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Three-Dimensional Visualization
Published in Diego Galar, Uday Kumar, Dammika Seneviratne, Robots, Drones, UAVs and UGVs for Operation and Maintenance, 2020
Diego Galar, Uday Kumar, Dammika Seneviratne
Many datasets consist of more than three attributes and do not allow a simple visualization as 2D or 3D plots. Examples of multidimensional (or multivariate) data are tables from relational databases, which often have tens to hundreds of columns (or attributes). Since there is no simple mapping of the attributes to the two dimensions of the screen, more sophisticated visualization techniques are needed. An example of a technique which allows the visualization of multidimensional data is the parallel coordinate technique (Inselberg & Dimsdale, 1990) (see Figure 6.1), which is also used in the scalable framework (see Figure 6.7). Parallel coordinates display each multidimensional data item as a polygonal line which intersects the horizontal dimension axes at the position corresponding to the data value for the corresponding dimension (Keim, 2002).
Concepts of Visual and Interactive Clustering
Published in Charu C. Aggarwal, Chandan K. Reddy, Data Clustering, 2018
The difficulty of displaying multidimensional points with more than three dimensions in a single view instead of multiple linked views can be alleviated by using parallel coordinates [28, 27]. Parallel coordinates display a multidimensional data vector as a set of connected line segments (polyline) drawn in a two-dimensional space. The active domain of each dimension of the multidimensional data space is represented by an axis. All axes are scaled to the same size and drawn in parallel. Each end point of a polyline segment is placed at one of the parallel axes. The position of it there is computed by mapping the numerical value of the data vectors’ respective dimensions onto the line segment of the respective axis. Thus, the polyline corresponding to a multidimensional data vector connects the numerical values of that vector mapped onto the parallel axes. An example of a single data vector taken from the Iris data set is shown in Figure 19.3(a).
Model Fit Assessment and Improvement
Published in Norman Matloff, Statistical Regression and Classification, 2017
Another graphical approach uses the freqparcoord package, written by Yingkang Xie and me [104]. To explain this, we must first discuss the notion of parallel coordinates, a method for visualizing multidimensional data in a 2–dimensional graph.
Mediating governance goals with patients and nurses satisfaction: a multi-actor multi-objective problem including fairness
Published in International Journal of Production Research, 2023
Valentina Bonomi, Renata Mansini, Roberto Zanotti
In this section, we delve into the correlation between measures by analysing the impact of using a specific goal as the first objective function in a triplet solved through hierarchical optimisation. We investigate how this affects the values of the remaining objectives, as shown in Figure 2. Additionally, we examine how changing the priority order of goals in the triplet impacts the solution values, as illustrated in Figure 5. Figure 2 provides a comparison of the different objective functions associated with the same stakeholder. We use a parallel coordinates graph, which is a type of data visualisation tool that displays and compares multivariate data. Each vertical axis corresponds to a variable (goal), enabling easy observation of the relationships between goals and identification of any patterns or trends in the data. The purpose is to easily depict the correlations among measures of the same stakeholder.
Information visualisation for efficient knowledge discovery and informed decision in design by shopping
Published in Journal of Engineering Design, 2019
Audrey Abi Akle, Bernard Yannou, Stéphanie Minel
A parallel coordinates plot is a graph displaying multiple criteria without drastically increasing the complexity of the display (Inselberg 2009). This graph was designed to work on high dimensional problems. It avoids the limits of orthogonal coordinate systems by placing each axis of coordinates in parallel. The design of a PCP is done in 4 steps: We start from a simple scatterplot with 3 design points (Figure 4a.)We operate a projection of the points on the y-axis and on the x-axis (Figure 4b.)Then we connect the coordinates of the points projected on the 2 axes by lines (Figure 4c.)Finally, we place the axes in parallel (Figure 4d.).
Batch process control and monitoring: a Dual STATIS and Parallel Coordinates (DS-PC) approach
Published in Production & Manufacturing Research, 2018
Miriam Ramos-Barberán, Miriam Vanessa Hinojosa-Ramos, José Ascencio-Moreno, Francisco Vera, Omar Ruiz-Barzola, María Purificación Galindo-Villardón
Parallel Coordinates as a graphical representation system was proposed by Alfred Inselberg from which -dimensions could be represented in a two-dimensional system (Inselberg & Dimsdale, 1990). As Dual STATIS, parallel coordinate plotting is used to display multi-dimensional data in two dimensions in order to identify homogeneous patterns of data among many different variables (Heinrich & Weiskopf, 2013). When lines present a similar behavior, this tool is very useful in identifying clusters between observations (Inselberg, 2009). In this sense, Parallel Coordinates can be used for ‘visual clustering’, i.e. to find groups of similar points based on visual features such as the proximity of lines or line density (Heinrich & Weiskopf, 2013). For control and monitoring, Parallel Coordinates capacity for clustering and summarization are of great importance in plotting confidence regions (Dunia et al., 2012).