Map-in-Parallel-Coordinates Plot (MPCP): Field Trial Studies of High-Dimensional Geographical Data Analysis

Abstract

As the world has become increasingly digitalized in recent years, high-dimensional data with geographical location coordinate attributes, mainly referring to latitude and longitude, have been accumulated and spread to many disciplines. It is challenging to analyze such data. The map-in-parallel-coordinates plot (MPCP) is an incorporate visual analysis method that can express, filter, and highlight high-dimensional geographical data to facilitate data exploration and comprehension. In this paper, the MPCP underwent a series of field trial studies to verify its applicability, adaptability, and high efficacy in the real-world. The results of the evaluation were positive, which provides reasonable proof and new insights into the benefits of using MPCP to visually analyze high-dimensional geographical datasets.

1. Introduction

With the in-depth evolution of global informatization, data collection channels in various fields are complex and diverse, data collection methods are diverse, and sampling granularity is more refined, so that data can describe objective objects, natural phenomena, and all aspects of human life in a detailed, comprehensive, and real-time manner, which has already shown the characteristics of high dimensions.

High-dimensional data contain more abundant and diverse information and rules, such as gene expression data, atmospheric and oceanic data, trade and economic data, traffic trajectory data, geographical information data, etc. It provides the necessary data sources and evaluation framework for the study of national governance system construction, weather forecast, disaster prevention and reduction, government livelihood management, pollution prevention and control, scientific research, etc., which are closely related to national economic development, human life, and the natural environment [1,2,3,4,5].

Visual analysis is an important means of high-dimensional data mining and analysis [6]. It can quickly and intuitively explore and study potential objects, processes [7], and events in the data, help analysts interpret complex data, understand complex events, discover hidden laws, draw conclusions, and make judgments. The decision-making process relies heavily on discovering knowledge and extracting useful information from data [8,9]. These abilities have a profound influence on economy, environment, climate, social life, and other aspects [10]. Visual analysis techniques are increasingly applied to decision support systems in various fields [11].

Two distinct visual analysis methods—maps for the visual analysis of geographical location attributes and a parallel coordinates plot (PCP) for high-dimensional general attributes—are, respectively, used in all visual analysis methods for high-dimensional geographical datasets which contain high-dimensional general attributes and geographical location attributes that are mainly represented by latitude and longitude coordinates. The primary purpose of this paper is to develop an incorporate visual analysis method that allows for the holistic visual analysis of high-dimensional geographical data in just one view due to this problem of using separate visual analysis methods.

Considering that maps are the most ideal visualization method for expressing geographical location attributes, and the value of the PCP in representing a large number of dimensions, this paper embedded a map into a parallel coordinates plot (MPCP). The polylines are then used to connect geographical location attributes with high-dimensional general attributes, to achieve a smooth and seamless transition between these two visual analysis methods. To intuitively and effectively explore hidden knowledge in the data and reveal the relationship between geographical location attributes and high-dimensional general attributes, the filter and highlight of visual interaction methods were also designed for the MPCP to help analysts study the details of the data in the limited screen space. To investigate the benefits and evaluate the efficiency and usefulness of the MPCP, this paper performed a visual analysis experiment using two datasets from the real-world and conducted a series of field trial studies.

The first part of this paper introduces the background of the MPCP’s design. The key literature for this study, including research on the PCP and geographical location visualization, is reviewed in Section 2. The design and main characteristics of the MPCP are illustrated in Section 3. Section 4 provides two case studies that illustrate the value of the MPCP in the visual analysis of high-dimensional geographical dataset. Section 5 describes field trial studies in detail. Section 6 outlines the results of the evaluation. The key conclusions, a description of the MPCP’s important contributions, an evaluation of the limitations, and an outline of potential future initiatives to address these constraints are included in Section 7.

2. Related Works

2.1. High-Dimensional Data Visual Analysis

The PCP [12,13,14] is a classic and efficient method in the field of high-dimensional data visual analysis. In the PCP, each axis is in a series of mutually parallel coordinate axes which serve as representative of one of the high-dimensional dimensions of the data, with the variable value corresponding to the position on the axis. Then, by connecting the values of each dimension with a polyline, high-dimensional data can be mapped onto a two-dimensional (2D) plane. Consequently, high-dimensional data can be intuitively understood and analyzed.

The PCP has not only achieved good practical results in various scientific research fields, such as computer science [15,16,17,18], health science [19], ecology [20], materials science [21] and other fields, but also has a concise form and strong scalability. In many cases, the PCP is a mature technique for tracking, investigating data records, and uncovering patterns in high-dimensional datasets.

However, when the dataset includes latitude and longitude as geographical location attributes, and if these attributes were visualized by the PCP, there is a certain analysis effect, but it is not logical or even valid. For instance, N. Vanitha et al. evaluated the tropical cyclone (TC) dataset, one of the most destructive forms of natural disasters, and utilized the PCP to show the relevant models of TC characteristics. They also used the values on the coordinate axis to display the latitude and longitude [22], as shown in Figure 1a. Zhiyuan Zhang et al. also used the PCP to visually express latitude and longitude values [23] to study high-dimensional climate data, as shown in Figure 1b. Using the PCP to display latitude and longitude by numerical values is unreasonable. Even if analysts are specialists in their particular fields of study, they must be familiar with latitude and longitude as geographical coordinates in order to readily identify the locations they represent. This is obviously not user-friendly and it requires a long learning and training period. Geographical information is most meaningful when it is displayed on a map, so this approach is flawed.

Moreover, the visual analysis task that demands jumping and comparisons between different visual analysis methods requires considerable time and mental consumption, which limits analysts’ abilities to explore data, which may limit their ability to verify known content [24]. It also makes it difficult to identify the association between geographical location attributes and high-dimensional general attributes.

2.2. Geographical Locations Visual Analysis

The visual metaphor of geographical location attributes is highly specialized. Two-dimension (2D) maps and three-dimensional (3D) earth are the most commonly used visual analysis methods. By integrating various visual channels and interactive methods, geographical data in various fields can be visually analyzed [25], which has become an increasingly popular method [26].

A COVID-19 dataset was studied by Youliang Chen et al., who used maps to illustrate the data and discovered strong relationships between epidemic frequency and air temperature, precipitation, and relative humidity. In addition to helping policymakers manage existing and potential epidemics, this study can be used to successfully forecast and manage outbreaks. Furthermore, public health policy development can be aided by knowledge of illness distribution at the national level [27]. Sohini Dudhat et al. conducted a spatiotemporal study of marine mammal stranding event data off the coast of India using maps in conjunction with other analytical techniques. They discovered new continuous hotspots on the northwest coast and scattered hotspots on the southeast coast. Better awareness of the condition and dangers of marine animals in Indian seas will result from the development of a regional emergency response center in the area [28]. A web-based visualization tool called Digital Earth Viewer could gather data from many sources and display it both spatially and temporally. Based on Digital Earth, Valentin Buck et al. proposed a scalable web-based visualization framework to visually analyze high-dimensional data from multiple data sources. The method helps to contextualize mixed observational and simulated data in time and space [29].

The use of maps to visualize geographical location attributes can be intuitive, convenient, and efficient. Moreover, other general attributes can be visualized via a variety of visual channels, including color, heatmap, timeline, point, line, and area. For example, Zuchao Wang et al. used lines to show the track of a hurricane on a map [30]. Xiaoru Yuan et al. used color to display seismic data [31]. The number of attributes that may be presented on a map is limited, making it difficult to display many attributes on a single map. For high-dimensional geographical data, if multiple visual channels are used to visualize multiple dimensions on one map simultaneously, the visualization effect will be chaotic. It may cause problems with data cognition and understanding. It is also difficult to determine the correlation between attributes.

3. Map-in-Parallel-Coordinates Plot

The MPCP is an incorporated visual analysis method for maps and PCPs that allows high-dimensional geographical data exploration and reasoning in a single view. The three visual design principles of interactive visual analysis applications are “overview first, details, zooming, and filtering on demand” [32].

At its core, the MPCP is an all-in-one view that contains a PCP and map. The PCP provides the visualization of high-dimensional general attributes in a 2D plane and the microscopic visualization of the statistical characteristics of attributes in each coordinate axis. Points are used to display latitude and longitude attributes in the map. These two methods are visually represented in the same view and are seamlessly linked by polylines so that any interaction is holistic. In addition, statistical coloring, highlighting, and filtering data visual interactive analysis methods are also implemented for the MPCP. The overall view of the MPCP is shown in Figure 2.

The joint visual analysis of the map and PCP has been explored in many works [33,34,35,36,37,38,39]. The purpose of this study is to develop an incorporate visual analysis method, which can facilitate visual interactive data exploration and high-dimensional geographical data visual analysis. The implementation of the MPCP enabled us to conduct a series of field trial studies of this approach to verify whether it could assist analysts’ explorations and in-depth studies of their data, whether it is valuable, whether it is easy to use, and whether it is more efficient than other methods.

The MPCP is a web-based application. The core implementation of the MPCP is the D3.js [40] visualization library. D3.js offers a high level of customization, enables the free implementation of diverse visual encodings, and the ability to develop a variety of interactive features with accurate color matching. The user interface of D3.js is attractive and friendly.

3.1. Parallel Coordinates Plot

Visualizing and exploring with high-dimensional data is a basic requirement of the MPCP. The PCP is well suited to this task because it can display multiple attributes simultaneously on a 2D plane using a series of axes parallel to each other and supports a wide range of types of data, including ordinal, categorical, and quantitative [41]. The PCP provides a broad perspective of the data’s overall trends and relationships while evaluating a lot of attributes.

The PCP evolved into a powerful visual analysis tool by enabling interactive manipulation and having a good mathematical basis. An axis is used to represent an attribute, and its value represents the attribute’s magnitude. The representation of high-dimensional data in the PCP is represented by polylines which connect all values for each dimension, and it can be expressed by a linearly independent system of equations as follows:

$$\frac{x_1-a_1}{u_1}=\frac{x_2-a_2}{u_2}=\cdots =\frac{x_n-a_n}{u_n}$$

(1)

From the above formula:

$$x_{i+1}=k_i{x}_i+b_i,i=1,2,3,\cdots ,n$$

(2)

where $k_i=\frac{u_{i+1}}{u_i}$ is the slope and $b_i=\left(a_{i+1}-k_i{a}_i\right)$ is the intercept on the $x_{i+1}$ axis.

The mathematical foundation of the MPCP guides the programming of the MPCP. The latitude and longitude attributes are represented using the map as a special axis, and they are seamlessly connected to high-dimensional general attributes using polylines.

One of the main benefits of the PCP is the ability to quickly interpret the overall state of the data. A static PCP relies on tracking the movement and orientation of polylines. The MPCP contains interactive features that allow the dynamic filtering of polylines. Filtering polylines is achieved by dragging and dropping a region on the axis to highlight the polylines you want to see while darkling the others, as shown in Figure 3. By doing this, data from all dimensions are filtered, and only data falling within this region are shown. To eliminate filters, click somewhere else on the axis. Any number of dimensions can be used to create such a selection box. Additionally, each selection box has the ability to manually drag the range up or down, altering the data points that are filtered and dimmed.

The problem of determining how the data are distributed across various dimensions is one issue with PCP data analysis. It is especially problematic when there are many data points intersecting the same value, in which case the overlap makes it difficult to find the distribution of the data. To help understand the statistical features on each dimension, the MPCP provides an interactive analysis method with statistical coloring on each axis. Statistical coloring is the assigning of color to the polylines of one dimension to the attribute value [42], providing an overview of the data distribution for each dimension. The drop-down list is used to toggle the attributes to be used for statistical coloring. The color legend is displayed above the MPCP. As shown in Figure 2, statistical coloring was performed with the gross regional domestic product (GRDP) attribute.

One drawback of the PCP is that it is challenging to find a polyline among numerous polylines and perform detailed analysis, because excessive data will lead to overlapping and the occlusion of polylines, which brings difficulties to visual analysis. The MPCP allows polylines to be highlighted in bold when the mouse hovers over them for an extensive study of the relevant data [43]. The edge of the geographical region on the map that corresponds to this polyline is also bolded at the same time. Accordingly, the current geographical region and the associated polyline are bolded simultaneously while the mouse hovers over the map to aid with intuitive identification, as seen in Figure 4. The polyline and the map are both highlighted in this special highlighting interaction of the MPCP.

In addition, each polyline across the axis [44] in the MPCP is a curve of a certain radian, which cannot only make the visualization effect beautiful and smooth, but it also helps to reduce the overlap and occlusion of polylines and enhance visual cognition.

3.2. Geovisualization

Map visualization is provided to facilitate the observation and interpretation of latitude and longitude attributes in the data. This is an essential element of the MPCP that makes it simple and natural to investigate the correlation between geographical features and high-dimensional attributes. The map was embedded in the PCP so that these two approaches could be viewed together and interactively analyzed.

By default, the MPCP renders the latitude and longitude attributes as points. The edges and points of the region should be presented together if the data reflect a regional situation since, in these instances, it may be helpful. In order to achieve this, the MPCP created a highlighting interaction technique by bolding the polyline and the boundary of the geographical area.

3.3. Data Inspection

Maintaining the capacity to access raw data is essential while studying data in order to view precise information and analyze visual presentation features related to the specifics of the data.

There are two ways to examine and view the raw data in the MPCP. A tooltip is the first thing that appears when the mouse is hovered over a polyline or the area of the map, as shown in Figure 4. Additionally, a data table that lets you browse all the data is included. This paper employed a grid with built-in data filtering and sorting features from the free and open source jqWidgets framework [45]. When the mouse hovers over the data table, the polyline and geographical location corresponding to the current piece of data are highlighted in bold, as shown in Figure 5.

Moreover, the MPCP uses acronyms for the attribute names above each axis because the full attribute names are too long. The below data table (Figure 6) is a separate explanation table that describes the meaning and units of each attribute.

4. Case Study

This paper provides two case studies that demonstrate how the MPCP is useful in helping to investigate and comprehend high-dimensional geographical datasets so as to emphasize the potential value of the MPCP.

4.1. Basic Conditions of China Dataset

In this paper, the MPCP is first tested on the basic conditions of the China dataset, which includes two geographical location attributes of latitude and longitude and seven general attributes of GRDP, resident population at year-end (RP), local fiscal tax revenue (LFTR), number of medical and health institutions (MHI), all residents’ per capita disposable income (PCDI), educational fund (EF), and forest coverage rate (FCR). The material was obtained from the National Bureau of Statistics website (http://www.stats.gov.cn/tjsj/ accessed on 2 June 2022) and was collected for this case from 2013 to 2019. The purpose of this case study is to explore the relationship among population, economy, healthcare, education, and environment, and consider the relationship between this information and geographical location. A demonstration of this case study is available at http://18.223.136.39:8080/mpcp/page1.html (accessed on 2 June 2022).

An essential first step is to analyze the relevant data, utilizing the highlighting interaction approach so as to discover new insights and investigate relationships. We can see that the data volume is not large, and there is no serious overlap and occlusion. Statistical coloring enables the analysts to understand the distribution of each dimension. We can use the drop-down list to statistically color each of the seven properties, while selectively highlighting polylines or geographical areas.

The GRDP attribute is statistically colored first, as shown in Figure 7a. If we hover the mouse over the bottom polyline, and it is obvious that the gross domestic product (GDP) of Guangdong Province was the highest in 2013, and the number of permanent residents, fiscal taxes, and educational expenditures were all the highest in China, while all indicators of Tibet were the lowest in China, as shown in Figure 7b. By filtering the data on the GRDP axis and selecting the regions with an upper-middle level of GDP, it is not difficult to find that the provinces with high GDP are all coastal provinces, as shown in Figure 7c.

Then, the attribute of MHI was statistically colored, and the polylines above the medium and high level are filtered, as shown in Figure 7d. The MHI is likewise considerable in populous provinces. The analysis presented above reveals two things: the first one is that southeast coastal regions benefit from geographical advantages, which improves economic development; the second one is that the number of healthcare institutions match the population in China.

This case study illustrates exploratory data analysis based on visual analysis. This enables the analysts to decide which dimension to color statistically, how to highlight polylines and geographical locations, and how to filter data. The final stage is to review the details of the raw data to support the confirmation of what was found.

4.2. Basic Agriculture Conditions of China Dataset

In this paper, the MPCP visual analysis method is also applied in the basic agriculture conditions of the China dataset to explore, study, and consider the influence of geographical location on crops. The dataset was collected from the National Bureau of Statistics official website (http://www.stats.gov.cn/tjsj/ accessed on 2 June 2022)). It includes seven attributes of quantity, the rural population (RP), pesticide usage (PU), total sown area of crops (TSAC), food production (Food), the slaughter quality of poultry (SQP), fruit production (fruit), total production of aquatic products (TPAP), and two geographical location attributes of latitude and longitude. This case collected data from 2006 to 2019. A demonstration of this case study is available at http://18.223.136.39:8080/mpcp/page2.html (accessed on 2 June 2022).

The visualization results of the MPCP are shown in Figure 8a. Through statistical coloring and highlighting interactions, it can be clearly found that Henan province has the largest rural population, the largest population, the highest crop sown area, and the highest total grain output. From studying its geographical location, it can be concluded that the central plains region is the Yellow River basin, with abundant water resources, more plain areas, and a moderate climate, which is particularly suitable for the growth of crops. Henan Province is a significant agricultural province as a result of the excellent climate, geography, and populace.

According to the filtered data, as shown in Figure 8b, the agricultural indicators of provinces with a small agricultural population are all at the lowest level in China. The geographical analysis of these provinces mainly includes municipalities directly under the central government and southwest regions. It is not difficult to find a reason that due to the high level of urbanization in big cities, there is little land available for agricultural development. Southwest regions are not suitable for the growth of crops because of the harsh climate and geographical environment, higher elevation, more mountainous areas, sparsely farmed land, and water scarcity. The analysis could therefore reveal that the growth of crops is strongly influenced by geography.

4.3. Disscussion

The two case studies mentioned above provide an overview of the use of the MPCP, which enables the analysts to conduct a more thorough visual analysis and discover more insightful information. The MPCP has a broad range of applications. High-dimensional geographical data from a variety of fields can be visually analyzed by the MPCP.

The aforementioned cases show that the MPCP visual analysis method has obvious advantages. In high-dimensional geographical data analysis tasks, view design incorporation can enhance understanding of the data and enable efficient, accurate, and intuitive data analysis.

The primary distinction of the MPCP from earlier methods is the embedding of the map in the PCP. The MPCP removes switching between two separate methods, in contrast to existing multi-view approaches, and can easily observe data trends using continuous curved polylines without the need for geographical expertise.

Interaction methods are essential in the MPCP and are developed exclusively for the MPCP. Users can choose data items using interactive methods and explore in-depth data details, which is a significant factor to support analysts in exploring data. As a result, the interactive design of the MPCP is particularly practical, and the interface design is more user-friendly.

5. Evaluation

For the purpose of evaluating the overall usefulness of the MPCP, a series of field trial studies were conducted. Field trial studies are open-ended analyses, which allow analysts to explore and analyze a routine data analysis task. Because the adaptability of the MPCP was one of the main design goals, it was important to ensure that the MPCP could handle datasets in different domains. To confirm that the MPCP could be generalized to different domains, the analysts were divided into two groups and conducted field trial studies using datasets from two different domains.

We recruited 43 participants for this study from a university, including 28 undergraduate, master’s, and doctoral students and 15 faculty members. Among them, there were 31 male participants and 12 female participants, ranging in age from 23 to 55 years. We ensured that each participant was familiar with the meaning of the datasets used in the experiment and the technical terms for PCP and map visualization, had no experience with the MPCP, and was not colorblind. The MPCP was hosted on a server on campus and accessed via a website, and the participants browsed and conducted field trials using their own displays.

5.1. Research Questions

For the purpose of directing the MPCP field trial studies, four research questions have been devised, which are:

Q1: What degree of exploration of high-dimensional geographical datasets is supported by the MPCP?

Q2: To what extent does the MPCP support the detailed analysis of high-dimensional geographical datasets?

Q3: How useful is the MPCP in the visual analysis of high-dimensional geographical datasets?

Q4: Is it easy to utilize the MPCP?

5.2. Study Design

The purpose of field trial studies is to offer empirical evidence that can be utilized to answer research questions. The field trial studies were procedurally divided into six structured stages [46]: first, informed permission; second, pre-study questionnaire; third, overview of the MPCP and task training; fourth, the independent use of the MPCP and two other methods for comparative data visual analysis; fifth, post-study questionnaire; and sixth, interview and discussion.

Basic information about the participants and their experience of the discipline of high-dimensional geographical data visual analysis, and other visual analysis tools usage, was gathered using the pre-study questionnaire. This material was utilized to judge whether the participant has enough experience in the discipline of high-dimensional geographical data visual analysis to be considered an expert.

Before the task began, we gave participants a quick overview of the visualization and experimental tasks, including knowledge about visualization, the use of interactive analysis in visualization and data exploration, a description of the high-dimensional geographical datasets, and the usage of relevant visualization tools. Then, task instructions were given to everyone. The job is the same in both the training stage and the main stage. In order to familiarize and understand the basic conditions of the China dataset and the basic agriculture conditions of the China dataset, the participants were directed to use three visual analysis methods to analyze potential knowledge and relationships in the datasets.

After training, the participants were divided into two groups and invited to explore the two datasets using three visual analysis methods. In this paper, the PCP and geo-coordinated parallel coordinates (GCPC) [46] methods were selected to compare with the MPCP.

Currently, two categories can be distinguished between PCP-based visual analysis methods for high-dimensional geographical datasets. The first, and more popular of the approaches, combines the PCP, maps, and other methods (such as scatter-plots, histograms, and box plots) together with interactive methods, such as the approaches proposed by Xiaoru Yuan et al. [31] and Robert M. Edsall et al. [47], as well as the GCPC method. The second employs two parallel coordinate axes to directly visualize the latitude and longitude values that represent geographical location information, such as the visual analysis methods used by N. Vanitha et al. and Zhiyuan Zhang et al. in their study [22,23].

From the first category of methods, we choose the GCPC method for comparison to show the advanced level of our design because the GCPC method also uses the PCP and map. The GCPC method uses the combined method of the map and PCP to visually explore high-dimensional geographical data. Geographical location information and high-dimensional attributes are visually expressed in two different views.

The second category of methods directly use the coordinate axes to express latitude and longitude values, the same as other general attributes.

To illustrate the advanced character of the MPCP, the PCP was used as the baseline condition, while the GCPC method is a relatively mature method of using the PCP to combine with the map and has been evaluated by experts. Participants were asked to perform open-ended visual data analysis using these three methods of analysis, respectively. In order to ensure that the analytical task is completed without issue, there is no deadline or time limit established for the data analysis. We recorded the response time and error rate of each participant after the task. Error rate refers to the probability of errors in all conclusions obtained by the participants from the three visual analysis methods.

When both groups of participants self-reported the completion of the task, they were required to fill out a questionnaire to evaluate their impressions of the capabilities for the exploration and analysis of the MPCP, focusing on evaluating the MPCP method’s ability to visually analyze data [48,49], as well as the usefulness, usability, and effectiveness of the major features [50]. All items were presented in statement form. On a 5-point Likert scale (strongly agree, agree, neutral, disagree, and strongly disagree), the participants were able to rate their level of agreement.

Finally, we conducted interviews and discussions where the participants had the opportunity to convey their reality of using MPC. In addition, we designed six guiding questions to compare the results of using the three methods: 1. Which of the three approaches do you believe will make it easiest to visualize high-dimensional geographical datasets? 2. What aspects of the MPCP beat alternative techniques? 3. Can high-dimensional geographical data analysis and exploration be made more effective by using the interactive methods and auxiliary methods of the MPCP? 4. To what extent does the MPCP support the study of high-dimensional geographical datasets across a range of disciplines? 5. What problems arise when using the MPCP? 6. What functions or interactive techniques do you wish the MPCP to include that are not now available? These qualitative data provide in-depth explanations of the participants’ perceptions of the approach’s worth and utility, supporting quantitative answers on the questionnaires.

5.3. Settings

Field trial studies were conducted independently in two high-dimensional geographical datasets in different fields. Consequently, there are slight differences in the way the studies are conducted, the number of participants, and their experience with visual analysis. Here, we explain the configuration of the field trail studies.

The first group consisted of 21 participants, and the field trail study used the basic conditions of the China datasets. The second group consisted of 22 participants, and the field trail study used the basic agricultural conditions of the China dataset.

These two groups are divided equally between men and women, their research fields are interdisciplinary, and their levels of visualization are similar. After each participant completed four open-ended visual analysis tasks using the three methods, the questionnaire was completed, and, finally, the discussion was conducted.

6. Results

6.1. Support for Data Exploration (Q1)

To what extent does the MPCP support the investigation of high-dimensional geographical datasets in the first research question? Five statements are provided about the utility of the MPCP in exploratory data analysis in the questionnaire after the comparison task, including exploring the population of the data, exploring a subset of the data, understanding the data, discovering new knowledge, and discovering association relationships.

The summary responses for each group of participants are shown in Figure 9. Although there were some neutral attitudes, participants in both trial groups generally or strongly agreed that the MPCP was a valuable visual analysis method for exploring high-dimensional geographical datasets.

Overall, the participants’ responses regarding the MPCP in terms of data exploration indicated that they perceived benefits in the MPCP. Participants can analyze different aspects of data as a whole in one view, especially the correlation analysis of geographical location attributes, which is convenient, quick, and clear at a glance. Therefore, we believe that the MPCP largely supports the exploration of high-dimensional geographical datasets.

6.2. Support for In-Depth Data Analysis (Q2)

To what extent does the MPCP support the exploration of high-dimensional geographical datasets in the second research question? Four descriptions were provided in the questionnaire to assess this problem, namely whether the correlation between attributes can be analyzed, whether the distribution of data can be analyzed, whether the data can be distinguished, and whether the data can be compared. The summary responses for each participant are shown in Figure 10.

The participants in both groups rated that the use of the MPCP for detailed data analysis as consistent. Although the evaluation was generally positive, the evaluation of the analysis of relationship between the attributes with the MPCP was slightly negative, requiring further discussion. Some participants who have experience in using the PCP stated that the PCP has inherent difficulties in the correlation analysis of the two attributes that are far apart, and that this flaw also exists in the MPCP. The axis-switch interactive analysis method can solve this problem well.

Overall, we believe that the MPCP offers solid support for the in-depth analysis of high-dimensional geographical datasets.

6.3. Overall Useful for Visual Analysis (Q3)

The third overall research question focused on how useful the MPCP is for high-dimensional geographical dataset visual analysis. To illustrate the potential value of the MPCP, we compare the MPCP with two other high-dimensional geographical data visual analysis methods to show that our design is more efficient, convenient, and practical.

The response time results are shown in Figure 11. Obviously, the MPCP takes the least amount of time, indicating that the design of visual encodings and the interactive methods significantly improved the efficiency of the MPCP.

Figure 12 displays the error rate of open-ended analysis. The MPCP has a significantly lower error rate than the PCP and GCPC. Clearly, other factors, such as interactive methods, may affect performance. Although training can offset this effect, participants consistently agree that the MPCP has advantages over the PCP and GCPC, as evidenced by response times and error rates. Furthermore, there was nearly no tradeoff between response time and error rate, that is, a faster performance did not increase the error rate.

To ascertain whether and to what degree our recorded results of response time and error rate are influenced by the three visual analysis approaches, using the online social science statistics application SPSSPRO (https://www.spsspro.com/ accessed on 25 March 2023), we conducted an analysis of variance (ANOVA) [51,52,53,54,55] and created the following hypotheses for both response time and error rate results:

$$\left\{\begin{array}{c}{H}_0: {\alpha }_1={\alpha }_2={\alpha }_3=0,\\ H_1: {\alpha }_1,{\alpha }_2,{\alpha }_3 are not all zero.\end{array}\right.$$

(3)

where α represents the visual analysis method factor. The results are shown in

Table 1. Results of ANOVA for response time of the open-ended analysis.

Variable Name	Variable Value	Sample Size	Mean Value	Standard Deviation	F	p
Response time	PCP	43	11	1.988	82.093	0.000 ***
	GCPC	43	9.558	1.677
	MPCP	43	6.442	1.328
	Total	129	9	2.539

Note: the significance levels indicated by *** is 1%.

and

Table 2. Results of ANOVA for the error rate of the open-ended analysis.

Variable Name	Variable Value	Sample Size	Mean Value	Standard Deviation	F	p
Error rate	PCP	43	0.052	0.008	578.301	0.000 ***
	GCPC	43	0.039	0.006
	MPCP	43	0.009	0.003
	Total	129	0.033	0.019

Note: the significance levels indicated by *** is 1%.

.

For the results of response time in Table 1, we rejected hypothesis $H_0$. The p value of variance analysis is 0.000 *** ≤ 0.05, so the statistical result is significant, indicating that different methods have significant differences in terms of response time.

Similarly, for the error rate, as shown in Table 2, we also rejected the hypothesis $H_0$. The p value of variance analysis is 0.000 *** ≤ 0.05, so the statistical result is also significant, indicating that different methods have significant differences in terms of error rate.

In summary, the comparison results further demonstrate the value of the MPCP in analyzing high-dimensional geographical data.

Moreover, six statements from the TAM2 instrument [50] were offered, focusing on topics of usefulness, such as increasing performance, effectiveness, productivity, and so on. Figure 13 presents the aggregated results of these measures.

The response to these evaluations about the overall usefulness was mostly positive. This, together with open-ended comparison analysis, proves that the MPCP is very useful in practical application.

Moreover, the MPCP provides a solution for both the incapacity of the PCP to illustrate geographical data and the difficulties maps face in displaying high-dimensional data. Evidently, the MPCP can be presented in the same area more comprehensively than the GCPC method. The interactive methods of the MPCP are more fluid and convenient; analysts can understand all aspects of the dataset as a whole, which can help with the retrieval process of attribute correlation. Without switching views and without separating geographical attributes’ visualization from general attributes’ visualization, the MPCP is clearer and more intuitive.

6.4. Overall Ease of Use (Q4)

The simplicity of usage of the MPCP is the topic of the final question. This purpose can be accomplished by using six TAM2 instrument components [50]. The response to these measures is shown in Figure 14.

The response to this assessment was positive. This is sufficient to demonstrate the value of the MPCP in analyzing high-dimensional geographical data. Therefore, we believe that the MPCP is easier to use. We speculate that this development is mostly due to the intrinsic effectiveness of visual encoding. The map in the MPCP is seamlessly incorporated with the PCP, and the advantages of the two visual encodings are brought into play at the same time. The visual encodings of high-dimensional general attributes and geographical attributes is incorporated into an inseparable whole, which makes it possible to perform holistic visual encoding and exploratory analysis of high-dimensional geographical datasets.

6.5. Discussion

To make the MPCP more reasonable and optimal, we summarized the responses of the participants to the six questions in the interviews and discussions in the form of the following four points. 1. Among the three high-dimensional geographical data visual analysis methods, the MPCP is undoubtedly the best in terms of performance, which is reflected in the design of visual encoding and the design of efficient interactive methods. 2. The main feature of the MPCP is to solve the problem of visualization separation between geographical attributes and high-dimensional general attributes. 3. In many disciplines, the MPCP can support the visual analysis of high-dimensional geographical datasets; however, when there are a lot of data records, polylines will overlap and become obscured. This problem is an inherent defect of the PCP, which the MPCP also cannot avoid. 4. Another inherent flaw of the PCP is the introduction of ambiguity in the analysis of relationships between non-adjacent attributes. There are many ways to solve this problem. For the MPCP, the manual axes resorting interactive method [56] is more suitable.

7. Conclusions

The MPCP has the advantages and characteristics of the visual perception of the map and PCP; it overcomes the inherent limitation that the PCP cannot directly express latitude and longitude and overcomes the limitation that a map cannot visually express high-dimensional attributes. We demonstrate how to use the MPCP in real-world datasets and test the performance of the MPCP through a series of field trial studies. The results showed that the MPCP is more efficient, convenient, and easy to use. Moreover, the MPCP has a strong generality in the visual analysis of high-dimensional geographical dataset [57].

However, the MPCP also suffers from some drawbacks, such as the lack of clarity in analyzing relationships between non-adjacent attributes. Another example is that participants suggested support for more forms of geographical attributes.

In the future, we aim to investigate the visual analysis method of high dimensional data, including many other types of geographical location attributes, such as trajectory attributes, regional attributes, geospatial data, etc. A method which incorporates a 3D Earth and PCP could be further considered, and the real-time datasets could be visually analyzed.