparing differences across
multi-regional MRL standards. Finally, we present MRLvis, a visual analytics system that supports users to
compare and analyze multiple regional MRL standards from multiple perspectives, including food classification and MRL values. A case study involving six global regions demonstrates the method’s
effectiveness.
Keywords Visual analytics Tree comparison Inherited attributes MRL standards Food safety
1 Introduction
In the context of globalization, food safety has become a major concern for countries worldwide (Chen et al.
2023; Wang et al. 2022; Dong et al. 2024). Pesticide residues are one of the primary contributors to food
safety issues (Chen et al. 2022). For official supervision and regulation, countries or regions have
K. Lu Y. Chen (&) Z. Luo
Beijing Key Laboratory of Big Data Technology for Food Safety, Beijing Technology and Business University, Beijing
100048, China
E-mail: chenyi@th.btbu.edu.cn
K. Lu
E-mail: lukangqi@hotmail.com
Z. Luo
E-mail: lzhiying1223@foxmail.com
Y. Dong
School of Computer Science, University of Technology Sydney, Ultimo, NSW 2007, Australia
E-mail: yu.dong-3@alumni.uts.edu.au
C. Lv
School of Information Science and Technology, Northeast Normal University, Changchun 130024, China
E-mail: luc649@nenu.edu.cn
K. Lu et al.
established maximum residue limit (MRL) standards, which define the legally permissible maximum levels
of pesticides in food (National Health and Family Planning Commission of PRC & The Ministry of
Agriculture of the People’s Republic of China & State market regulatory administration 2021). The MRL
standard reflects, to some extent, the level of regulation concerning pesticide residues in food within a
country or region (hereafter collectively referred to as region). However, significant variations in MRL
standards across different regions create barriers and challenges for food safety regulation and international
trade, leading to difficulties in achieving global trade integration. Therefore, it is essential to compare MRL
standards across regions in intelligent and effective ways. Comparing these regional MRL standards can
facilitate improvements in domestic regulations and enhance the import and export of food products,
ultimately promoting safer food trade practices and fostering international cooperation.
Typically, the MRL standards specify the food classification system and the MRL values of pesticide
residues in various foods, characterized by a hierarchical structure and multi-dimensional attributes. The
food classification systems, the types of pesticides involved, and the MRL values for each pesticide in
various foods may vary significantly across different regional MRL standards. Additionally, pesticide MRL
values are commonly inherited within the food classification tree, meaning that when a pesticide limit value
is applied to a food classification, all foods under that classification must adhere to this limit unless special
provisions exist for certain foods. When comparing across regional MRL standards, it is crucial to compare
both their food classification trees (i.e., classification systems) and the inherited attribute values within those
trees (i.e., MRL values). Comparing such multiple hierarchies with inherited attributes is inherently
complex.
Most existing MRL comparison methods rely on manual comparison or tabular tools to compare multiple MRL values between two standards one by one, which is inefficient, inaccurate, unintuitive, and makes
it difficult to compare inherited MRL values within the food classification tree. In recent years, visual
analysis technology has emerged as a powerful tool, utilizing visual interactive interfaces to integrate human
perception and cognitive abilities into the data processing process. This approach combines and enhances
the complementary strengths of human intelligence and machine intelligence, enabling more effective
analytical reasoning and decision-making (Chen et al. 2022). It allows users to analyze data at a deeper level
and from multiple perspectives (Shi et al. 2023; Chen et al. 2024), quickly uncovering hidden patterns and
characteristics within the data (Fu et al. 2017; Wu et al. 2023; Yu et al. 2023). Visual analytics has made
remarkable progress aiding many fields and is beginning to be applied to the comparison of multilevel
structures (Bremm et al. 2011; Beck et al. 2014).
We propose a method (HIAC) to visually compare multiple hierarchies with inherited attribute values,
using the task of comparative analysis of MRL standards across multiple regions as a case study. The
problem of comparative analysis of MRL standards is abstracted into a multiple pesticide maximum residue
limit value tree (MRLtree) after inheriting the limit values. Based on HIAC, we designed and implemented a
visual comparison system for multi-regional MRL standards (MRLvis, as shown in Fig. 1), which supports
multi-level comparative analysis of MRL standard differences across regions. The main contributions are
summarized as follows:
• We proposed a visual modeling method for constructing trees with inherited MRL values, called
UniMRLtree. First, according to the MRL standard, an MRLtree is constructed for each pesticide in each
MRL standard system by recursively assigning values. Then, multiple MRLtrees for the same pesticide
across different regions are hierarchically merged, and their MRL values are integrated to generate a
UniMRLtree. This unified pesticide limit value tree contains food classifications from multiple regions
and inherited MRL values, providing a foundation for the subsequent comparison of food classifications
and MRL values across regions.
• We introduced two visualization design solutions for comparing both structures and inherited attributes.
The two proposed solutions, UniMRLtree for multiple regions, and the MRL values matrix heatmap, are
designed to visualize both the structural differences between hierarchies and the variations in inherited
attribute values. The UniMRLtree for multiple regions uses these shapes nested within the nodes of the
UniMRLtree to represent differences in food classifications and pesticide limit values across regions. In
addition, multiple Sunburst plots are used to show the differences in the food groups associated with the
selected nodes in each region. The MRL values matrix heatmap visualizes the distribution of pesticide
values for various food products in each region.
• We designed a multi-region MRL standards visual comparative analysis system, called MRLvis. The
system is implemented to support multi-level comparative analysis of the differences in MRL standards
across regions, from the food classification structures to individual MRL values. Case studies involving
Visual Comparison of Hierarchies with Inherited Attributes...
Fig. 1 MRLvis system interface with rose graph. (a) UniMRLtree for multiple regions view, using a node-link tree with Rose
or Petal nodes, showing the classification of food products and the MRL values for selected pesticide in multiple regions. (a1)
When the mouse hovers over the Rose node, the hover box displays the name of the food represented by the node and the path
of the food classification it belongs to, as well as the MRL value of the selected pesticide in the food in each region. If the path
of the food in each region’s classification is different from the path in the current UniMRLtree, it is indicated in red font. (a2)
When the user clicks on a node in the UniMRLtree, that node and its children will be highlighted. (b) Food classification trees
of multiple regions view, showing the hierarchy of food classification by region. (c) MRLs count statistics for selected pesticide
view, showing the number of foods or classification with MRL values for selected pesticide (Methomyl) by regions. (d) MRL
values matrix heatmap view, where each row is a region, each column is a food, the cell at the intersection of the rows and
columns indicates the MRL value, the darker the color the larger the MRL value. It shows a comparison of MRL values for
selected pesticide (Methomyl) in various foods in a specific food group (Foods) in each region. (d1) shows a comparison of
MRL values for selected pesticide (Methomyl) in various foods in ‘‘Leafy vegetables’’ in each region. (d2) is when the mouse
hovers over a cell, the hover box displays the MRL value and its corresponding food name. (e) Comparative statistics of MRL
values view, showing the statistical results of the differences in MRL values of the selected pesticide in selected food between
other regions and China. Here, showing the number of MRL values in the specific food (Peach) that are stricter, identical,
looser and unique in each region compared to China. (f) Comparative details of MRL values view, showing the ‘‘EU’’ list of
‘‘looser’’ MRLs compared to China
fruits and vegetables in six regional MRL standards were conducted to demonstrate the usefulness and
effectiveness of the HIAC method.
2 Related work
In this section, we briefly review three parts specifically related to our work: visual representation of trees,
comparison of hierarchical structures, and comparison of hierarchical data in food safety.
K. Lu et al.
2.1 Visual representation of trees
Existing algorithms for the visual representation of hierarchical structures can be categorized into node-link,
space-filling, and hybrid methods.
The node-link method uses points of different shapes to represent objects, and the connecting lines
between the points indicate the parent–child relationships between the objects (Graham and Kennedy 2010).
For example, Gray et al. (2023) used the node-link method to display hierarchical structures and proposed a
readable tree layout method. While the node-link method clearly presents the hierarchical structure, its space
utilization is low.
The space-filling method uses spatial nesting to represent hierarchical structures, with the area of shapes
such as rectangles, circles, or polygons representing the magnitude of an object’s attribute values. Görtler
et al. (2017) proposed a novel circular tree graph and introduced a hierarchical, force-based circle-filling
algorithm to compute the bubble tree. Wang et al. (2020) used an orthogonal Voronoi tree graph to represent
the hierarchical structure. The space-filling method has high space utilization, but its presentation of
hierarchy is less clear compared to the node-link method.
The hybrid method combines both the node-link and space-filling methods, leveraging the strengths of
each to effectively display both hierarchical structure and attribute values. For example, Chen et al. (2015)
proposed an interrelated two-class hierarchical data visualization method, using the node-link method for
the classification structure of food products, a ring of the rising sun to represent the classification structure of
pesticides, and connecting lines between the two classes of nodes to express the pesticide detection relationships in foods. Chen et al. (2016) proposed a technique combining space-filling and node-linking
methods, using the space-filling method to compress the tree into a concise aggregated dendrogram (AD)
and clustering similar ADs using the node-linking method to generate a visual summary of the topological
relationships between selected subtrees.
Although hierarchical data visualization methods are relatively mature, targeted visualization methods
are still needed to enable effective visual comparisons of MRL standards across multiple regions, addressing
both hierarchical structures and node values.
2.2 Comparison of hierarchical structures
The comparison of hierarchical structures can be understood as the comparison of tree structures (Pandey
et al. 2021). Common methods for tree visualization comparison are typically classified into three categories: juxtaposition, superposition, and animation.
Juxtaposition involves placing two or more trees side by side for comparison. BarcodeTree, proposed by
Li et al. (2019), juxtaposes multiple trees and allows for the simultaneous comparison of topology and node
attribute values in up to 100 trees. Holten and Van Wijk (2008) enhance the display of differences by
linking the nodes of the two trees and incorporating an edge bundling technique.
Superposition refers to merging two or more trees into a single aggregate tree. Lee et al. (2007) proposed
a method to superimpose two trees into one, visualizing two structural uncertainties. Dong et al. (2020)
proposed a visualization method that uses a tree metaphor to superimpose three trees into a single hierarchical structure.
Animation involves observing changes in nodes across different tree structures through frame switching.
For example, Card et al. (2006) designed TimeTree, which allows users to switch between tree structures at
different points in time by dragging a timeline. However, changes in node positions can often make
comparison more challenging.
When comparison tasks involve both structural and attribute differences, superposition-based methods
generally offer better performance because users do not need to frequently switch their view, resulting in a
lower cognitive load. Therefore, we considered using superposition to merge multiple hierarchical trees with
inherited attribute values for comparing regional MRL standards.
2.3 Comparison of hierarchical data in food safety
Currently, most hierarchical comparisons in the field of food safety rely on manual comparisons, table-based
tools, or visual comparative analysis. Liang et al. (2022) and Lv et al. (2018), among others, used a
combination of manual comparison and table-based methods to compare China’s MRL standards with those
of other regions, both of which are inefficient and lack effective visualization.
Visual Comparison of Hierarchies with Inherited Attributes...
The visual comparison method offers a new approach to comparing MRL standard data. Luo et al.
(2022) proposed a visual comparison and analysis method for food classification trees (FCTs) in MRL
standards, which can compare the structure and the number of node attributes in FCTs across two regions.
Although this method also considers the inheritance relationships of limit values within food classifications
in MRL standards and compares the number of pesticides for which limits have been set in each food or
food classification after inheritance, it cannot directly compare the differences in pesticide residue limit
values in each region’s MRL standards, nor can it statistically analyze the range and severity of pesticide
residue limit values common to multiple regional standards.
The comparative visual analysis method for complex hierarchical data proposed by Chen et al. (2018)
allows for comparing MRL standards between two regions, but it does not account for the inheritance
relationships of limit values within food classifications in MRL standards, nor can it compare MRL standards across multiple regions simultaneously.
In summary, existing visual comparison methods cannot simultaneously compare the structural differences in food classifications and the differences in inherited limit values in MRL standards across multiple
regions. To address these issues, this paper designs and implements MRLvis to solve the aforementioned
problems.
3 Dataset and analytical tasks
3.1 Introduction to MRL standards
The MRL standard data contain information on foods, pesticides, a list of food classifications, and the MRL
value for each pesticide in each food classification or specific food (National Health and Family Planning
Commission of PRC & The Ministry of Agriculture of the People’s Republic of China & State market
regulatory administration 2021). Food classifications in the MRL standards are used to define the scope of
application of the MRLs for pesticides. The MRL value represents the maximum legally permissible
concentration of a pesticide in or on the surface of an agricultural product. The MRL standard data for each
region are typically available in the form of regulatory documents. We have collected MRL standard data
for fruits and vegetables from six regions: China (CN), the United States (US), the European Union (EU),
Japan (JP), Australia (AU), and the Codex Alimentarius Commission International Organization (CAC), as
shown in Table 1. For example, in China, the MRL for the pesticide ‘‘Methomyl’’ in ‘‘Peach’’ is 0.2 mg/kg.
The MRL value of a pesticide in food is related to the food classification. China’s MRL standard for food
classification data is shown in Table 2, e.g., ‘‘Orange’’ belongs to the classification:‘‘Fruits’’—‘‘Citrus fruit.’’
When the MRL value of a pesticide is applied to a food category, it is applicable to all foods under that
food category, unless there are special provisions, i.e., the MRL value is inherited. For example, the Chinese
MRL standard does not specify the limit value of the pesticide terbufos in ‘‘Orange,’’ and the upper food
category of ‘‘Orange’’ is ‘‘Citrus fruit,’’ the limit of terbufos in ‘‘Citrus fruit’’ is 0.01 mg/kg, so the limit
value of terbufos in ‘‘Orange’’ is 0.01 mg/kg. In order to better compare the MRL standards of multiple
regions, it is necessary to look at both the way foods are classified in each regional standard and the MRL
values for pesticides in each food.
3.2 Dataset of MRL standards
In this paper, the MRL standards on fruits and vegetables in six regions, including CN, US, EU, JP, AU,
CAC, are used as the main research dataset. The number of fruits and vegetables, the number of pesticides,
and the number of pesticide residue standards in the MRL standards for these six regions are shown in
Table 3.
3.3 Analytical task of MRL comparative
Since 2012, the authors’ team has been collaborating with a group of experts in the field of food science to
develop a series of methods and systems for the visual analysis of pesticide residue data (Chen et al.
2017, 2018, 2022,2023 ,2024), all of which involve multiple regional MRL standards. Over the past 10 years
of cooperation and research, we have gained a deeper understanding of MRL standards and discovered
significant differences between the MRL standards of various regions, particularly in terms of food
K. Lu et al.
Table 1 Example of MRL standards data for six regions
Product
Peach
Cherry
Celery
Apple
Pesticide
Methomyl
Bifenazate
Permethrin
Malathion
CN
0.2
2
2
2
US
5
2.5
5
8
EU
0.01
0.01
0.05
0.02
JP
2
2
2
0.5
AU
1
2.5
5
Null
CAC
0.2
Null
2
0.5
Notes: The unit of MRL value is mg/kg, null means that there is no MRL value for this pesticide for this food in this region
Table 2 Example of food classification in Chinese MRL standard
Product
Orange
Apple
Tomato
Melon
Primary
Fruits
Fruits
Vegetables
Vegetables
Secondary
Citrus fruit
Kernel fruit
Eggplant vegetables
Melon vegetables
Tertiary
Null
Null
Tomatoes
Small Melon
Quaternary
Null
Null
Null
Null
Notes: Null indicates that the food does not have this level of food classification
Table 3 Statistics on the number of foods, pesticides and MRL values in the MRL standard data involving fruits and
vegetables
Region
Food
Pesticide
Standard
CN
222
333
2658
US
136
260
906
EU
492
420
75341
JP
297
504
19089
AU
226
314
2479
CAC
26
11
122
classification and pesticide limit values. Experts in the field of food science have also expressed an urgent
need for more effective methods to help them compare and analyze MRL standards across multiple regions.
To address this need, we recently conducted an extensive literature review on MRL standards from
multiple regions and invited three experts (E1-E3) from different fields to participate in several rounds of
interviews to gather requirements and actual needs for comparative analysis of MRLs from different
perspectives. E1 is an expert in the field of pesticide residues in China and has been studying the differences
between MRL limits in China and other regions for many years. E2 is an expert in international food safety,
with a primary research focus on differences in MRL limits for food products across various regions. E3 is
an expert in visualization, specializing in the comparison of data across multiple hierarchical structures.
Based on our research foundation, literature review, and expert interviews, we have summarized the task of
comparing and analyzing multiple regional MRL standards as follows:
Task 1. Quickly compare the hierarchical structure differences in MRL standards across multiple
regions.
Task 2. Identify differences in limit values of MRL standards from multiple regions. Compare MRL
values from both macro- and micro-levels, from both pesticide and food perspectives.
Task 3. Statistics and analysis of MRLs for pesticides that are co-existing in multi-region MRL standards. Specifically, a food product was selected and the number of pesticides with more strict, the identical,
more loose and unique MRLs in that food or food classification in other regions compared to the MRLs
specified in China was counted and details of the differences in the limit values of the various pesticides
were shown.
Based on the above analysis tasks, we propose HIAC, a method for comparing the inherited attribute
values in multiple hierarchies. The entire pipeline of HIAC is shown in Fig. 2.
4 UniMRLtree
4.1 Construction of MRLtree with recursive assignment
According to the definition of MRL standards, when a pesticide limit value is applied to a food classification, all foods within that food classification should comply with that limit value, unless there are special
provisions. Therefore, MRL values are inherited in the food classification system. Considering the
Visual Comparison of Hierarchies with Inherited Attributes...
Fig. 2 Pipeline of HIAC
hierarchical structure of food classification and the inheritance characteristics of limit values, this paper
constructs a MRLtree for each pesticide according to the food classification system of each region. The
nodes of the MRLtree are the food or food classification of the corresponding region, and the links between
the nodes indicate the parent–child relationship in the food classification. The attribute value of the leaf node
is the MRL value of the food for the selected pesticide. If the leaf node does not define the MRL value, it is
necessary to query the ancestor node for recursive assignment. Consider a hierarchical structure T with
nodes set N. For each node n 2 N, let vðnÞ denote its attribute value, and pðnÞ denote its parent. The root
node level is defined as 0, with lðnÞ indicating the level of node n.
The recursive query for the attribute value Qðn; lÞ for any node n is determined by:
8
vðnÞ;
if vðnÞ 6¼ ;
>
<
Qðn; lÞ ¼ QðpðnÞ; l 1Þ; if vðnÞ ¼ ; and l [ 1
ð1Þ
>
:
vðpðnÞÞ;
if vðnÞ ¼ ; and l ¼ 1
As shown in Fig. 3, an MRLtree for Carbendazim in China is constructed, with light green nodes representing food classifications and orange nodes representing specific foods. The Carbendazim limit value for
‘‘Lemon’’ is 0.5 mg/kg, and for ‘‘Pear’’ it is 3 mg/kg. When querying ‘‘Hawthorn,’’ it is found that there is
no specific Carbendazim limit value for ‘‘Hawthorn’’ in China’s MRL standard. However, the parent node of
‘‘Hawthorn,’’ i.e., ‘‘Kernel fruits,’’ has a Carbendazim limit value of 3 mg/kg; thus, the Carbendazim limit
value for ‘‘Hawthorn’’ is inherited as 3 mg/kg.
K. Lu et al.
Fig. 3 MRLtree of Carbendazim in China. The structure of the tree is the food classification system specified in the MRL
standard of China. The attribute value of each node is the MRL value of Carbendazim in the food represented by that node
4.2 Visual modeling of the UniMRLtree
In order to more comprehensively compare the differences in MRL standards of different regions after
inheritance, we constructed a visual modeling method, namely UniMRLtree. We mark a set of hierarchical
trees as fT1 ; T2 ; . . .; Tk g, where each tree Ti consists of a node set Ni . Assume Ta is the benchmark tree, and
we aim to merge the other trees fT1 ; T2 ; . . .; Tk g with Ta to form a merged tree Tm , following the defined rule
of homogeneous parts merging and heterogeneous parts addition by steps:
Step 1. Identify the homogeneous parts as Oa between Ta and other Ti , and list their nodes’ attribute
value sets for each node in Oa .
Step 2. For heterogeneous parts, defined as Ei , in any Ti not belonging to Oa , add them to Ta , keeping
their structure and node attribute values.
Step 3. For each node nm in the merged tree Tm , the set of tree structures and attribute values Pðnm Þ for
nm is determined by the union of sets from the corresponding node’s location and attribute values in all
homogeneous parts, united with the tree structures and attribute values from the corresponding nodes in all
heterogeneous parts. Given the total number of trees k, with k1 representing the number of trees contributing
to homogeneous parts and k2 representing the number of trees contributing to heterogeneous parts such that
k1 þ k2 ¼ k, the structure and attribute value set Pðnm Þ for node nm in the merged tree Tm can be determined
as follows:
!
!
k1
k2
[
[ [
Oi ðnm Þ
Ej ðnm Þ
Pðnm Þ ¼
ð2Þ
i¼1
j¼1
The process of UniMRLtree construction is shown in Fig. 4. First, based on China’s food classification tree
for the hierarchical integration of MRLtrees in other regions. For example, the classification of F1 in Region
1 is exactly the same as that of F1 in China, but F4 and F10 are not available in China, so a new branch
needs to be added to the UniMRLtree. Second, traverse all the nodes on the UniMRLtree to merge the node
attributes. For example, the F7 node in the UniMRLtree, queries three MRLtrees, including China, Region
1, and Region 2, and finds that the node has the limited value of Carbendazim in all three regions, then the
names of the three regions and the limited value of each region are used as the attributes of the F7 node in
the UniMRLtree. By using a hash table to store the tree nodes, the time complexity time of constructing a
UniMRLtree is reduced from the regular Oðn log nÞ to O(n). The UniMRLtree provides a basis for further
multiple regions MRL standard comparisons and analyses, and supports comparisons of inherited attribute
values across multiple hierarchies.
Visual Comparison of Hierarchies with Inherited Attributes...
Fig. 4 Construction process of UniMRLtree. Merge the MRLtrees of three regions, China, Region 1 and Region 2, to construct
the UniMRLtree of the three regions, where the red letters in the MRLtree denote the limit value of the node defined in the
MRL standard, and the blue letters denote the limit value of the node obtained after inheritance
5 Visualization design
To better illustrate the differences in pesticide residue limits across multiple regions, we have designed two
visualization solutions: the UniMRLtree for multiple regions view and the MRL values matrix heatmap
view. This section provides a detailed description of the design and implementation of these two solutions.
5.1 UniMRLtree for multiple regions view
The UniMRLtree for multiple regions view provides a visualization of the overall structure of the UniMRLtree. This view utilizes node-linking, high-level node mapping, and node backtracking paths to clearly
present the hierarchy (Task 1). Specifically, the view uses the node-linking method to display the hierarchical structure of the UniMRLtree. Nodes represent food products or food classifications, and links between
nodes represent parent–child relationships. When a user selects a node of interest, that node and all its child
nodes are highlighted, as shown in Fig. 1a2.
Second, a node category mapping method is implemented. Brown square nodes represent the root nodes
of the UniMRLtree, and blue square nodes represent the top-level food classification nodes, such as fruits
and vegetables, as shown in Fig. 1a. Additionally, a node path backtracking algorithm is designed so that
when the user selects a node, the classification path from the root node to the selected node in the
UniMRLtree and MRLtree (with MRL values for several regions) is displayed via a hover box, as shown in
Fig. 1a1.
K. Lu et al.
Thirdly, the hierarchical structure of food classifications in each region is presented using a Sunburst
plot, as illustrated in Fig. 1b.
UniMRLtree for multiple regions view nests the improved Rose and Petal graphs on UniMRLtree nodes
to show the differences in food classification and MRL values in the multiple regions MRL standards (Task
2). Specifically, different regional regulations, standards and regulatory systems lead to large differences in
the range of MRL values. In order to compare the relative magnitude of MRL values for selected pesticides
for the same food across multiple regions, we improved the rose graph and used the color coding to map
different regions. The area of the sectors in the rose graph maps the MRL values for each region, with larger
areas indicating larger (more looser) values. The angle and radius of each sector are calculated as follows:
Step 1.1 The angle of each region Ai is calculated as:
vi
Ai ¼ PN1 2p ði ¼ 0; 1; 2; :::; N 1Þ
ð3Þ
j¼1 vj
Where N denotes the total number of regions with MRL value for the region represented by the current node,
i is the number of the sector, vi denotes the MRL value for the selected pesticide for the current food product
in the area represented by each region.
Step 1.2 We found that the MRL values of some nodes vary significantly. To display the data with
different value ranges more clearly in the visualization, we adjusted the radius of the sectors in the rose
graph. Specifically, to reduce the gap between data ranges, we applied a logarithmic transformation to
process the values. the radius Ri is calculated as follows:
Ri ¼ lnðvi 50Þ 15
ði ¼ 0; 1; 2; :::; N 1Þ
ð4Þ
The rose graph allows for a visual comparison of MRL values for different areas on a given food product,
but may cause visual errors when comparing MRL values for the same region on different foods. This is due
to the fact that the angle and radius of each area on a food node are calculated in a way that only the value of
the current node is considered, which can lead to errors in the size of the mapped region of the same area on
different food nodes compared to the true value. In order to solve this problem, we designed the petal graph,
which can compare the size of pesticide limits defined for the same pesticide in each region in different food
products, as shown in Fig. 5a. The petal graph is evenly divided into sectors according to the number of
regions compared, with each sector representing one region, and color coding is used to map the different
regions. First, fix the radius of the petal graph, according to the value range of all nodes on UniMRLtree to
calculate the fan angle of each region on each node, the larger the MRL value, the larger the corresponding
fan angle, as shown in Fig. 5a5. Nodes without MRL values are shown with black circles as shown in
Fig. 5a6. The angle of each fan region is calculated as follows:
Step 2.1 Divide a circle into N equal parts, and the starting angle of each region Si is calculated as:
Si ¼
2p
i
N
ði ¼ 0; 1; 2; :::; N 1Þ
where N is the number of regions to be compared and i is the number of the sector.
Step 2.2 The end angle of each region Ei is calculated as:
vi
2p
ði ¼ 0; 1; 2; :::; N 1Þ
Ei ¼ Si þ
N
vmax
ð5Þ
ð6Þ
where vi denotes the MRL value for the selected pesticide for the current node food in the area represented
by each region, and vmax denotes the maximum value of the MRL value for the selected pesticide for the
food in all regions.
In order to display the complex classification relationships between foods and the numerous hierarchical
data in a limited space, we use optimized layout algorithms such as drag-and-drop operations and forcedirected layout to ensure the readability of the view. Users can search for food names to locate the nodes, as
shown in Fig. 5a3, and drag and drop the nodes to a blank area to re-layout the view if there is an occlusion
between the nodes for further analysis.
Visual Comparison of Hierarchies with Inherited Attributes...
5.2 MRL values matrix heatmap view
The MRL values matrix heatmap view is used to display a macroscopic overview and subtle differences in
the MRL standards for various foods across different regions for the selected pesticide (Task 2).
The MRL values matrix heatmap view is generated based on the pesticide and food classification nodes
selected by the user in the UniMRLtree View, as shown in Fig. 1d. Each row of this view represents a
region, and the food products follow a depth-first traversal order, expanding along the horizontal coordinates. This not only maintains the organization of the data, but also reflects the inheritance relationships and
classification logic among the foods.
The color gradient from pink to blue maps the strictness of the pesticide MRL values. Pink maps smaller
MRL values. Blue maps larger MRL values. This intuitive color coding, coupled with the filtering of nodes
with no value, i.e., nodes with no MRL value in any of the six regions are not displayed, improves the view’s
intuitiveness and space utilization. Hovering over a region in the MRL values matrix heatmap view provides
detailed information on the pesticide limit values for the corresponding food in that region, as shown in
Fig. 1 d2.
6 MRLvis system implementation
We designed and implemented MRLvis, a HIAC-based visual analytics system for multi-region MRL
standards. The system interface of MRLvis is shown in Fig. 5, which consists of seven parts, including: a
control panel and six views. It is described as follows: The control panel contains (a1), (a2), (a3) and (a4),
where (a1) is a switch button for the node embedded graphs in the UniMRLtree, which can switch the
display of rose or petal graph; (a2) is a pesticide selection box; (a3) is a food node search box; and (a4)
switches the display state of food nodes in the UniMRLtree. (a) UniMRLtree for multiple regions view is an
overall overview view of the UniMRLtree, showing the food classification in the six regions and the MRL
value differences in selected pesticides for each food. Each node represents a food or food classification, and
the user can select with a button to use either petal or rose graph to show the differences in MRL values for
each food item for the selected pesticide in each region. Also, this view supports users to search, locate and
drag nodes. (b) Sunburst plots are used to show the paths of food classification of the selected nodes in the
six regions (Task 1). (c) MRLs count statistics for select pesticide view shows the number of foods or
classification with MRL values for the selected pesticide ‘‘Permethrin’’ by regions. (d) MRL values matrix
heatmap view shows MRLs for selected pesticide in each region are shown. The vertical coordinates
represent regions, the horizontal coordinates represent foods, and the color shades of the squares map the
magnitude of the MRL values for the selected pesticide in each food. For a more detailed quantitative
comparative analysis, after the user selects a food node in UniMRLtree, (e) A stacked bar chart will be used
to show the number of MRL values in the selected food or food classification that are stricter, identical,
looser and unique in each region compared to China (Task 3). (f) The Comparative details of MRL values
view provides the user with a complete comparative list of MRL values for selected pesticide in each food
(Task 3).
Overall, the system takes into account the inheritance of attribute values between hierarchical levels and
provides users with a comprehensive and in-depth tool for comparison of multiple regions MRL standards
through the HIAC methodology, enabling a better understanding of the differences in food classification and
the differences in inherited MRL values in different regions.
7 MRLvis evaluation
To verify the effectiveness of MRLvis, we invited three experts to evaluate the system. We began by
explaining its operation to help them become familiar with it. The experts were then encouraged to explore
the system freely, engage in discussions, and document their findings. Additionally, we conducted in-depth
interviews with the experts and collected their feedback.
K. Lu et al.
Fig. 5 MRLvis system interface with petal graph. a UniMRLtree for multiple regions view. a5 Select the pesticide
‘‘Permethrin’’ and the food ‘‘Kiwifruit,’’ mouse hovering over the petal node, compare the food classification differences of
‘‘Kiwifruit’’ in the six regions, and explore the inheritance of the MRL values of ‘‘Permethrin’’ in the MRLtree of each region.
a6 Nodes without MRL values are shown with black circles. b Food classification pathways for the selected food ‘‘Kiwifruit’’
in six regions (Food classification trees of multiple regions view). c The number of foods or classification with MRL values for
the pesticide ‘‘Permethrin’’ by regions (MRLs count statistics for select pesticide view). d The MRL values for the pesticide
‘‘Permethrin’’ in the food classification ‘‘Leafy vegetables’’ (MRL values matrix heatmap view). e The number of MRL values
in the ‘‘Kiwifruit’’ classification that are stricter, identical, looser and unique in each region compared to China (Comparative
statistics of MRL values view). f List of MRLs that are ‘‘Stricter’’ in ‘‘EU’’ compared to ‘‘CN’’ (Comparative details of MRL
values view)
7.1 Case 1: comparison of food classification for multiple regions and validation of MRL value
inheritance
As shown in Fig. 5a5, three experts selected the pesticide ‘‘Permethrin’’ and hovers mouse over the food
‘‘Kiwifruit,’’ in the hover message box, the expert E1 learned that the path of the node ‘‘Kiwifruit’’ node in
the UniMRLtree is: ‘‘Food’’—‘‘Fruits’’—‘‘Berries and other small fruits’’—‘‘Small climbers’’—‘‘Skins not
edible Small climbers’’—‘‘Kiwifruit.’’ The expert E2 found that the CAC does not have this food through
the UniMRLtree for multiple regions view, and comparatively analyzes the differences in the paths of food
classification for ‘‘Kiwifruit’’ in the other five regions, as shown in Fig. 5b. The experts stated: ‘‘The food
has a more similar hierarchy in the JP and AU regions.’’
Then the experts explored the correctness of MRL value inheritance. The E1 saw that ‘‘Kiwifruit’’ has an
MRL of 2 mg/kg for the pesticide ‘‘Permethrin’’ in China, and with our assistance, the experts queried the
Visual Comparison of Hierarchies with Inherited Attributes...
Fig. 6 a Rose graph of ‘‘Melon’’ and ‘‘Sweet pepper’’ are shown. b Mouse hovering over the node. c The petal graph of
‘‘Melon’’ and ‘‘Sweet pepper’’ are shown
original data and learned that ‘‘Kiwifruit’’ does not have a defined MRL for ‘‘Permethrin’’ in China, so it
was determined that the MRL was derived by inheriting the MRL from the ancestor node.
In order to determine the source of inheritance of this MRL value, the E2 looked at the UniMRLtree for
multiple regions view and found that the upper level food classification in China for the food ‘‘Kiwifruit’’
was ‘‘Skins not edible Small climbers’’ and that there was no MRL value defined in the standard for the
pesticide ‘‘Permethrin’’ for this food. In the UniMRLtree for multiple regions view, he found that the
previous food classification of the food ‘‘Kiwifruit’’ in China is ‘‘Skins not edible Small climbers,’’ and there
is no MRL value for the pesticide ‘‘Permethrin’’ in the standard for this food. He then found that the upper
level of classification of the food ‘‘Skins not edible Small climbers’’ was ‘‘Small climbers,’’ and through
checking the original data, he found that there was no MRL value defined in the standard of the pesticide
‘‘Permethrin’’ for this food either. He also found that the upper level of classification for the food ‘‘Small
climbers’’ is ‘‘Berries and other small fruits,’’ and found that the MRL for the pesticide ‘‘Permethrin’’ was
2 mg/kg in the original data. This suggests that the MRL for ‘‘Permethrin’’ in China for ‘‘Kiwifruit’’ was
inherited from the MRL for ‘‘Berries and other small fruits’’.
Then he found a node ‘‘Strawberry’’ under the classification ‘‘Berries and other small fruits’’ that has an
MRL definition in China, and he wanted to verify that food products with special definitions would not be
covered by the MRL values of the parent classification. He checked the UniMRLtree for multiple regions
view and found that the MRL limit for ‘‘Strawberry’’ in China is 1 mg/kg, which verified the correctness of
the attribute inheritance. The experts E1-E3 pointed: ‘‘It is very important that the MRL attribute inheritance
is correct, which is the basis for MRL comparative analysis.’’
7.2 Case2: comparison of MRL values among multiple regions
Three experts selected the pesticide ‘‘Methomyl’’ on the control panel, and the UniMRLtree for multiple
regions view displayed the MRL values of the pesticide ‘‘Methomyl’’ for fruits and vegetables in various
regions. By zooming out the view with the mouse wheel, the experts saw the complete UniMRLtree as
shown in Fig. 1a, which presented a macroscopic overview of the MRL values for this pesticide across
different regions. The experts observed numerous red and blue nodes, indicating that CN and US had a
larger number of foods with MRL values for ‘‘Methomyl.’’ Additionally, the areas of US food nodes were
generally larger than those of CN, suggesting that the MRL standards for ‘‘Methomyl’’ were more lenient for
US foods. This compared the MRL values of multiple regions at the macro-level from a pesticide perspective. Then, the experts searched for the food ‘‘Peach,’’ and the UniMRLtree for multiple regions view
automatically located the ‘‘Peach’’ node. Three experts all found that the rose graph on the ‘‘Peach’’ node
has six areas of sectors, indicating that there is ‘‘Methomyl’’ in six regions, as shown in Fig. 1a1. The
experts hovered over the node ‘‘Peach’’ and found that the MRL value for the US is the largest and that for
the EU is the smallest. This compared the MRL values of multiple regions at the macro-level from a
pesticide perspective.
Then the expert E3 observed two neighboring nodes ‘‘Melon’’ and ‘‘Sweet pepper.’’ He found that the
area of red and blue colors in ‘‘Sweet pepper’’ is significantly larger than that in ‘‘Melon,’’ as shown in
Fig. 6a, and asked us whether this is the MRL value. In fact, the MRL values for both regions are 0.2 mg/kg.
K. Lu et al.
We explained to him that ‘‘this is due to the rose graphing algorithm, rose graph can visualize the magnitude
of pesticide values in different regions in the same food node, but cannot be applied to compare the pesticide
limits in each region in two different food nodes; whereas, petal graph can be applied in this case as shown
in Fig. 6c.’’
Next, the expert E3 clicked on the root node in the UniMRLtree, and the MRL values matrix heatmap
view displayed the distribution of MRL values for the pesticide ‘‘Methomyl’’ across various fruits and
vegetables in different regions. He observed that the MRL values for various foods in CN were relatively
small, those in JP and AU were relatively large, and the MRL values for some foods in the US were higher
than those in the other five regions, as shown in Fig. 1d. This compared the MRL values of multiple regions
at the macro-level from a food perspective.
To further analyze from a microscopic perspective, he clicked on the lower-level node ‘‘Leafy vegetables’’ in the UniMRLtree. The MRL values matrix heatmap view was updated accordingly, as shown in
Fig. 1d1. By hovering the mouse over these squares, he viewed the names of these foods and details of their
MRL values, as illustrated in Fig. 1d2. This compared the MRL values of multiple regions at the micro-level
from a food perspective.
7.3 Case3: statistical analysis of MRLs in multiple regions
As shown in Fig. 1, the experts searched for the pesticide ‘‘Methomyl’’ in the control panel. Figure 1c
presents the number of foods with MRLs for ‘‘Methomyl’’ in six regions, and found that CN has the highest
number of MRLs for ‘‘Methomyl’’ among the six regions, followed by the US. At the same time, he
considered that the analysis of differences in MRL values in a food was very important in international trade
and food regulation. He clicked on the ‘‘Peach’’ node in the UniMRLtree for multiple regions view, and the
Comparative statistics of MRL values view showed a macro-overview of the differences in MRL values by
region for ‘‘Peach.’’ He found that the EU has the highest number of MRLs for ‘‘Peach’’ of all the regions,
and he was particularly concerned about the differences in food MRL values between other regions and
China, and clicked on the more stringent areas in the stacked bar chart of the EU, generating a Comparative
details of MRL values view. This detailed shows the MRL values for these 68 pesticides in China and the
EU. He said that when China exports ‘‘Peach’’ to the EU, it needs to focus on the MRL values of pesticides
that are unique to the EU and the MRL values of these 68 pesticides in the EU, this can be found in Fig. 1f.
7.4 Expert interview
We conducted in-depth interviews by inviting three additional experts (E4-E6), who correspond to E1-E3 in
their each expertise, to gather their feedback based on case study explorations.
First, all three experts highly praised the interface design and interactive experience of MRLvis. When
discussing the UniMRLtree for multiple regions view, E4 commented: ‘‘We currently use explicit structures
visualized as two juxtaposition trees for comparisons; while, visual analytics systems for three or more trees
are still relatively rare.’’ He inquired whether the system can support the comparison of more than six
regions, to which we affirmed that it can. The system has potential scalability, it only requires merging data
from other regions into UniMRLtree according to the HIAC method we provided. He agreed with this but
also concerned that if the system’s target users are currently limited to the field of pesticide residues. He
suggested that if an interface could be provided for users to upload their own hierarchical data, the system
could automatically generate a view of the merging tree, thus catering to a broader field. Additionally, he
noted that differences in the hierarchical structure of multiple regions’ food classifications can currently only
be observed manually, which needs improvement. E5 stated: ‘‘Embedding a rose graph on UniMRLtree
allows for the visual comparison of pesticide limits between different regions on a single node, but not
between different nodes. The introduction of petal graph solves this problem perfectly, and I think the
functionality of switching freely between petal graph and rose graph, as designed in MRLvis, is excellent.’’
While, E6 remarked that the MRLvis views interact well with each other, but he would like the Comparative
details of MRL values view to have an export functionality.
Visual Comparison of Hierarchies with Inherited Attributes...
8 Conclusion and future work
In this paper, we present HIAC, a visualization-based method for comparing inherited attribute values across
multiple hierarchies, using the example of multi-regional MRL standards. HIAC fully accounts for the
relationship of inherited attribute values within complex hierarchical structures and offers entire pipeline
from visual modeling to visual analytics system for enabling comprehensive comparisons across thousands
of nodes within multiple MRL standards. Through validation with case study and expert interview, we have
demonstrated not only the effectiveness of HIAC in comparing inherited attribute values across multiple
hierarchies but also its scalability and potential for broader applications. This paper introduces an innovative
comparison method in the field of food safety, breaking through the limitations of traditional approaches and
providing a valuable reference for comparing inherited attribute values across hierarchical structures.
Despite its strengths, the current version of HIAC does not yet provide a quantitative measure of the
differences between hierarchies with inherited attribute values. In future work, we plan to explore a graph
neural network-based approach to quantify the similarity between multiple hierarchies with inherited
attributes. We anticipate that this direction of research will further enhance the understanding and application of multi-hierarchical structure comparisons, opening up new possibilities for in-depth analysis and
practical implementation.
Author contributions Kangqi Lu was involved in conceptualization, formal analysis, methodology, data curation, visualization,
programming, original draft, and writing—reviewing editing. Yi Chen was responsible for conceptualization, formal analysis,
methodology, project administration, resources, validation, supervision, writing—reviewing and editing, and funding acquisition.
Zhiying Luo contributed to conceptualization, methodology, data curation, visualization, and writing—original draft. Yu Dong
took part in visualization, formal analysis, and writing—reviewing and editing. Cheng Lv participated in supervision and
writing—reviewing and editing.
Funding This work was supported by the National Key Research and Development Program of China (Grant
No.2022YFF1100905) and the National Natural Science Foundation of China (NSFC) under Grant No.U23B2009.
Data availability Not applicable.
Declarations
Conflict of interest The authors have no Conflict of interest to declare that are relevant to the content of this article.
Consent for publication Yes.
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