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Clutter-Reduction Technique of Parallel Coordinates Plot
for Photovoltaic Solar Data
Abstract. Solar energy supplies pure environmental-friendly and limitless
energy resource for human. Although the cost of solar panels has declined
rapidly, technology gaps still exist for achieving cost-effective scalable
deployment combined with storage technologies to provide reliable,
dispatchable energy. However, it is difficult to analyze a solar data, in which
data was added in every 10 minutes by the sensors in a short time. These data
can be analyzed easier and faster with the help of data visualization. One of the
popular data visualization methods for displaying massive quantity of data is
parallel coordinates plot (PCP). The problem when using this method is this
abundance of data can cause the polylines to overlap on each other and clutter
the visualization. Thus, it is difficult to comprehend the relationship that exists
between the parameters of solar data such as power rate produced by solar
panel, duration of daylight in a day, and surrounding temperature. Furthermore,
the density of overlapped data also cannot be determined. The solution is to
implement clutter-reduction technique to parallel coordinate plot. Even though
there are various clutter-reduction techniques available for visualization, they
are not suitable for every situation of visualization. Thus this research studies a
wide range of clutter-reduction techniques that has been implemented in
visualization, identifies the common features available in clutter-reduction
technique, produces a conceptual framework of clutter-reduction technique as
well as implements one of the techniques at solar energy data visualization.
Keywords: Conceptual Framework, Clutter-reduction Technique, Parallel
Coordinates, Solar Energy, Visualization
1 Introduction
Solar energy is an environmental-friendly energy generated from light. This type of
energy is generated by two different technologies namely photovoltaic (PV) and
concentrated solar power (CSP). For continuous research in the area of solar energy,
data on solar environment has been collected from various types of sensors. These
data are continuously streaming into database every 10 minutes [1], thus ended up
with huge amount of data. The huge amount of data is necessary for producing high
quality of analysis result. During analysis, data are plotted via visualization method to
assist researchers in extracting knowledge hidden behind these data.
One of visualization techniques that is used to visualize solar energy dataset is
parallel coordinates plot. This is due to the fact that parallel coordinates plot is
suitable for visualizing not only huge dataset but also streaming data which
continuously added into the database. Moreover, parallel coordinates plot is a
visualization method for multivariate data which can be used to analyze the many
properties of a multivariate dataset. This visualization method consists of polyline
which describes multivariate items that intersects with parallel axes that represent
variables of data. Parallel coordinates plot is one of the popular visualization
technique for huge dataset. This is because relationships among data can been viewed
in a single graph [2].
However, the relationship and frequency of data polylines at particular spot are
difficult to extract due to huge data. They cause the polylines to overlap on each other
thus, clutter the visualization. A high amount of overlapping lines will hinder the
analysis process such as extracting meaningful pattern [3][4]. In such a case,
relationships between parameters of solar energy cannot be seen visually. Not only
data relationship, data density around the highly overlapped polylines areas also could
not be identified. The solution to such issues is to implements clutter-reduction
techniques to the visualization.
Clutter-reduction technique can simplify the view of parallel coordinates plot.
Even though there are various clutter-reduction techniques available to help view
cluttered parallel coordinates plot, not all of them are suitable in every situation of
visualization. In order to choose the right technique, we need to understand each of
the features available in the clutter-reduction techniques of parallel coordinates plot.
Thus, this paper will review 10 of the parallel coordinates plot with clutter-
reduction techniques that have been published recently. The difference between these
techniques in term of features for enhancing the parallel coordinates plot method will
be identified. Finally, this research produce a conceptual framework for such
clustering techniques, so most suitable features of clutter-reduction techniques will be
implemented to solar data parallel coordinates plot visualization.
This paper is organized into a few topics, which are Introduction, Literature
Review, Method, and Conclusion. These topics will cover the studies of a wide range
of clutter-reduction techniques that has been implemented in visualization, it also
identifies the common features available in clutter-reduction technique, produces a
conceptual framework of clutter-reduction technique as well as implements one of the
techniques at solar energy data visualization.
2 Literature Review
This section will discuss the literature review of the following topics; Solar Energy,
Photovoltaic Energy, Data Visualization, Parallel Coordinates Plot as well as Clutter-
Reduction Technique for Parallel Coordinates Plot.
2.1 Solar Energy
Solar energy supplies a pure environmental-friendly and limitless energy resource for
human [5]. The energy in sunlight can be converted into electricity, heat, or fuel.
Although the costs of solar panels have declined rapidly, technology gaps still exist to
achieve cost-effective scalable deployment combined with storage technologies to
provide reliable energy [6]. This type of electricity source can be generated by two
different technologies namely photovoltaic (PV) and concentrated solar power (CSP).
This research will focus on PV technology, since the solar data collected for this
research is done by this system.
2.2 Photovoltaic (PV) technology
Photovoltaic (PV) technology does the conversion of energy from sun to electricity
without harming the environment [7]. Therefore, it is classified as green energy.
There are two main components of PV namely PC panel and PV inverter in the
process of energy conversion from sun to the public grid network. A PV panel
consists of a number of PV cells which directly convert light energy into electricity by
the photovoltaic effect. On the other hand, PV inverter is a power electronic
component to convert the power from PV panels to AC power and injecting into the
public grid.
The researchers are focusing on finding the efficient and effective method to
generate maximum electricity output from the solar panel. In order to do that,
performance of current solar generator system must be known. However, with the
huge amount of data frequently acquired from the sensor, it is hard to capture the
meaning behind these data. This can be solved with the help of data visualization.
2.3 Data Visualization
Data visualization can be defined as the use of computer-supported, interactive, visual
representation of data to boost cognition, or the extraction and use of knowledge [8].
Data visualization is a procedure to help represent the complex data in an effective
way. Large-scale data is often supported with graphic visualizations to help better
understand the data and results [9]. The visualization helps provide insights that
cannot be matched by traditional approaches [8].
There are many data visualization techniques has been developed to efficiently
reduce the mental workload and enlarge user’s perception of the data [10]. Different
visualization techniques should be selected depending on the objective. For example,
Parallel Coordinates Plot is suitable for visualized multidimensional information or
dataset.
2.4 Parallel Coordinates Plot (PCP)
Several visualization methods for multi-dimensional data have been proposed in
recent years such as scatterplot matrices (SPLOM), Multi-dimensional scaling (MDS)
and parallel coordinates plot [11]. Parallel coordinates plot has become a standard for
multidimensional data analysis and has been widely used for many researches [12].
This is because parallel coordinates plot is good for presenting overviews of the
overall data, raw data set, and for showing relationships among the dimensions. This
visualization method consists of polyline which describes multivariate items that
intersects with parallel axes that represent variables of data. The design of 2D parallel
axes allows the simultaneous display of multiple dimensions, and thus, high-
dimensional datasets are visualized in a single image [13]. Fig. 2 shows an example of
traditional parallel coordinates plot in color.
Fig. 2. Traditional Parallel Coordinates Plot [11].
Parallel coordinates plot is suitable for visualizing a huge set of data like solar
energy data, which are continuously added into the database frequently. However,
parallel coordinates plot has several issues when it is applied to large datasets, such as
line occlusion, line ambiguity, and hidden information [14]. The abundance of data
causes the polylines to overlap from each other and disrupt the visualization. Making
it arduous to extract data relationship and density from the parallel coordinates plot
[2]. Thus this cluttered data and their frequency need to be highlighted. The next
session will discuss about the clutter-reduction technique for parallel coordinates.
2.5 Clutter-Reduction Technique for Parallel Coordinates Plot
With huge amount of plotted data displayed together, excessive edge crossings make
the display visually cluttered and thus difficult to explore [15]. A clutter-reduction
technique is a solution to reduce the visual clutter in parallel coordinates. This
technique is a method that render a fewer polylines with the aim of better highlight
structures in the data. There are many ways to reduce visual clutter such as by using
variation of colors at polylines, allowing user interactions to manipulate the
visualization view, as well as implementing clutter-reduction based algorithm in
parallel coordinates.
Based on the study of clutter-reduction techniques in the Method section, there are
three types of clutter-reduction based algorithm, which are clustering, bundling and
axis reordering algorithm. Some of the clutter-reduction techniques implements more
than one of these algorithms.
Fig. 3. Parallel Coordinates Plot with clustering algorithm [16].
Clustering algorithm is a technique where polylines are curved to a point of cluster
group making them more distinguishable [14]. The Fig. 3 shows the visualization of
parallel coordinates after implementing clustering algorithm. These techniques can be
classified into four categories, which are partitioning methods, hierarchical methods,
density-based methods and grid based methods [17].
Fig. 4. Parallel Coordinates Plot with bundling algorithm [12].
Bundling techniques provide a visual simplification of a graph drawing or a set of
trail, by spatially grouping graph edges or trails. This algorithm converts the cluster
group of polylines into a stripe line. Thus, it simplifies the structure of visualization
and become easier to extract the meaning or understanding in term of assessing
relations that are encoded by the paths or polylines [18]. Fig. 4 shows the
visualization of parallel coordinates after implementing bundling algorithm.
The visual clutter also can be reduced by reordering the vertical axes. The axes of
the dimension in parallel coordinates plot can be positioned in accordance to some
effective rules such as similarity of dimensions to achieve good visual structures and
patterns. The axes can be arranged either manually by the viewer or by using axis
reordering algorithms that automatically arrange the vertical axis to a minimal number
of visual clutters. Some of the popular algorithms that reorder the axes in parallel
coordinates plot are Pearson’s Correlation Coefficient (PCC) and Nonlinear
Correlation Coefficient (NCC) [19].
3 Method
There are four steps that has been taken to identify the suitable features that should be
implemented in clutter-reduction technique for parallel coordinates plot of solar data.
These steps are, studying clutter-reduction techniques of parallel coordinates,
extracting the common features available in clutter-reduction techniques, producing
the conceptual framework of clutter-reduction technique as well as proposing the
features of clutter-reduction technique that are suitable for solar data.
3.1 Study of Clutter-Reduction Techniques for Parallel Coordinates Plot
Since there are so many clutter-reduction techniques to overcome the clutter in
parallel coordinates plot, the 10 latest techniques are chosen to be studied. All the
chosen clutter reduction-techniques are applicable to traditional parallel coordinates
plot.
3.2 Extract the Common Features of Clutter-Reduction Techniques
Based on the study of a few techniques, several features has be listed and compared in
order to improve the readability of parallel coordinates plot. The Table 1 shows the
comparison of the clutter-reduction techniques and the features that have been studied
on this paper.
Table 1. List of clustering techniques and its attributes.
Technique
Visual
Interaction
Algorithm
Colour
transparency
Colour
by cluster
group
Highlight
the
selection
Brushing
Scaling/
Zooming
Manual
Reordering
Adjustable
Parameter
Drill-
Down
Automatic
Reordering
Polyline
Reduction/
Compression
Clustering
types
Bundling
[20] RBPCP
Yes
Yes
Yes
Yes
Yes
No
Yes
No
Yes
No
-
Yes
[12] Bundling
with Density
Based
Clustering
Yes
Yes
Yes
Yes
No
Yes
No
No
No
Yes
Density
Yes
[14]
Rodrigo’s
Bundling
No
Yes
No
No
No
No
Yes
No
No
Yes
Density
Yes
[21] NPCP
Yes
Yes
No
Yes
Yes
No
Yes
Yes
Yes
No
Hierarchical
Yes
[22] Cupid
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Hierarchical
Yes
[23]
Navigation
Information
Visualization
of PCP
Yes
No
Yes
Yes
Yes
Yes
No
No
No
Yes
-
No
[11] Cluster-
Aware
Arrangement
No
No
Yes
No
No
No
No
No
Yes
No
Hierarchical
No
[24]
Orientation-
Enhanced
PCP
Yes
No
Yes
Yes
No
Yes
Yes
Yes
No
No
Hierarchical
No
[25] DSPCP
Yes
Yes
Yes
Yes
No
Yes
No
No
No
No
Density and
Partition
No
[26]
Progressive
Parallel
Coordinates
Yes
No
Yes
No
No
No
No
No
Yes
Yes
Hierarchy
No
There are 12 features that can be extracted from all the studied clutter-reduction
technique. These techniques may have more than one of these features. These features
can be devided into three categories, which are visual, interaction and clutter-
reduction algorithm.
3.3 Conceptual Framework of Cluttered-Reduction Technique for Parallel
Coordinates Plot
After conducting the study on clutter-reduction techniques for parallel coordinates
plot, a conceptual framework of the common features existed in these techniques has
been produced. Fig. 5 shows the conceptual framework of the features in clutter-
reduction techniques for parallel coordinates plot.
Fig. 5. Conceptual Framework of the features in Cluttered-Reduction Techniques for Parallel
Coordinates Plot
Based on Fig. 5, the features of clutter-reduction technique for parallel coordinates
plot can be categorized into three types, which are color features, user interaction and
clutter-reduction based algorithm.
The first feature is visual. Based on the studied technique, the main visual aspect
is color usage at polyline. There are three ways of using color at the polylines. The
first one is using different color to differentiate between different cluster groups of
polylines. The different colored cluster group helps to easily differentiate between
each group and see the pattern of the data went through the each parallel axes. Thus,
the relationship between each colored stripe can be seen clearly. The second way of
using color is by using semi-transparent color on polylines. The color of polylines
becomes clearer and saturated as the semi-transparent polylines overlapped between
each other. The highest density of the polylines area will display the highest color
saturation. The techniques like Oriented-Enhanced Parallel Coordinates Plot [24] use
the saturation to represent the density of the polylines at the edge crossing polylines.
The color of other stripes will be look washed out or more grayish. The third way is
by highlighting the selected cluster group. The color of unselected cluster group will
turn grayish or transparent when one or more of cluster groups are selected. This
helps to see the pattern of selected group clearer without being interrupted by the
display of other polylines. There are some techniques such as Edge-bundling using
density-based clustering [12] and DSPCP[25] use the saturation of the color to
highlight the area or stripe which is selected by the viewer.
The next feature is interactivity in parallel coordinates. Each technique allows the
viewer to manipulate the view of the parallel coordinates in many ways. Some of the
common interactions are brushing, scaling/zooming, reordering, as well as modify the
parameter. Brushing is a selection tool that enables the viewer to select a range of
polylines. This can be done by dragging and clicking the mouse pointer around
intended area. The tools will change the color of the selected polylines in more
saturated color and makes the other polylines colors appear washed out or grayish.
Some of the clutter-reduction techniques makes the view expands the selected
polylines after making the selection. Scaling enable zooming in the parallel
coordinates for the purpose of viewing more information of the particular area of
polylines in detail. Reordering allows viewers to change the arrangement of the
vertical axes and/or the order of the cluster groups, so they can reveal the hidden
meaning behind each of the arrangement. The ability of changing the parameter of the
plot such as the ratio of the unit of the parallel axes helps the viewer to modify the
presentation of the visualization into a more comprehensive version. Drill-down
feature allows users to select a specific polyline instead of cluster group to see more
detail about the selected polyline.
There are several types of clutter reduction algorithm found in the study, which
are automatic axes reordering algorithm, polyline reduction algorithm, clustering
algorithm and bundling algorithm. Most of the studied clutter-reduction techniques
use more than one type of algorithms.
The first algorithm is axis reordering. Axis reordering is a technique that basically
changes the ordering of axis to achieve the minimal number of visual clutter. This
arrangement can be either done manually by the viewer or automatically by using
algorithm such as Pearson’s Correlation Coefficient (PCC). Some of the techniques
that implement this algorithm are Two-Axes Reordering [19] and Cluster-Aware
Arrangement [11].
The next type of algorithm is polylines reduction/compression. Some of bundling
techniques use polyline reduction algorithm to render a group of polylines or cluster
group into a single stripe line, for example, Bundling Technique with Density Based
Clustering [12] and Rodrigo’s Bundling [14]. This polyline reduction algorithm
simplifies the view of visualization. Polyline compression algorithm compresses the
volume of data, which reduces the number of polylines to minimise the workload of
the CPU, thus the rendering time becomes significantly faster. For example,
Progressive Parallel Coordinates can achieve similar degree of pattern detection as
with the standard approach by only using 37% of all data [26]. However, this
algorithm lacks the support of data that changes frequently. This is because the
reduction techniques need to recalculate the number of polylines every time which
requires high resources of computer processor.
The next type of algorithm is clustering. Many clustering algorithm has been
made. In this paper, only three types of clustering algorithm that have been studied,
which are hierarchical, density and partition. The basic idea of hierarchical clustering
algorithms is to construct the hierarchical relationship among data in order to cluster.
Suppose that each data point stands for an individual cluster in the beginning, the
most neighboring two clusters are merged into a new cluster until there is only one
cluster left. The main advantages of hierarchical clustering are its suitability for data
sets with arbitrary shape and attribute of arbitrary type, the hierarchical relationship
among clusters are easily detected, and has relatively high scalability in general. The
downside is the time complexity is high and it is necessary to preset a number of
clusters. The next algorithm is density cluster. The basic idea of density clustering
algorithms is that the data which is in the region with high density of the data space is
considered to belong in the same cluster. The advantage of density based clustering is
high efficiency of clustering process and suitable for data with arbitrary shape.
However, this algorithm produces low quality clustering results when the density of
data space is not even, a lot of memory is needed when the data volume is big, and the
clustering results are highly sensitive to the parameters. The last clustering algorithm
is partition clustering. The basic idea of partition clustering algorithms is to regard the
center of data points as the center of the corresponding cluster. The main advantages
of this algorithm are low in time complexity and high computing efficiency in
general. One of the partition clustering, K-mean, is well known for its simplicity and
feasibility [27]. This technique is based on distance matrix. Euclidean distance is used
as a distance criterion. The algorithm starts with k initial seeds of clustering. All n
data are then compared with each seed by means of the Euclidean distance and are
assigned to the closest cluster seed [28]. However, the partition based clustering is not
suitable for non-convex data, relatively sensitive to the outliers, easily drawn into
local optimal, the number of clusters needed to be preset, and the clustering results are
sensitive to the number of clusters.
The last algorithm is bundling, or also known as edge bundling. This algorithm
clusters the data in every dimension and sets these clusters in relation to each other by
bundling the lines between two axes. The bundles are then rendered using polygonal
stripes. The advantage of stripe rendering is that this method is responsive even for
very large amount of data. This is because instead of rendering line in each dimension
independently, this method renders a bundle of lines as one polygonal stripe. This
makes the rendering time independent to the number of observation points. The
downside of edge bundling is the loss of visual correspondence to classic parallel
coordinates plot [12]. This method will not allow the viewer to see particular
information of a polyline because it is already combined with a group of polylines and
displayed as a stripe.
3.4 Proposed Cluttered-Reduction Technique for Parallel Coordinates Plot of
Solar Data
The current solar data has been taken from Green Energy Research Centre (GERC) at
UiTM Shah Alam, Selangor. These data have been already visualized with Parallel
Coordinates Plot by the researcher from this organization. The proposed cluttered-
reduction technique will be implemented in current parallel coordinates visualization
to improve some of the aspects. The improvements that are going to be done includes
the ability to see the relationship between the polylines and to see the density of the
particular area of the plot. The features that are suitable for visualizing solar data in
parallel coordinates plot are identified. Fig. 6 shows the features that will be added in
proposed cluttered-reduction technique for visualizing solar energy data by using
parallel coordinates plot.
Fig. 6. Proposed Cluttered Reduction Technique for solar energy data.
The proposed techniques will cover all these categories of features, which are
color, interaction and cluttered-reduction algorithms. All the interaction and color
features adds advantage to the parallel coordinates to the viewer, so there is no
problem for implementing the most of color and interaction features. The color
feature helps the analysts to differentiate the density of data around highly overlapped
polylines areas, which is one of the main problem of visualizing a huge size of solar
dataset in parallel coordinates plot.
The next problem to solve is to make the relationship in solar data easier to
comprehed and identified. The solution is by implementing some clutter-reduction
based algorithms to simplify the presentation of visualization. However, not all
algorithms are suitable for solar energy data.
First, it is worth noting that in the photovoltaic system of solar panel, the data are
frequently added into database every 10 minutes [1]. This means that the algorithm
must be suitable for data streaming. Thus, polyline compression algorithm cannot be
used for this situation. Next is to choose a clustering algorithm that is suitable for
solar data. Since the main focus of this research is to solve the relationship issue,
hierarchy based clustering gives an advantage among the three types of clustering.
Bundling algorithm will also be implemented in solar data, so the users can have more
insights and knowledge over the data directly from the overview [14]. Since bundling
algorithm has already been implemented, automatic reordering is unnecessary since
the reason of reordering the axis is to reach the minimal number of visual clutter.
Bundling algorithm has already solved the visual clutter issue.
4 Conclusion
Parallel coordinates plot alone will not help in comprehending the data easily. This
proposed technique will enhance the speed and accuracy in extracting the meaning
behind the solar energy data. The relationship between the data can be seen more
clearly and the density of overlapped area of polylines can be identified by
implementing the proposed clutter-reduction technique. This proposed technique is
not only suitable for solar data, but it also is suitable to be applied at parallel
coordinates plot for other streaming data that are updated in real time.
The conceptual framework in this paper can be a guideline in choosing the
suitable parallel coordinates plot, not only limited to proposed technique, for their
dataset. There is still room especially in term of visual that can be explored to enhance
the comprehension of parallel coordinates plot other than color aspects.
5 Acknowledgement
The authors would like to thank Faculty of Computer and Mathematical Sciences, as
well as Universiti Teknologi MARA for facilities and financial support.
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