List of Visualizations



Time series plot

Plots one or more variables over time. Alternatively, the X axis may also be defined by another data attribute which represents a chronologic order, for example an ID. Visplore supports line charts for continuous time series and data points for discrete samples. Additonal features include collapsing time spans, overlaying moving averages, and much more.



How to get this visualization

Time series plots are available in all cockpits, typically in the lower half of the cockpit. Time series plots will only be offered if the "Time axis" role has been defined for the cockpit. The visualized time series are selected outside of the time series view in one of the overviews of all variables. In some cockpits, pairs of time series will be selected, for example when analyzing correlations ("Correlations" cockpit).

Configuration

Note

Time series plots provide multiple selection modes, such as rectangle, X interval, Y interval, and lasso. However, if multiple time series are shown with individual scalings, the only selection option is "X interval".

Further information

about parameterization and zooming.



Histogram

Visualizes the distribution of a quantitative variable and allows for comparing the distributions of multiple classes, for example the categories of a categorical data attribute.



How to get this visualization

The histogram is available in the cockpits "Trends and Distributions", "Multivariate drill-down" (Visplore Professional), and "Curve Property Definition" (Visplore Professional). The visualized variable is selected outside of the histogram in one of the overviews of the variables.

Configuration

Further information

about parameterization and zooming.



2D Scatter Plot

Study correlations and clusters for two variables. The points correspond to the imported data samples. 2D scatter plots in Visplore provide multiple selection tools such as lasso, flexible coloring options, and support overlaying regression functions.



How to get this visualization

The 2D Scatter plot is available in several cockpits, for example "Trends and Distributions", "Correlations", and "Multivariate drill-down" (Visplore Professional). The visualized variables are selected outside of the scatter plot in overview visualizations of the variables. 2D Scatter plots are also part of some other cockpits, for example as "Predicted vs. Observed" plots in the cockpits "Deviation Monitor" and "Multivariate Regression".

 

Configuration

  • Axes [1]: Click on the axis labels (gray background) to choose between the variables just being selected. You can also flip the axes in the view options menu.
  • Axis scaling: Adjust the scaling of the axes by zooming or by using the sliders [2] located at the left and bottom borders of the view.
  • Color: Click on the gray area in the top left corner [3] to use color, for example to visualize additional data attributes.
  • Point size and transparency: Adjust the visual appearance in the view options menu [4]. The transparency allows for conveying the density of the data.
  • Regression polynomial: The view options menu [4] item "Trend overlay" lets you overlay linear, squared, or cubic polynomials. Moving the mouse close to the function plot [5] shows the regression function, the root-mean-squared-error and the R² metric in the tooltip.
  • Non-selected data: It can be desirable to show only data corresponding to the selection in another view rather than the entire data. This can be configured in the view options menu [4] item "Non-selected data".
  • Automated zooming: The view options menu [4] item "Automatic zooming" lets you zoom automatically to highlight data which is selected in another view.
  • Selection mode: In the view options menu [4] you can choose between rectangle selection (i.e., an intersection of intervals on the X and Y axes), interval on X, interval on Y, lasso selection, and straight line selection.
  • Image background: In the view options menu [4] you can specify graphics files such as PNGs and JPGs to provide that context, and the align them precisely with the scaling of the data.

Further information



Bar Chart / Stacked Bar Chart

Common visualization technique to compare classes. The length of the bars may represent, for example, the magnitude of each class. Bar charts in Visplore let you nest multiple categorical data attributes, support various options for sorting the bars, and display additional quantities via the color of the bars. They can also be configured as stacked bar charts.



How to get this visualization

Bar charts are available in most cockpits, provided that the data contains at least one categorical data attribute and/or time stamp. In many cockpits, bar charts are contained in the top right part of the cockpit. For example, the cockpits "Trends and Distributions", "Correlations", "Summaries", and several other cockpits of Visplore Professional contain a tab group titled "Drill down" which contains bar charts.

Configuration

Further information

about visualizing categorical data.



Heatmap

Visualization technique to show information of two dimensions. In Visplore, both dimensions (i.e. axes) are defined by categorical data attributes which may also be nested. Cell color and cell area display information such as the magnitude of the category combination or a statistical measure of another quantitative variable. Common use cases of heatmaps include cross-tabulations of categorical data attributes and visualizations of data categories over time. In the latter case, one axis is defined by temporal data categories such as calender months.



How to get this visualization

Heatmaps are available in most cockpits, provided that the data contains at least one categorical data attribute and/or time stamp. In many cockpits, heatmaps are contained in the top right part of the cockpit. For example, the cockpits "Trends and Distributions", "Correlations", "Summaries", and several other cockpits of Visplore Professional contain a tab group titled "Drill down" which contains heatmaps.

Configuration

Interaction

Clicking on a row or column label (i.e. the name of a category) [6] selects that category to be highlighted or filtered in other views. You can also click on cells to select combinations of categories and drag a rectangle to select multiple categories.

Further information

about visualizing categorical data.



Pivot Table

Common technique to summarize quantitative data, e.g. for reporting. Visplore lets you define rows and columns by categorical data attributes which may also be nested, and offers numerous statistics for summarization. Pivot tables may also show percentages and differences for comparing rows or columns. Besides reporting, a common use case is to prepare data for export.



How to get this visualization

Pivot tables are available in most cockpits, provided that the data contains at least one categorical data attribute and/or time stamp. In many cockpits, pivot tables are contained in the top right part of the cockpit. For example, the cockpits "Trends and Distributions", "Correlations", "Summaries", and several other cockpits of Visplore Professional contain a tab group titled "Drill down" which contains pivot tables.

 

Configuration

  • Rows: Clicking the centred vertical label [1] at the left-hand side of the view allows for switching the categories used to define the rows. You can nest multiple data attributes using the "+" signs [3] and change their order using drag and drop. Clicking the "/" character [2] between the names flattens the hierarchy by concatenating the categories. This can be helpful for sorting category combinations.
  • Columns: By default, columns show some statistics of the selected variable(s). The displayed statistics can be configured using "Configure view" in the view options menu [4]. Columns can also be subdivided by categorical data attributes using the "+" signs [5] next to the lables on top of the view.
  • Sorting rows or columns: Click on a column header [6] to sort the rows by that column. Moreover, any categorical data attribute assigned to either rows or columns supports for sorting its items, for example alphabetically, by their size, or any custom order. In the dialogue for custom ordering within in the centred vertical label [1], it is also possible to hide categories and to display sub-totals (check the option "Combined").
  • Displayed values: The item "Cell labels" in the view options menu [4] configures the precision of the displayed values.
  • Percentual results: The item "Absolute / relative results" in the view options menu [4] switches between absolute values and relative values, for example the percentage of data per cell. References can be specified in the dialog shown when enabling relative results.

Further information

about visualizing categorical data.



Spreadsheet Table

A table showing non-aggregated data records. The table automatically filters to the selected data (i.e., the "Focus") for displaying details of user-selected data records such as outliers. Other common use cases are data editing and data export.



How to get this visualization

Spreadsheet tables are available in all cockpits in the bottom right area of each cockpit. In some cockpits, it may be necessary to explicitly expand them by clicking on the vertical gray area titled "Table".

 

Configuration

  • Select / order data attributes: Choose and re-order the data attributes [1] to be displayed in the table. Several cockpits specify placeholders (shown in italic), for example to show selected variables early in the table.
  • Sort rows: Click on a column header [2] to sort the rows by that column.
  • Scrolling: Use the sliders [3] at the left border and at the bottom to scroll the view.
  • Display bars: Columns showing quantitative variables may also visualize the values as bars. This can be enabled by hovering the column header [2] and clicking on the floating button.

Interaction

Further information



Statistics Overview

Lists all numerical variables and summarizes them by their statistics. The main use case is to select variables for visualization in other views. Additonal use cases are to order variables by information such as the percentage of missing values and to export the table.



How to get this visualization

Statistics overviews are available in the cockpits "Trends and Distributions" and "Multivariate drill-down" (Visplore Professional). Some other cockpits also offer similar tables of variables. The displayed variables can be filtered by their names in the text edit field above of the view.

Configuration

The configuration is similar to Pivot tables. As the main difference, the rows of the Statistics overview correspond to the variables of the data.

Interaction

Click on the name of a variable to select (only) that variable for visualization in other views. Use the check boxes next to the variables (or alternatively the Control or Shift keys) to select multiple variables.

Further information



Heatmap of variables

Powerful method to visualize dozens of variables without clutter. It can, for example, be used as an overview for anomaly detection, trend analysis, correlation analysis, and it is suitable to trace patterns across sensors over time.



Interpretation

The rows of this heatmap correspond to the variables. The columns (i.e., the X axis) can be defined by the user. By default, the columns are temporal units such as calendar days, and can be switched to display any other categorical data attribute such as grades, order IDs, etc. The color displays statistics, for example the mean per cell (default), the standard deviation, and the percentage of missing values. Reading rows from left to right thus conveys how variables change over time (in case that columns are temporal units), or how they differ between categories such as order IDs. Cells with particularly high or low statistics stand out.

Reading the plot vertically allows for comparing variables. To support this, the heatmap standardizes the variables by default so that the visualization becomes independent of their scales. Furthermore, variables can (and are by default) ordered in a way so that similar variables are adjacent. This emphasizes patterns that occur across several variables.

How to get this visualization

Heatmaps of basic statistics are available in the cockpits "Trends and Distributions" and "Multivariate drill-down" (Visplore Professional). The displayed variables can be filtered by their names in the text edit field above of the view.

Other cockpits also offer heatmaps of variables, and display cockpit-specific statistics by color such as the Pearson correlation (cockpit "Correlation") and goodness-of-fit measures (cockpit "Deviation Monitor" in Visplore Professional).

Configuration

Further configuration options (e.g., percentual comparisons between columns) are similar to other visualizations of categorical data.

Interaction

Dragging a rectangle within the visualization with the left mouse button selects the variables of the touched rows as well as the categories of the touched columns. This becomes most effective in combination with the Time series plot below: The heatmap serves as an overview of the data, and the time series shows details of the selected part (hint: enabling "Automatic zooming" in the time series makes this interplay even smoother).

Further information



Histogram overview

Visualizes small histograms for all variables as a quick preview for exploring their univariate distributions. This tool is particularly useful for comparing data subsets.



Interpretation

The variables are ordered by their mutual information with the data selection (the "Focus"). For example, assume you selected a certain time period. The histogram overview will not only highlight the data distributions of that period for all variables, but will also bring those variables on top where the selected period is distributed most differently than the rest of the data. This facilitates to find variables characterizing the selection. The mutual information is conveyed by the intensity of the gray background.

Likewise, the histograms can be used to compare data categories by color (e.g., via the "Compare" features). Also in this case, the histograms will be ordered so that top-ranking variables show the biggest difference in the distribution of the categories. This can help answering questions such as "which variables show a different behavior for A than for B?", where A and B can be, for example, order IDs, user-defined time periods, clusters, and much more.

How to get this visualization

Histogram overviews are available in the cockpits "Trends and Distributions" and "Multivariate drill-down" (Visplore Professional). The displayed variables can be filtered by their names in the text edit field above of the view.

 

Configuration

  • Ranking criterion: Clicking the centred label above the color legend [1] lets you choose whether to use the data selection for highlighting and variable ranking, or a categorical data attribute.
  • The header [2] lets you resize the histograms.

Interaction

Clicking on a variable selects that variable for visualization in the other views. For selection multiple variables, press the "Control" key on your keyboard while clicking the variables.

Further information

about visualizing many numerical variables.



Parallel Coordinates

Parallel coordinates are a visualization technique to display multiple variables. The strength is to rapidly see how clusters and outliers are distributed across over ten variables. Another use case is to specify multidimensional filters.



Interpretation

Each variable is represented by a vertical axis which draws the minimum of the respective variable at the bottom and the maximum at the top. Each data sample is drawn as a line strip that intersects all axes at the positions corresponding to its values. In case you know radar charts: Parallel Coordinates are closely related to radar charts, but the axes are aligned in parallel to each other rather than meeting at the same center point.

Parallel Coordinates work best if the number of data samples is rather small (e.g., up to a few hundreds) or if the data has multiple distinctive clusters. In this case, the intensity of the color reflects the density of the data. For larger data sets, Parallel coordinates can be helpful in combination with data selection, because Parallel coordinates convey the distribution of selected data quite well. Furthermore, a common use case is to define and tune selections on multiple variables, for example for optimization problems with multiple criteria. In this case, the criteria correspond to the axes.

How to get this visualization

The Parallel Coordinates are available in the cockpits "Trends and Distributions" and "Multivariate drill-down" (Visplore Professional). The visualized variables are selected outside in one of the overviews of the variables.

Configuration

Interaction

Select data by dragging (with the left mouse) vertically along an axis. This specifies an interval on that variable. Selections on multiple axes can be defined, for example, via the orange "&" symbol in the toolbar next to the selection.

Further information



Duration Curve

Duration curves visualize the distribution of one or more variables. Their strength is that they precisely convey the percentage of data below / above each value level and also work well for multi-modal distributions.



Interpretation

The Y axis represents the scale of the variable(s). The X axis is always scaled from 0 to 100 and represents the percentage of data. For example, a line intersecting the X value of 20 at an Y value of 1000 means that 20% of the data of that variable (ignoring potential missing values) are larger than 1000 while, conversely, 80% of the data are smaller than 1000. Broad horizontal sections thus correspond to ranges with many samples while steep slopes correspond to ranges with few data samples.

How to get this visualization

The Duration Curve technique is available in the cockpit "Trends and Distributions". The visualized variables are selected outside in one of the overviews of the variables.

Configuration

Disable connection: If the data has non-connected clusters, it can make sense to disable the connection in the view options menu [1].

Further information



3D Scatter Plot

Study correlations and clusters for three variables. The points correspond to the imported data samples.



How to get this visualization

The 3D scatter plot is available in the cockpits "Trends and Distributions" and "Multivariate drill-down" (Visplore Professional). The visualized variables are selected outside of the 3D scatter plot in one of the overviews of all variables. If you select more than three variables, the first three selected variables will be shown.

 

Configuration

  • Axis scaling: Each axis can be scaled individually in the options menu [1] of the view.
  • Point color: Click on the gray area in the top left corner [2] to use color, for example to visualize an additional data attribute.
  • Projection: You can switch between perspective and orthographic projection in the view options menu [1].

Navigationn

Further information



Stacked Categories

Visualizes up to four categorical data attributes (and possibly more by nesting them) as stacked uni-dimensional heatmaps. The two main use cases are (1) to select categories and combinations of categories in multiple data attributes and (2) to characterize data selections in other views.



How to get this visualization

Stacked category views are available in most cockpits, provided that the data contains categorical data attributes and/or a time stamp. In many cockpits, this view is contained in the top right part of the cockpit. For example, the cockpits "Trends and Distributions", "Correlations", "Summaries", and several other cockpits of Visplore Professional contain a tab group titled "Drill down" which contains this view titled as "Categories".

Configuration

Interaction

Clicking on a category in one of the heatmaps selects it just as in other views of categorical data. The other heatmaps automatically filter to that category. Clicking on a category in another heatmap can then be used to easily specify composite selections, such as Status = Error and Month = June and Time of Day = 10 to 12 AM.

Passively, selecting data in other views (for example a certain time period or a cluster in a scatter plot) filters the stacked categories so that it is immediately visible, which categories the selection corresponds to. For this use case, it can be helpful to sort the categories by their size.

Further information



Correlation Matrix

Visualizes two-dimensional patterns and clusters for up to dozens of variables. Color indicates correlations between variables. The main strength is to discover correlations and groups of correlated variables.



Interpretation

The variables define columns and rows of a half-diagonal matrix. Each cell of the matrix corresponds to a pair of variables and (typically) shows a small scatter plot. The color of a cell conveys the degree of correlation between the two variables, by default as the Pearson correlation. Positive correlations are shown in red tones, negative ones in blue (the color mapping can be configured). By default, cells are drawn white where the correlation is not statistically significant according to the p-Value or when no correlation can be computed, e.g., because all values of a variable are identical. Precise values for the correlation coefficient and the p-value can be read from the tooltip that appears when hovering a cell, or by exporting the matrix as a data table.

Please note:

How to get this visualization

The scatter plot matrix is available in the cockpits "Correlations" and "Property Correlation" (Visplore Professional). The displayed variables can be filtered by their names in the text edit field above of the view.

 

Configuration

  • Displayed variables: In addition to the text filter [1] above the view, the item "Select variables" in the view options menu [2] can be used to define the set of shown variables and a custom order for them. Hovering variable names shows an "x" [3] for removing a variable from the matrix.
  • Order of variables: The item "Order variables" in the view options menu [2] supports alphabetical order, custom order, or order by the statistic, i.e., the correlation coefficient by default. In the latter case, the mostly correlated pair of variables is placed on top, and each row adds that variable where the correlation is largest with any of the variables before.
  • Display of scatter plots: The small scatter plots can be disabled in the view options menu [2].
  • P-test: The test of the p-values can be switched off and the p-value used as threshold for visualization can be adjusted in the view options menu [2] item "Hide insignificant pairs".
  • Visualized statistic: in the "Correlations" cockpit, the statistic can be changed by clicking the centred label [4] above the color legend, for example to Spearman's rank correlation coefficient. The statistic "Focus distinction" expresses to which degree the Focus (if any) defines its own cluster and is thus separated from the rest of the data.
  • Scaling: The scales of variables can by adjusted by clicking on their name and choosing the "Adjust range" option.

Interaction

Clicking a cell shows the corresponding two variables in the other views of the cockpit. For large matrices, please use the gray scroll bars at the left and at the bottom.

Further information

about analyzing correlations.



Target Correlation Heatmap

Visualizes the correlations between many variables and one target variable. The strengths are the scalability for up to hundreds of variables, and the possibility to break down the correlations, for example by different data modalities.



Interpretation

Each row corresponds to a variable. Color indicates the Pearson correlation with a target variable. Positive correlations are shown in red tones, negative ones in blue (the color mapping can be configured). The columns (i.e., the X axis) can be defined by the user. They can, for example, be temporal units such as calendar weeks in order to assess the stability of correlations over time, or other data categories in order to compute the correlations separately for structurally different parts of the data.

How to get this visualization

The target correlation heatmap is available in the cockpits "Correlations" and "Property Correlation" (Visplore Professional). The displayed variables can be filtered by their names in the text edit field above of the view.

 

Configuration

  • Target variable: Clicking the centred label [1] above the color legend lets you choose the target variable.
  • Correlation Statistic: Clicking on this label [1] also lets you choose the correlation statistic.
  • Columns: Clicking the centred label [2] at the bottom of the view allows for subdividing the correlations. You can nest multiple data attributes using the "+" signs [3] and order the categories as needed.
  • Sorting the variables: Clicking the vertically centred label [4] at the left border lets you sort the variables.
  • P-test: The test of the p-values can be switched off and the p-value used as threshold for visualization can be adjusted in the view options menu [5] item "p-Value".

Interaction

Clicking on a cell selects the two variables for visualization in the other views.

Further information



Calendar

Displays a heatmap in a pre-configured calendar layout. Rows correspond to calendar months and the cells represent calendar days. The information represented by color and area can be defined by the user.



How to get this visualization

The calendar is available in many cockpits, provided that the data contains a time stamp. In many cockpits, the calendar can be found in the top right part of the cockpit. For example, the cockpits "Trends and Distributions", "Correlations", "Summaries", and several other cockpits of Visplore Professional contain a tab group titled "Drill down" which contains a calendar.

Configuration

Interaction

Clicking on a row label selects the corresponding year / month to be highlighted or filtered in other views. You can also click on cells to select individual days.

Further information



Horizon graphs

An innovative visualization method to display dozens of time series without clutter while preserving details like spikes and oscillations. Use cases include (1) fast plausibility checking of sensor data, (2) detailed comparison of time periods, e.g. for root-cause analysis, (3) searching patterns across time series, (4) tracing events and patterns along sensors of a continuous process.



Interpretation

Each row corresponds to a time series (i.e., a variable). For each time series, its range is subdivided in equally-sized levels which are overlaid for visualization, as shown by the following illustration:

The color indicates the level (e.g., high, medium, low) while the shape of the time series is shown by the border between levels.

Reading rows from left to right conveys the change of variables over time. Reading multiple rows vertically tells, when events such as spikes or drops occurred in time relative to other time series. By default, the horizon graph plot in Visplore normalizes each variable so that the visualization becomes independent of their scales.

The strength of horizon graphs is their ability to visualize many time series while preserving their details. Because color is a strong visual cue, they support a rapid perception of patterns very well - much better and much more scalable than by stacking normal time series plots on top of each other.

The vertical order of the rows can also be used for advantage: Clusters of similar time series are well-perceived if they correspond to adjacent rows - Visplore supports sorting the variables by their similarity. Another good practice is to order the rows manually so that they reflect the order of the sensors along a continuous process. This is a very effective visualization of a process history.

Hint:

To familiarize with horizon graphs, it's helpful to compare patterns with the usual time series plot below in the same cockpit. When hovering the horizon graphs, the time below the mouse cursor is highlighted in the time series plot below, which may facilitate this matching.

How to get this visualization

The horizon graph plot is available in the cockpit "Trends and Distributions". The displayed variables can be filtered by their names in the text edit field above the view.

Configuration

Interaction

Further information



Multi-variable bars

Bar chart for comparing multiple variables which are distinguished by color. The axes can be subdivided by categorical data attributes.



How to get this visualization

Multi-variable bars are available in the cockpits "Summaries" and "Multivariate drill-down" (Visplore Professional). The variables are selected outside the view in one of the overviews of all variables.

Note: This view is very similar to usual bar charts, except that color is reserved to distinguish the variables and can not be defined by the user.

Configuration

Further information



Aggregated line graphs

A line graph visualizing aggregated values of one or more variables, for example for trends or average daily profiles. You can subdivide the axes by categorical data attributes.



How to get this visualization

Aggregated line graphs are available in the cockpit "Summaries". The displayed variables are selected outside the view.

Configuration

Note: Color is used to distinguish variables.

Further information



Box plots

Summarize the distribution of a variable by its median, its inter-quartile range and the range containing 95% of the data. A common use case is to compare categories by their distributions. You can subdivide both axes of the view by additional categorical data attributes.



Interpretation

Box plots are a common statistical chart type for summarizing uni-modal distributions, for example normally distributed data. The inner, filled box indicates the range containing 50% of the data, i.e., the lower end is the 25% percentile and the upper end is the 75% percentile. The border between the dark and light gray areas is the median. The outer "whiskers" show the range containing 95% of the data. The lower end is the 2.5% percentile and the upper end is the 97.5% percentile.

How to get this visualization

Box plots are available in the cockpits "Summaries" and "Multivariate drill-down" (Visplore Professional). The displayed variables are selected outside the view.

Configuration

Note: Color is used to distinguish variables.

Further information



Curves

Visualizes a large number of curves. Examples of curves include daily profiles of an energy load, signatures of many machine operations, batches in batch production, spectral data, and much more. All curves share the axes where X typically represents the time since the beginning of each operation. Key features of this view are interactive tools for selecting curves and aggregated visualizations of curve clusters.

Note: this visualization is only available in visplore professional.



How to get this visualization

There are two different ways to visualize curves:

  1. Extract the curves from (long) time series data by using the cockpit "Pattern Search and Comparison". This cockpit offers multiple options for extracting curves, including temporal cycles such as days and weeks, patterns found by pattern search, and any contiguous time periods which are selected by the user.
  2. Load data with curve-typed data attributes. Such data attributes may come from separate CSV files being indexed from a "main" CSV file, or they can be imported via the APIs to Python and Matlab. For curve-typed data, the cockpit "Multivariate drill-down" offers a curve view that is collapsed by default as a vertical gray area titled "Curves" in the lower right part of the cockpit. The cockpit "Curve Property Definition" also has a curve view and allows for defining features on the curves.

Configuration

Interaction

You can select curves using the following two selection tools. The active tool can be chosen in the view options menu [2].

Further information



Curves vs. Curves

Plots two curve-typed data attributes against each other. A typical use case is the visualization of large numbers of (planar) movements and trajectories where the X- and Y- components of the movements are given as curves.

Note: this visualization is only available in visplore professional.



How to get this visualization

The visualization is available in the cockpit "Multivariate drill-down" (Visplore Professional) if the data contains two or more curve-typed data attributes. Such data attributes may come from separate CSV files being indexed from a "main" CSV file, or they can be imported via the APIs to Python and Matlab. In the cockpit "Multivariate drill-down", expand the vertical gray area titled "Curves" in the lower right part.

Configuration

Interaction

You can select curves using a line tool which selects all curves that intersect the user-defined line.

Further information

about the cockpit "Multivariate drill-down".



Sensitivity analysis and response surface tool

This is an interactive tool for visualizing multivariate regression models. The most common use cases include sensitivity analysis, "what if" analysis, and model validation. The main purpose is to visualize the expected impact of changes in independent variables on a quantitative target variable as predicted by a regression model. These dependencies can be visualized as explicit and implicit function graphs as well as 3D response surfaces.

Note: this visualization is only available in visplore professional.



Interpretation

Assume you have a regression model of a target variable y as a function of three independent variables x1, x2, x3, i.e., y = f(x1, x2, x3). This tool then visualizes how changes of x1, x2, and x3 affect y. The main idea is to visualize this information by breaking it down to multiple lower-dimensional plots, namely function plots, iso-contour plots, and 3D surface plots. All these plots are essentially slices through the four-dimensional cube (x1, x2, x3, y), as shown by this illustration:

To visualize the function graph y = f(x1), for example, the parameters x2 and x3 must be held constant. Likewise, for plotting y = f(x2), x1 and x3 must be held constant, and so on. The principle is thus to specify a user-defined vector (the "focal point") that provides values for all parameters which are not directly visualized in a plot. This vector is graphically represented as sliders that can be dragged by the user to navigate within x1, x2, and x3. The following example shows how a plot can change by altering another parameter outside the plot.

The basic layout is a row of line plots, i.e., y = f(x1), y = f(x2), y = f(x3). Dragging the slider in one plot affects the function graphs in all other plots. Note that parameters can also be categorical. In this case, the predicted value for each category is visualized.

Optionally, the tool also visualizes parameter combinations as additional plots: Implicit function plots show the interaction of two parameters on the target y as iso-contours, while 3D function plots show the combined effect of two parameters on y as a (response) surface in 3D.

In addition to the regression function, the tool also displays the data samples of the loaded data set around the function. This can be used for a qualitative model assessment and also conveys, if the prediction for certain parameter combinations are backed by data at all.

More details are described in this paper:

H. Piringer, W. Berger, and J. Krasser. "Hypermoval: Interactive visual validation of regression models for real-time simulation." In Computer Graphics Forum, vol. 29, no. 3, pp. 983-992, 2010.

How to get this visualization

This tool can be found in the cockpit "Multivariate Regression". It is available once a model has been created.

Configuration

Interaction

The main interaction is to drag the sliders that define the focal point. This allows for answering questions such as, "what would happen to the target, if the parameters changed in a certain way?".

Further information

about the cockpit "Multivariate Regression".




License Statement for the Photovoltaic and Weather dataset used for Screenshots:
"Contains public sector information licensed under the Open Government Licence v3.0."
Source of Dataset (in its original form): https://data.london.gov.uk/dataset/photovoltaic--pv--solar-panel-energy-generation-data
License: UK Open Government Licence OGL 3: http://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/
Dataset was modified (e.g. columns renamed) for easier communication of Visplore USPs.