=Paper=
{{Paper
|id=Vol-2578/BigVis8
|storemode=property
|title=Web-based Scalable Visual Exploration of Large
Multidimensional Data Using Human-in-the-Loop Edge Bundling in Parallel
Coordinates
|pdfUrl=https://ceur-ws.org/Vol-2578/BigVis8.pdf
|volume=Vol-2578
|authors=Wenqiang Cui,Girts Strazdins,Hao Wang
|dblpUrl=https://dblp.org/rec/conf/edbt/CuiSW20
}}
==Web-based Scalable Visual Exploration of Large
Multidimensional Data Using Human-in-the-Loop Edge Bundling in Parallel
Coordinates==
https://ceur-ws.org/Vol-2578/BigVis8.pdf
Web-based Scalable Visual Exploration of Large
Multidimensional Data Using Human-in-the-Loop Edge
Bundling in Parallel Coordinates
Wenqiang Cui Girts Strazdins Hao Wang
Department of ICT and Natural Department of ICT and Natural Department of Computer Science
Sciences Sciences Norwegian University of Science
Norwegian University of Science Norwegian University of Science and Technology
and Technology and Technology Norway
Norway Norway hawa@ntnu.no
wenqiang.cui@ntnu.no gist@ntnu.no
ABSTRACT data items are mapped to lines (or edges) intersecting the axes at
Visual clutter and overplotting are the main challenges for vi- their respective values. The embedding of an arbitrary number of
sualizing large multidimensional data in parallel coordinates, parallel axes into the plane allows for the simultaneous display of
which greatly hampers the recognition of patterns in the data. many dimensions to provide a good overview of the data, which
Although many automatic clustering and edge-bundling methods reveals intrinsic patterns and trends. However, when datasets are
have been used in parallel coordinates to reduce visual clutter and large, PCPs create visual clutter and overplotting in which lines
overplotting, a scalable, transparent, and interactive approach are crossed and plotted on top of one another, overwhelming
that allows analysts to interact with large data and generate the display, and obscuring the underlying patterns. This hides
interpretable results of visualization in real time is lacking. To information and hampers the recognition of patterns in the data.
solve this problem, we propose an approach, human-in-the-loop Edge bundling [7] and automatic data clustering [10] are two
edge bundling, to visually explore and interpret large multidimen- widely used approaches to reduce visual clutter and overplotting
sional data in parallel coordinates. This approach combines data in PCPs. Edge bundling bends similar lines to the center of vi-
binning-based clustering and density-based confluent drawing, sual clutters in groups to create more informative visualizations.
which reduces much data processing time and rendering time. It Automatic data clustering aggregates data points in groups that
provides novel interactions, such as splitting, adjusting, and merg- can be visualized in an illustrative fashion using different forms
ing clusters, to integrate human judgment into the edge-bundling of edge bundling.
process. These interactions make the underlying clustering trans- However, when datasets become large, these methods face
parent to users, which allow users to generate interpretable visu- challenges in supporting real-time interactions (limiting the vi-
alization without complex data clustering. The scalability of our sual response in a few milliseconds) along with mechanisms for
approach was evaluated through experiments on several large information abstraction. Without interactions, these automatic
datasets. The results show that our approach is scalable for large methods provide only groups that may contain interesting com-
multidimensional data, which supports real-time interactions binations of dimensions and data points, but do not give analysts
on millions of data items in web browsers without hardware- control over the data clustering and visualization processes, and
accelerated rendering and big data infrastructure-based data pro- do not offer opportunities for analysts to take advantage of their
cessing. We used a case study to highlight the effectiveness of judgments and expertise.
our approach. The results show that our approach provides an In this study, we propose a web-based visual analytics sys-
interpretable way of visually exploring large multidimensional tem that uses data binning-based clustering and density-based
data in parallel coordinates. confluent drawing to create a new edge-bundling paradigm in
PCPs for large multidimensional data. To the best of our knowl-
KEYWORDS edge, this is the first web-based system that supports the HITL
(human-in-the-loop) edge-bundling process in PCPs through
interactive visualization, human-in-the-loop, visual exploration,
specific interactions, such as splitting, adjusting, and merging
multidimensional data, big data, parallel coordinates
clusters of each dimension, for large multidimensional data. The
contribution of this study are as follows:
1 INTRODUCTION
A multidimensional dataset contains numerical or categorical • New paradigm for edge bundling in PCP. Our approach
dimensions (or features), with n (n > 3) dimensions and m data provides a novel edge-bundling paradigm (HITL edge
items. To avoid confusion, in this paper, a data item is an n- bundling) for the visual exploration of large multidimen-
dimensional point, and a data point is the projection of a data sional data in PCPs. With the real-time interactions, such
item to a particular dimension. Parallel coordinate plots (PCPs) as splitting, adjusting, and merging clusters, it enables
are widely used, and have become a standard tool for visualizing analysts to integrate their judgments and expertise into
multidimensional data [6]. In PCPs, axes corresponding to the the data clustering and edge-bundling processes of large
number of dimensions are aligned parallel to each other, and multidimensional data.
• Fast, scalable, and transparent edge-bundling algo-
Copyright © 2020 for this paper by its author(s). Published in the Workshop Proceed-
ings of the EDBT/ICDT 2020 Joint Conference (March 30-April 2, 2020, Copenhagen, rithm. To support the real-time interactions of large data
Denmark) on CEUR-WS.org. Use permitted under Creative Commons License At- in PCPs, we propose a fast, scalable, and transparent edge-
tribution 4.0 International (CC BY 4.0)
bundling algorithm that consists of two parts: 1) a data
EDBT 2020, March 30-April 2, 2020, Copenhagen, Denmark Wenqiang Cui, Girts Strazdins, and Hao Wang
binning-based clustering method, and 2) density-based context visualization in PCPs to represent outliers [9]. In this
confluent drawing. study, we use one-dimensional (1D) binning to cluster data points
• A web-based visual analytics system. We build a web- for each dimension with the following three considerations:
based visual analytics system to support HITL edge bundling • In PCPs, for a single dimension, the clusters must be or-
in PCPs for large multidimensional data. dered because the data points are ordered.
• Experiments, and a case study. We conducted experi- • A data point belongs to only one cluster.
ments and a case study on several datasets to highlight • For large data, to support HITL edge bundling in PCPs, the
the benefits of HITL edge bundling in PCPs for large mul- clustering process must be fast, scalable, and transparent
tidimensional data. to analysts.
The remainder of this paper is organized as follows: Section 2 With the first and second considerations, for each axis, the data
presents the proposed approach. Section 3 reports the experi- points are binned into ordered and adjacent clusters, which is
ments, a case study, and discusses the result. Section 4 draws shown in Figure 3. Since a data point belongs to only one cluster,
the conclusions of this study and discusses directions for future there is no overlaps between clusters. This reduces the overplot-
work. ting of clusters in PCPs created by multidimensional clustering
methods, such as DBSCAN [5]. As shown in Figure 3, for each
2 SYSTEM AND METHODS axis, the data points are first grouped into the same number of
In this section, we first describe the HITL edge-bundling process clusters. For a particular axis, the initial clusters have the same
with our system. Then, we introduce the methods used in the initial diameters. Users then use the control points to split, adjust,
system and the novel interactions provided by the system. and merge clusters (see Section 2.4), which makes the clustering
process transparent for analysts. For an axis with k initial clusters
2.1 System Overview (the initial value of k is configured by users), the initial diameter
Figure 1 shows the overview of our system. The system first L is computed as:
visualizes multidimensional data in a classic PCP without edge L = (dmax − dmin )/k
bundling. For example, in Figure 1 (A), the Cars dataset [1] is
visualized in a classic PCP without edge bundling. The system where dmax and dmin are the maxima and minima, respectively,
then bundles the edges according to the initial clusters for each of the data points on the corresponding axis. For an axis, the
dimension as shown in Figure 1 (B). The system supports HITL initial control points Pi denotes the boundaries of clusters, which
edge bundling by allowing analysts to split, adjust, and merge are computed as:
clusters for each dimension, which is shown in Figure 1 (C). Pi = dmin + i × L, i = 1, 2, ..., k − 1
During the HITL edge-bundling process, the system can update
the visualization according to the corresponding interactions Then, a data point d is grouped into a cluster Ci as:
in real time for large multidimensional data. This makes the
(
Pi−1 < d < Pi , i = 1, 2, ..., k − 1
underlying clustering process transparent to analysts. With the d ∈ Ci if
d > Pi−1, i = k
interactions, analysts can integrate their judgments and expertise
into the edge-bundling process to generate visualizations that To reveal the internal patterns and distribution of data, we com-
can be better interpreted. For example, in Figure 1 (C), by creating pute the density of each pair of clusters and use it for density-
an empty cluster that ranges from 6 to 8 and a cluster with 0 based confluent drawing (see Section 2.3). For two adjacent axes
diameter (ranges from 8 to 8) at 8 on the axis cylinders, we found axisn and axisn+1 , a cluster pair (Caxis
i j
, Caxisn+1 ) consists of a
n
that all cars with eight cylinders in the dataset weighted between cluster in axisn and another in axisn+1 , where Caxis
i is the i-th
3354 and 5140 kilograms. Moreover, by highlighting the subsets j
n
that contains cars with eight cylinders in red, the patterns of cluster in axisn , and Caxisn+1 is the j-th cluster in axisn+1 . For
other features of these cars are clearly highlighted. two adjacent axes, an edge containing two data points (dn , dn+1 )
The rudiment of our system is the combination of data binning- that belongs to a pair of clusters is defined as:
based data clustering and density-based confluent drawing, which i
(dn , dn+1 ) ∈ (Caxis
j i
, Caxisn+1 ) if dn ∈ Caxis
j
∧dn+1 ∈ Caxisn+1
supports the real-time interactions for large multidimensional n n
data without hardware-accelerated rendering and big data infrast- The density D i,j of a pair of clusters is computed as:
ructure-based data processing. Figure 2 shows the workflow of j
i
N (Caxis , Caxisn+1 )
our system, where the HITL process is highlighted in the dashed D i,j = Í n
, n = 1, 2, ...
j j
line rectangle. The system first uses data binning to cluster data i
i=1 j=1 N (C axis n , C axis n+1 )
i
Í
points for each dimension with the default settings. Then the
j
density of each pair of clusters on two adjacent axes is computed, where N (Caxis
i
n
, Caxisn+1 ) is the number of edges that belong to
and the edges are bundled and rendered through density-based the cluster pair (Caxis
i j
, Caxisn ).
confluent drawing. Finally, users create a more interpretable vi-
n
The clustering process, including computing the clusters and
sualization of edge bundling through the interactions, including the density of cluster pairs, is linearly dependent on the number
splitting, adjusting, and merging clusters. of dimensions, the number of data points, and the number of
clusters (see Section 3.1). This fast and scalable clustering process
2.2 Data Binning-Based Clustering is the basis of real-time interactions (see Section 2.4), which
Data binning groups a number of more or less continuous values supports HITL edge bundling for large multidimensional data in
into a smaller number of given data intervals (also called "bins") to PCPs.
transform numerical variables into their categorical counterparts Categorical variables are not clustered using the above method.
[12]. Multidimensional binning is used to implement focus + Instead, we treat each category as a cluster.
Web-based Scalable Visual Exploration of Large Multidimensional Data Using Human-in-the-Loop Edge Bundling in Parallel
Coordinates EDBT 2020, March 30-April 2, 2020, Copenhagen, Denmark
47 5140 8 25 455 230 47 5140 8 25 455 230
A
221
C 4577 22
405
212
199
7
37 4258 7 21 358 184 187
37 355
4014 19 331
6 308
3684
145
28 3377 6 16 262 138 3354 5.5
27
5 15
4.5 188 104
18 2495 4 12 165 92 18 2484
4
75
3.5 10
9
9 1613 3 8 68 46 9 1613 3 8 68 46
mpg weight cylinders acceleration displacement horsepower mpg weight cylinders acceleration displacement horsepower
47 5140 8 25 455 230
B
40 4552 7.2 22 391 199
Initial Edge Bundling 34 3964 6.3 19 326 169
Human-in-the-loop Edge Bundling Process
28 3376 5.5 16 262 138
22 2789 4.6 14 197 107
15 2201 3.8 11 133 77
9 1613 3 8 68 46
mpg weight cylinders acceleration displacement horsepower
Figure 1: Overview of the system that supports HITL edge bundling in PCPs. A. Visualization of the Cars dataset [1] in a classic
PCP. B. Edge bundling of the dataset with 3 initial clusters for each dimension. C. Interpretable edge bundling of the dataset with a
subset highlighted (continuous path over axes) in red, which is generated through user interactions.
Human in the Loop Edge bundling
Cluster
Control Point
Interpretable Visualization
Human Judgment
& Expertise
Data Interactions
Data Point
Rendering Diameter
Clustering Confluent Drawing
Figure 2: The workflow of the system.
Figure 3: Using 1D binning to cluster data points for each
2.3 Density-based Confluent Drawing axis in PCPs. The blue points are data points and the red points
Confluent drawing is a technique for bundling links in node- are control points. An edge between the axes represents two data
link diagrams. It coalesces groups of lines into common paths points that belong to two clusters respectively. Elliptical areas
or bundles based on network connectivity to reduce edge clut- represent clusters in an axis. The initial k is 2. For each axis, the
ter in node-link diagrams [2, 4]. In this study, we use confluent two initial clusters have the same diameter. The two red clusters
drawing to coalesce edges that belong to a pair of clusters to form a pair of clusters. Its density is 0.4.
reduce visual clutter in PCPs, where we use the clusters as nodes
and edges between them as links. Each pair of clusters then has
only one bundled edge, which is shown in Figure 4. This elimi-
nates the occlusion and ambiguity near the bundle joints created
by bundling techniques that bundle edges by spatial proximity. where Wmax is the width of a bundle with the density of one.
More importantly, it reduces rendering time by coalescing edges, Wmax is a constant and is configured by users.
which supports real-time interactions for HITL edge bundling of To guarantee C 1 -continuity across axes, we draw bundles as
large multidimensional data in PCPs. Bézier curves. Figure 4 shows the bundled edge of a pair of clus-
To reveal the information hidden by coalescing of the edges ters. Between two adjacent axes, the width of a bundle represents
and the distribution of the data points between axes, we use the the proportion of the data points (coalesced edges) that belong to
j
density D i,j of a pair of clusters (Cax
i
is n , C ax is n+1 ) to define the the corresponding cluster pair. This reveals the trend and distribu-
width Wi,j of the coalesced bundle as follow: tion of the data items as well as outliers in large multidimensional
Wi,j = D i,j × Wmax data in PCPs (see Section 3.2).
EDBT 2020, March 30-April 2, 2020, Copenhagen, Denmark Wenqiang Cui, Girts Strazdins, and Hao Wang
Cluster Center two new clusters. In Figure 5, the red dashed line circle on
Axis A is a newly added control point by double-clicking.
• Adjust clusters. All control points can be dragged along
Cluster Control Point the axes. Dragging a control point to a new position ad-
justs the boundaries and the diameters of the two adjacent
clusters. Figure 5 shows dragging the control point on Axis
B to a new position (red dashed line circle on Axis B).
Bé
zie
• Merge clusters. All control points can be double-clicked
rC
ur
to be deleted. The two adjacent clusters of the deleted
ve
Width control point are merged into a new cluster.
• Highlight bundles over axes. Hovering the pointer over
a bundle highlights it and its related bundles in red. Only
bundles with a density greater than a threshold will be
Figure 4: Using the density-based confluent drawing to highlighted. The threshold is a constant and is configured
bundle the edges that belong to a pair of clusters. For a by users.
pair of clusters, the bundled edge is rendered as a Bézier curve • Re-order axes. The labels of axes can be dragged to the
that starts from the center of a cluster and ends at the center of front or back of other labels to re-order them to the corre-
another. Its width represents the density of the cluster pair. sponding positions.
3 EVALUATION
In this section, we evaluate the scalability and the effectiveness
Bundle of our system through experiments and a case study on the Office
Mouseover
Axis Area Occupancy Detection dataset [3] and the Cars dataset [1].
Double Click
3.1 Experiments
Control Point To examine the scalability of our system, we synthesized several
Double Click & Drag large datasets based on the office dataset. All experiments were
conducted on the same laptop without big data infrastructure-
based data processing and hardware-accelerated rendering.
In our system, the HITL edge-bundling process contains two
time-consuming processes: the data binning-based clustering and
Label Area
Drag the density-based confluent drawing (rendering process). We first
performed a run time analysis of the clustering process. Table
Axis A Axis B Axis A 1 shows the run times (measured by the second) of the cluster-
ing process on large multidimensional datasets (with different
number of dimensions, data points, and clusters). According to
Figure 5: Interactions provided by our system for support- Table 1, the computation time of data binning-based clustering is
ing HITL edge bundling. Double click on the axis area to add linearly dependent on the number of dimensions, the number of
a control point to split a cluster. Double click on a control point data points, and the number of clusters. More importantly, this
to delete it to merge two clusters. Drag a control point along an data binning-based clustering is much faster than other cluster-
axis to adjust the adjacent clusters. Mouseover on a bundle to ing algorithms used for bundling edges in PCPs. For example,
highlight a subset with color. Drag an axis label to re-order the Palmas et al. [10] used a density-based clustering method for
axes. each dimension independently to bundle edges in PCPs, which
takes approximately 60 seconds to cluster 105 data points for
one dimension. By contrast, our clustering method takes approx-
2.4 Interactions for HITL Edge Bundling imately 1 seconds to cluster 106 data points for four dimensions.
In our system, in addition to common interactions in PCPs such
as re-ordering the axes and brushing (highlighting) [11], we use We then examined the efficiency of the rendering process by
specifically designed interactions to allow users to split, adjust, comparing the rendering time of our method with both the clas-
and merge clusters. Our system updates the visualization ac- sic PCP and Lima et al.’s edge-bundling PCP [5] that also uses
cording to user interactions in real time, which is the key to confluent drawing to coalesce edges. To compare the rendering
implement the HITL edge bundling process. These interactions time, all three PCPs were implemented with the same JavaScript
are supported by the combination of the data binning-based clus- library (D3.js) and rendered in Chrome. The times needed for
tering and the density-based confluent drawing. Figure 5 shows rendering the axes, labels, and stickers were not included, which
the interactions provided by our system, which are described as are constant regardless of the number of data points. Table 2
follows: shows the rendering time of the three methods (measured by the
• Split a cluster. Each axis has a clickable area (called axis second) on the datasets that has six dimensions and the different
area) around it, which is shown as gray rectangle area numbers of data items. For our method and [5], each dimension
around Axis A in Figure 5. Double-clicking on this area has 3 clusters. According to Table 2, the classic PCP and [5] take
adds a new control point to the corresponding position on 1.7672 and 3.6989 seconds to visualize 105 data points. The clas-
the axis. This control point splits the original cluster into sic PCP takes 8.7183 seconds to visualize 5 × 105 data points
Web-based Scalable Visual Exploration of Large Multidimensional Data Using Human-in-the-Loop Edge Bundling in Parallel
Coordinates EDBT 2020, March 30-April 2, 2020, Copenhagen, Denmark
Table 1: Run-time analysis of the data binning-based clus-
40 2077 24 1697 Occupied
tering
Dimensions Data Points Clusters Run-time 34 1661 23 1273
2 104 3 0.0169
2 104 4 0.0167 28 1245 22 849
3 104 3 0.0230
3 104 4 0.0277
2 105 3 0.0505 22 829 20 424
2 105 4 0.0554
3 105 3 0.0937 17 413 19 0 Not occupied
3 105 4 0.0996 humidity CO2 temperature light occupancy
4 105 3 0.1175 (a)
4 105 4 0.1404
4 105 10 0.2574 40 2077 24 1697
4 105 20 0.4139 37 1869 24 1485
4 105 30 0.5495 34 1661 23 1273 Occupied
4 105 40 0.6892
4 105 50 0.8872 31 1453 22 1061
4 106 3 0.8211 28 1245 22 849
4 106 4 0.9398 25 1037 21 636
22 829 20 424 Not occupied
Table 2: Comparison of the rendering time 20 621 20 212
17 413 19 0
humidity CO2 temperature light occupancy
Data Points Our Method Classic PCP [5]
(b)
103 0.00243 0.0273 0.0503
104 0.00231 0.1916 0.3740 40 2077 24 1697
105 0.00230 1.7672 3.6989
37
5 × 105 0.00229 8.7183 N/A 1843
1414
106
23
0.00248 N/A N/A 34
33
1609
Occupied
1131
31 1459
29 22
1308
and crashes the browser when visualizing 106 data points. The
27
743
1110
method [5] crashes the browser when visualizing 5 × 105 data 912
21
points. By contrast, the rendering process of our method is inde- 22
354
Not occupied
pendent of the number of data points, which takes approximately 662
177
0.002 seconds for each dataset. 17 413 19 0
humidity CO2 temperature light occupancy
3.2 Case Study (c)
To assess the effectiveness of our system, we compared our
method with the classic PCP and several algorithmic analysis Figure 6: The visualization of the office dataset in the clas-
methods with the office dataset. The office dataset uses the data sic PCP and our system. (a) Visualization of the office dataset
on temperature, humidity, light, and CO2 to detect the occupancy in the classic PCP. (b) Visualization of the office dataset in our
of an office room. It has five dimensions and 20,560 data points system with 4 initial clusters for each dimension. (c) Visualiza-
for each dimension. tion of the office dataset in our system generated by a user who
Figure 6 shows the visualization of the office dataset in the does not have knowledge of the dataset.
classic PCP and our system. Figure 6c shows the visualization
in our system, which is generated by a user who does not have
knowledge of the dataset. In Figure 6b and Figure 6c, the red Moreover, by integrating human judgments into the edge-
bundles are the subsets highlighted by hovering the pointer on bundling process, our method creates a interpretable visualization
the widest bundle between the axes of light and occupancy. The in PCPs for the office dataset. For example, during the HITL edge-
extreme narrow bundles (data points with extreme low densi- bundling process (from Figure 6b to Figure 6c), the user obtained
ties) are visualized as the dashed lines to detect and highlight the following findings:
the outliers (rare data points that raise suspicions by differing • Finding 1. The dataset contains outliers which are high-
significantly from the majority of the data [8]) in the dataset. By lighted by the dashed lines in Figure 6c.
comparing Figure 6a and and Figure 6c, it is clear that for large • Finding 2. When the value of light is smaller than 354
multidimensional datasets, our method reduces the visual clutter Lux, the room is considered unoccupied. When it is be-
and overplotting in the classic PCP and reveals the patterns in tween 354 and 1131 Lux, the room is considered occupied.
the data. The accuracy of this estimation is higher than 90% (the
EDBT 2020, March 30-April 2, 2020, Copenhagen, Denmark Wenqiang Cui, Girts Strazdins, and Hao Wang
Table 3: The comparison our system with the algorithmic this process, users can continuously gain insights from data and
methods in [3]. visualization.
Criteria Our Method [3] 4 CONCLUSION AND FUTURE WORK
Finding 1 Yes No In this study, we proposed HITL edge bundling and built a system
Finding 2 Yes Yes based on it to support the visual exploration of large multidi-
Finding 3 Yes Yes mensional data in PCPs. The system provides an interpretable
Finding 4 Yes Yes visualization, which reduces the visual clutters and overplotting,
Interpretability Interpretable Black-box process and eliminates the occlusion and ambiguity of large multidimen-
visualization of training the mod- sional data in PCPs. More importantly, the system provides the
with transparent els. specifically designed interactions, including splitting, adjusting,
clustering process. and merging clusters, to integrate human judgments into the
Processing time Real-time. Time for training edge-bundling process in real time. We evaluated the scalability
and selecting mod- and effectiveness of the system through experiments and a case
els. study. We compared our system with the classic PCP and the
algorithmic analysis methods. The results show that our system
provides a scalable and interpretable way of visually exploring
large multidimensional data in PCPs.
estimated sum of the densities of the two widest bundles Anchoring bundled edges in different positions, such as the
between the axes of light and the occupancy). mean/centroid position of all data points in a cluster, could be
• Finding 3. When the temperature is between 19 and 22 ℃, investigated in the future to improve the continuity across axes
the room is considered unoccupied. When the temperature and reveal more information of clusters. This requires more com-
is higher than 22 ℃, the room is considered occupied. putation and may delay the visual response of the interactions.
The accuracy of this estimation is higher than 80% (the The interactions and color effects (highlighting subsets in dif-
estimated sum of the densities of the two widest bundles ferent colors) of the system are not fully evaluated. This can be
between the axes of temperature and light). done in a qualitative user study in future work.
• Finding 4. Using all features may reduce the accuracy of
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of data. This process may take 1 or 2 minutes. However, during