A Review of Visual Analytics Approaches to Spatio-temporal Event Data

Spatio-temporal events can be described as discrete spatial occurrences that take place within a relatively short time duration. Examples of such events include earthquakes, mobile phone calls, tweets and incidences of disease. It should also be noted that discrete events can be extracted from continuous series of data. For example, while traffic and bicycle journeys can be seen as flows, the beginning and ends of each journey can be seen as an event.

Peuquet [1] provides a Triad framework for approaching spatio-temporal data, noting that spatio-temporal data have three components of location, time and objects, corresponding to three questions of where, when and what. Any visual analytics method dealing with spatio-temporal data must therefore be able to store and retrieve information relating to all three of these components. Under this framework, users typically wish to describe one component given that they have knowledge of the other two components. This yields three basic categories of questions: first, given the location (where) and time (when) of the data, describe the objects that were present (what); second, given the objects (what) present at a period of time (when), describe the locations they occupy (where); third, given the objects (what) present in a location (where), describe the time they took place (when).

In Bertin’s [2] categorization of analytical questions, the author divides queries into “levels of reading”. Under this classification, questions can be categorized as elementary, intermediate and overall. Within the context of spatio-temporal events, elementary questions relate to the individual attributes of data, such as individual locations, times and objects. An example of an elementary question would be, “Where were objects of type x at time t?” Intermediate and overall questions relate to changes or patterns over both spatial and temporal dimensions. An example of an intermediate or overall question would be, “How did the distribution of objects of type x change over time from t1 to t2?”

In the sections that follow, we review a range of publications that describe methods for visualizing and analysing spatio-temporal events. We address issues and criticisms associated with these methods, and describe clustering techniques that aim to help overcome these issues. As the literature spans a broad range of domains, we have chosen not to restrict our review to any single field. We therefore provide an overview of visual analytics methods, with a particular focus on analytical questions asked, and how each method helps answer the questions in each individual case.

The appropriate selection of a visualisation method, exploratory technique or sets of exploratory techniques depends on the task and on the characteristics of the data under analysis. Shrestha, et al. [3] provide a useful classification of visual analytics methods for spatio-temporal data. Here, the authors begin by asking whether the method is two- or three-dimensional, and whether it integrates or separates spatial and temporal views. The authors thus classify the methods into four categories: 2D separated view, 2D integrated view, 3D separated view, and 3D integrated view. We have chosen to adopt this simple classification scheme for our review.

1.1           Separated two-dimensional views

One of the ways to visualise spatio-temporal data is by using 2D separated views and the most common visualisation methods found in this literature review are: map animation, comap and other interactive synchronised views. Applications of these methods are mostly in fire incidents, syndromic surveillance, crime mapping and highway incidents. These techniques and their representative examples are described in the following sections. The possible research questions addressed here deal with accuracy, preference and effectiveness of the technique or set of techniques applied to spatio-temporal problems.

1.1.1           Map animation

Map animation is a well-established technique used to explore space-time problems. It is based on a layer snapshot concept as shown in Figure 1, with a raster structure where each snapshot or layer represents a particular time period and state of a particular case study. The snapshots are combined into a continuous sequence using animation software. When played, the animation simulates the illusion of movement, as shown in Brunsdon, et al. [4].

Fig. 1. The snapshot model (Brunsdon, et al. [4]).

A general criticism of the map animation technique is that of data duplication. More specifically in research and visual analysis, the technique is criticized due to its association with computer games and cartoon form products. However, the technique allows basic spatial analysis and assists providing answers to fundamental questions on what-where-when and therefore helps identify possible patterns in the data. As the animation can be frozen at any point, it can be useful for answering determining spatial variation at any point of time t.

An example of the software used in the map animation technique is given in Figure 2. A lap button is used in this example to overcome the possible problem of the user forgetting the relevant characteristics of the animated sequence especially for longer and more complex animations.

Fig. 2. Example of software used in map animation techniques (Brunsdon, et al. [4]).

An application of the map animation technique is also provided by Brunsdon, et al. [4] for the analysis of crime patterns. First a temporal granularity of day of week or hour of day is chosen to create and animate a crime sequence. The data is then divided into appropriate time slices to produce a series of risk surfaces which are then used to generate raster images. The raster time slices are loaded and ordered in the animation software producing an animated sequence which can be viewed and explored using the software embedded playback and map tools. From the animation, the key periods of time and locations where the majority of incidents happen can be identified. The results from this analysis indicate that incidents are concentrated in fairly small well-defined regions and happen mostly during the weekends.

The interactive nature and simplicity of this approach helps in generating a hypothesis by providing insights into patterns of various spatio-temporal data. However, one weakness of the technique is that it fails to present the continuous correlation between the spatial and temporal data.

1.1.2           Comap

The comap approach is based on the original idea of the coplot or conditional plot given in Brunsdon, et al. [4], and uses ‘small multiples’ of graphs to visualise changes in patterns from inspecting the relationship of a pair of variables (x and y) over time (z). This relationship is often illustrated using scatter plots. The main rules for performing the subsetting in the comap are that the range of each subset must have some overlap with each adjacent subset, and each subset must contain roughly the same number of observations. These rules are applied in order to avoid missing a pattern due to the selection of a particular time granularity.

Examples of the application of the comap approach are given by Asgary, et al. [5] and Corcoran, et al. [6] for the analysis of fire incidents in Canada and the United Kingdom respectively. The cause of fire incidents is investigated through the analysis and comparison of their spatio-temporal patterns. In both papers the authors use the comap approach for disaggregated data. Plug, et al. [7] also use the approach in crash analysis.

The multiple view graphs given by the comap technique provide an insight into the spatio-temporal patterns of data; however, they fail to show the interactions between space and time. An improvement of the comap approach is provided by Plug, et al. [7] where spider graphs are integrated into the comap system. Spider graphs can exemplify continuous changes of the frequency of phenomena over a time granularity such as hours within a day and comap also looks into spatial distribution of the phenomena at an orderly time interval, consequently hotspots over space from comap and time from spider graph can be compared and analysed. An example of the comap and spider graph configuration is shown in Figure 3 for vehicle crash analysis.

Fig. 3. Comap and spider graphs for vehicle crash analysis (Plug, et al. [7]).

The advantage of the comap approach compared with traditional methods such as animated maps is the ability to show the spatio-temporal patterns from the entire time period under study in a single visualisation. However, the comap can be potentially complex to interpret due to the multiple graphs being displayed at once.

1.1.3           Other approaches

Another approach briefly mentioned in [4] for spatio-temporal analysis is the use of linked plots. This technique is common to the isosurface and comap approaches, where several windows are drawn showing data variables in one or two dimensional views, such as dot plots and scatter plots. In this way data can be seen over the whole period of time at once. Mondrian, cdv, lisp-stat, and R statistical iPlots library are amongst the software packages for this type of data exploration. Limitations of this approach can include the complexity of interpretation and the use of excessive computer resources.

A variation of the linked views approach is the system proposed by Maciejewski, et al. [8], where large and complex data can be visualised and analysed using their advanced interactive visualization and analysis methods allowing the users to identify hotspots easily. Applications of this approach can be found in the analysis and identification of crime, health and terrorism patterns. A similar approach is provided by Jern, et al. [9], where colour-coded maps are used for linking spatial data with temporal data. An example of their visualisation software interface is presented in Figure 4. This interface is divided into six linked views separated by interactive splitters for easy user manipulation.

One technique or a combination of techniques may be used for providing insights into spatio-temporal patterns. The use of traditional methods such map animation and comap proves to be efficient in providing a general idea of the possible patterns. More sophisticated visualisation techniques may be used for a more complete analysis of spatio-temporal phenomena.

Fig. 4. GeoAnalytics’ visual interface (Jern, et al. [9]).

1.2           Integrated two-dimensional views

Another related visualization technique or method is that of the 2D integrated views. In this type of view both spatial and temporal information are visualized at the same time in one view. In general there are many occasions where graphs and visualizations are hard to read and analyse for various reasons. One would be if many incidents happen at one geographical location at different times were a lot of data points would be cluttered around to one spot.

Maps can be effectively used as tool to support analysis and visualization of spatio-temporal events. However, mapping data points that vary in time has always been a challenge. A famous presentation of a 2D integrated view of objects that takes place in space and time is Minard’s map of Napoleon’s Russian campaign of 1812 [10]. The integrated view of space and time is especially useful here, as the user can quickly answer questions relating to the size of Napoleon’s army at any location at any point of time.

Fig. 5. Minard’s map from 1861 of Napoleon’s Russian campaign of 1812 (Kraak [10]).

Map iteration is a valuable tool of visual analysis [11]. Iteration is presentation of state of a phenomenon at different time stamps visualized in a series of maps arranged in chronological order. Although it is possible to make findings and compare between different moments in time, this technique presents the issue of limited display space. Only a limited number of maps could be visualized together at “one screen”, thus making it hard to analyse the data in further detail.

With the use of today’s computers, their fast processing power and software dedicated to the visualization of data, we are able to produce improved visualizations of spatio-temporal events in 2D integrated views. We are capable to enhance the effectiveness of map integration technique by moving from static images of maps to highly interactive displays. This is made possible with the use of animations which solves the problem of limited monitor space regarding the map iteration mentioned in the previous paragraph. In animated maps or dynamic map displays the user is able to control the animation by use of software tools such as a “time manager” [11] and with the help of “active legends” first introduced by Kraak, et al. [12]. The latter display the time reference of the data that are currently presented on the visualization while allowing the analyst/viewer to control the animation. The time manager is a similar tool which allows users to select time intervals in the map. This is being done by the user specifying a starting moment and length.

Fig. 6. Time manager for controlling animation (Andrienko, et al. [11]).

The selected map display of a specific time stamp can be shifted back and forth along the time dimension by dragging a slider. This is called controlled animation, while an automatic animation is possible too by allowing the tool to iteratively shift between time intervals by a specified number of time unit. In controlled animation, the type of view is being used statically allowing the user to inspect the map at a fixed moment. With automatic animation, the user is able to dynamically observe map changes as the intervals move along the time axis. [11].

1.3           Integrated three-dimensional views

The space-time cube is an example of a three-dimensional view that integrates displays of space and time. It was first proposed by the geographer Hägerstrand in 1970 in a paper on time geography [13]. This visualization is fairly intuitive as space is presented as a two-dimensional plane, while time is presented as a height or z-axis. At the time, it was difficult to produce such visualizations, but modern technologies have made such graphics easier to render. The space-time cube has since become fairly common in presenting spatio-temporal events.

One advantage of the space-time cube is that it presents the complete dataset to users in one view. It is thus up to the user to manipulate the display, for example by rotating or zooming, to draw out complex patterns. Kristensson, et al. [14] note that by comparison, in traditional 2D visualizations, such as animated maps or maps controlled by time sliders, time is not represented visually. The user risks missing out on spotting temporal patterns as they are not conveyed on screen as one only sees a “time slice” of events.

In their exploration of earthquake data in Western Turkey from 1976 to 1999, Gatalsky, et al. [15] use a space-time cube to visualize the occurrence of earthquakes and search for patterns in their occurrences. In this instance, given the location and time that an earthquake took place, they first visualize its magnitude. They proceed to explore an intermediate question, whether patterns exist over time in any particular areas. However, the dataset contains more than 10,000 events over a 25-year period and the cube is initially too cluttered. By applying temporal filtering and focusing on a four-month window, patterns in the space-time cube become more visible. They then move the four-month window through the entire timeframe, much like a normal slider control, to search for patterns in the data. They are then able to identify several clusters of earthquakes that happen in quick succession.

Fig. 7. Use of a space-time cube to visualize occurrences of earthquakes (Gatalsky, et al. [15]).

One interesting modification to the space-time cube is proposed by Tominksi, et al.[16]. In this paper the authors propose the use of 3D icons to represent health information on a map, citing a hypothetical example of a user who wishes to study the incidences of six diseases in an area. In this case, the user might be asking an elementary question of which diseases were most prevalent during a certain year, or an intermediate question of whether there has been a change in disease incidences over time, perhaps in response to a new vaccine. The authors propose that the user could utilize a 3D pencil with six sides to represent linear time, as in Figure 8. Each side of the pencil represents one disease in a unique colour, and the saturation of the colour corresponds to the number of occurrences of the disease. The length of the pencil corresponds to the time axis. A further alternative icon proposed is a 3D helix as in Figure 9, to represent events of a cyclical nature. The helix is a spiral ribbon, and is likewise encoded with colours that represent the intensity of the disease. In this way, the cyclic nature of the diseases could be clearly displayed.

Fig. 8. Use of 3D pencils to visualize disease incidences (Tominski, et al. [16]).

Fig. 9. Use of 3D helixes to visualize cyclic disease incidences (Tominski, et al. [16]).

A major drawback of the space-time cube is cluttering, which happens when there are too many events to draw any useful conclusions about patterns. Gatalsky and Andrienko use temporal filtering [15] to make data visualization and analysis more manageable, while Tominski, et al. use clustering [16], as the colour intensity is a form of grouping events. Further clustering may be necessary to allow the user to better answer their initial questions, a technique we describe in section 3.

1.4           Separated three-dimensional views

Another approach in spatio-temporal events visualization is using a space-time cube view with separated windows representing two or more view options. In this example, given two windows, users can browse one event in the comparison window, and specify two events with different spatial and temporal ranges. Another window in browser can represent the parameters of the event or the timeline window for the time range and in the 3D spatial-temporal viewer window for the spatial range. Users can browse the histogram or the overview in the timeline window and identify a specific event to be visualized.

Fig. 10. Spatial-temporal exploration of Great Tang Shan earthquake and Song Pan, Ping Wu earthquake, two major seismic event series occurring in China in 1976 (Yuan, et al. [17]).

Figure 10 shows an exploration of earthquake occurrences in China in 1976 in a visualization provided by Yuan, et al. [17]. Within the timeline view provided below the space-time cube, two events of interest are chosen. Within the spatial zooming option, the user can fit two events on one space-time cube which is displayed in top window. Aggregated on the left side of the cube greener dots represent the Song Pan, Ping Wu earthquake which occurred in August 1976. On the right side, orange dots represent the Great Tang Shan earthquake in July 1976. In this case colour represents magnitude – the greener the dot, the lower the measurement of the earthquake’s magnitude. The z-axis, or height of the cube, contains representation of events in time, similar to the integrated 3D view. In this manner, the user is able to easily compare and contrast the characteristics of the two different events. Some analytical questions that could be answered here are how the Song Pan earthquake differed from the Tang Shan earthquake in magnitude, or the difference in the length of time and number of
aftershocks of each earthquake.

Fig. 11. Seismic event pattern comparison between Haichen earthquake (left) and Tang Shan earthquake (right) (Yuan, et al. [19]).

One of the applications for separating three-dimensional views of spatio-temporal data is for the comparison of two events which happened in different moments in time. Figure 11 shows a seismic event pattern comparison between two earthquakes which occurred in different places and time. The clearly observed higher frequency of events on the right bar is caused by larger amount of seismic stations and more sensitive instruments.

The usefulness of the 3D separated view approach is related to the user’s data manipulation and visualization preparation techniques. In order to make the final result of work legible, the user needs to be able to manipulate the view of visualization on every step of work preparation. Therefore, separated views of timeline window or spatial window enable the user to manipulate the view to obtain desired results.

One major issue when analysing and visualizing spatio-temporal events is the crowded visualization displays. These can be particularly indecipherable when a massive amount of data points is being visualized at the same time. Typically visualizations can hold a few thousand data points before they became unclear [18]. In a cluttered display, important features or patterns may become obscured by trivial ones.

The analyst has a number of refinement techniques that can be applied to the data to provide more manageable and useful visualizations. To begin with, in a three-dimensional display the user may try to rotate the space-time cube in order to spot hidden features or patterns. Furthermore, the analyst may apply filtering, either by space or by time, in order to analyse and visualize the data in more manageable slices. Spatial filtering can be something as simple as zooming in to an area of interest on a comap in order to detect patterns.

As an example of temporal filtering, Gatalsky, et al. [15] break down a 25-year period into 4-month time windows and cycle through each time window to identify patterns of earthquakes. One drawback of this process is that even the authors admit this procedure of pattern identification is fairly “laborious”. A further criticism of manual refinement techniques is that they are highly user-dependent and subject to human error; that is, one analyst may easily spot a pattern that another analyst misses when examining the same visualization from a dataset.

A typically faster way to address the issue is by using data aggregation techniques, as the analyst may be able to use computational and statistical methods instead of manually shifting through the data space. Aggregating spatio-temporal data can be a useful method to reduce the amount of data points visualized at the same time while including more of them on the user’s displays. In general, aggregation reduces the number of data points by transforming them in a smaller number of constructs that describe their properties [19]. In spatial aggregation, aggregates are considered to be grouped data points based on geographical or categorical properties. The purpose of creating aggregates is to have them used in the visualization displays instead of all individual data points in order to make the displays more simplified and understandable. Aggregates can be specified when needed or defined in advance [18]. The literature concerning clustering techniques is fairly rich and we describe in detail several methods of clustering or aggregating data in the next section.

To tackle spatial temporal visual analytic problems, clustering is commonly introduced as a tool of data reduction, data exploration and pattern recognition technique. Clustering groups of similar data into the same subset by using different clustering algorithms can achieve automatic classification without prior knowledge of data, compressing the dataset to gain computational advantage, and outlining the significant features of datasets, thus allowing analysts to make a decision based on the compressed dataset [20].

The use of clustering is not limited by its visualisation representation. It can be found in 2D, 3D, space time cube and other visualisation methods. Figure 4, Figure 8, Figure 9, Figure 10 and Figure 11, give examples of using different technique of clustering methodology. Based on the similarity of the data, the data was highlighted and grouped into assorted colours. There is no dominant clustering algorithm, nor a generalised clustering framework that can be applied to all research. Clustering algorithm selection depends on the dataset and the research objectives [21]. In the following section, we identify effective clustering methods in spatial and temporal datasets and discuss some other variation that researchers applied to different datasets to achieve their objective

3.1           Partition-based Algorithms

Partition-based algorithms assign all data points into clusters based on their similarity. Similarity is measured using some distance function between points and the centroid of clusters. Spatial and temporal event data are in nature similar in space and time, enabling the algorithms to perform as a data reduction, summarisation and analytical tool.

3.1.1           K-means algorithm

The K-means algorithm takes the following steps:

(1) Number of k cluster centres are selected and randomly being assigned to k data points.

(2) Assign all data points to the nearest cluster centre.

(3) Calculate the new cluster centre location by calculating the mean of all data points assigned to the cluster centre.

(4) Repeat the process until convergence and the location of cluster centre remain unchanged.

K-means algorithm is a popular algorithm due to its computational advantage, where large size dataset restricted complex data mining method.  In spatial-temporal dataset, it is known for its effectiveness grouping data points that are tending to be close at spatial and temporally.

Traditionally the K-means algorithm measures distance between data points using Euclidean distance:

distp1,p2= ∑i=1n(p1i-p2i)2

(1)

Due to the nature of Euclidean distance, the K-means algorithm performs well in dealing with spatio-temporal datasets. In spatio-temporal data, objects are usually close to each other in space and time. This makes partition based algorithm work well as a data reduction technique. The drawback of Euclidean distance is its only effective with a smaller number of dimensions in data. When applied to a high dimension dataset, the result will likely to be biased towards some attribute with a higher numerical number. Solutions to address this problem include data normalisation in all accessed data attributes, or instead using the square Mahalanobis distance (2). In the formula (2), S is the covariance matrix and the equation is in matrix representation where p1 and p2 represent vector of attribute in data points [20]. This intuitively standardises all data attributes to a scale from 0 to 1.

distp1,p2=(p1-p2)T*S-1*(p1-p2)

(2)

The K-means algorithm is sensitive to outliers and noise in data. It is best to be used on datasets with clear boundary and isolated clusters. In situation when there is no clear boundaries, it is being criticised for reaching local optima instead of global optima. In practice, it is common to run a K-means algorithm several times to avoid running into local optima [20].

3.1.2           K-medoid algorithm

Another partition-based algorithm technique was introduced as a method of data reduction and data aggregation technique on spatial and temporal datasets. The K-medoid algorithm chooses k number of data points to initiate the algorithm as follows:

(1) Number of k cluster medoids is selected and randomly being assigned to k data points.

(2) Assign all data points to the nearest cluster centre.

(3) Search for a non-medoid data point and compute the loss function with respect to all nearest data points.

(4) Set the new data point as the new medoid of the cost function result is smaller than the current medoid.

(5) Repeat the process from step 2.

The cost function of the K-medoid algorithm defined as below, where X represents data points and m represents the nearest medoid:

K= ∑i=1k∑(X-mi)2

(3)

The K-medoid algorithm is considered a better data reduction technique as it has a computational advantage over density-based clustering. Compared to other algorithms, it takes a data point from an existing dataset to represent a subset of data, while retaining the spatial and temporal information associated with that data point. Intuitively it is more suitable for using a data point to represent a larger cluster of data, then using a mean value which might not be meaningful when combined with spatial and temporal visualisation [21].

Figure 12 and Figure 13 represent the result of data reduction using a K-medoid algorithm on spatial temporal data. As observed in Figure 12, the amount of data in the dataset makes any trend and spatial relationship unobservable. The density of data causing any density relationship and distances has merged into one big red space; moreover there are some outliers on the left of the picture. The disadvantages were cleared away using data reduction, as shown in Figure 13.

Fig. 12. Visualization of a massive dataset (Whelan, et al. [21]).

Fig. 13. 2000 representatives after data reduction (Whelan, et al. [21]).

3.2           Density-based Algorithms

In contrast to partition-based algorithms, density-based algorithms are not intended to group all data points into clusters. Instead, they seek to highlight an area with high density. As a result, it is not required to select k (number of clusters) in density-based algorithms.  The cluster finding strategy of density-based algorithms is very different from that of partition-based algorithms, thus the results of two types of algorithms are different and have their own application in spatio-temporal datasets. Density-based algorithms work best in detecting events and data transformation [22], [23]. It should be noted that because density-based algorithms treat data points as noise, these algorithms may not be suitable for certain types of data reduction as much of the information is lost during the clustering process. Spatio-temporal events researchers exploit this property and leverage density-based algorithms to perform data transformation tasks.

3.2.1           DBSCAN algorithm

Density-based spatial clustering of applications with noise (DBSCAN) is an algorithm proposed by Ester, et al. [24] for density-based clustering. In this algorithm, instead of choosing the number of k clusters, it is required to select two parameters, eps and minpts. Eps is the distance to be defined by the researcher. Taking any data point p in the dataset, the neighbourhood of point p would be any point that has the distance to point p that is smaller than eps. Minpts is the minimum number of neighbours for the point p to be considered a cluster object [24].

Data points satisfying the two parameters above will be assigned as core points in clusters, whereas non-core points within the eps radius of core points will be categorised as the ‘edge’ of cluster. All other points are considered as ‘noise’. Researches use this method to aggregate data as part of their feature engineering. Events such as airport traffic, crime hotspot, and trends of mass mobility were identified using density-based clustering [25], [26] and [27].

3.2.2           Other algorithms

Inspired by DBSCAN, a few algorithms were developed based on the idea of density-based clustering. OPTICS is another generalised version of DBSCAN which extended the idea with hierarchical clustering structure. [23] Meanwhile, the DenStream [22] algorithm allows live clustering for streaming data.

Researchers [8][25][26][27] employ variations of density-based techniques to transform data into desired groups of highlighted events. In contrasted to partition-based clustering, not all data was assigned to clusters, and any data not fulfilling the assigned parameters was marked as noise and discarded in the visual analysis. This highlights the key difference in the two algorithm techniques.

On our review we aimed to report existing techniques that support analysis on spatio-temporal data. Our main information source was the publications available on the internet on data visualization of spatio-temporal events. We provided a detailed section of each visualization technique along with some benefits and disadvantages of using each method. We did not pick a particular domain as we were interested to provide a general context of tackling issues and analytical questions that arise when working with spatio-temporal data. Furthermore, we provided on our review an extended section on clustering algorithms that can be used as powerful tools to tackle spatio-temporal visual analytics problems.

In general, we find that the analyst’s choice of method of visual analysis is closely related to the types of analytical questions that one sets out hoping to answer, as discussed in the introduction. For cases where spatial relationships are of interest, it may suffice to have an animated two-dimensional map. For example, Brunsdon, et al. [4] set out to determine the variations in the pattern of crime over the day of week or hour of day. By plotting out crime incidences on a map and animating it, they are able to easily determine the pattern of crime at any time t, and scan for abnormal patterns.

In contrast, in cases where temporal relationships are of interest, it is often helpful to treat time as a dimension against which events can be plotted visually. In this case, a three-dimensional view is often needed. A major advantage of three-dimensional views is that the temporal relationship between events is preserved, and the analyst can easily visualize how events relate to one another over time. For example, Yuan, et al. [17] set out to analyse the similarities and differences between two different earthquakes over time. By treating time as a dimension, they are able to easily compare and contrast the seismic activities of the two earthquakes over time, an analysis that would have been much more difficult in a two-dimensional view.

Ultimately, we understand that the appropriateness of all the techniques reported on our review is subject to the basis of general principles of graphical representations. All methods above have their strengths and weaknesses and it is down to the analyst to decide which approaches will be used and how, depending on the nature of the data and primarily on the purpose of the analysis.

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