All plots in Mondrian are fully linked, and offer many interactions and queries. Any case selected in a plot in Mondrian is highlighted in all other plots.

Currently implemented plots comprise Histograms, Boxplots y by x, Scatterplots, Barcharts, Mosaicplots, Missing Value Plots, Parallel Coordinates/Boxplots, SPLOMs and Maps.

Mondrian works with data in standard tab-delimited or comma-separated ASCII files and can load data from R workspaces. There is basic support for working directly on data in Databases (please email for further info).

Mondrian is written in JAVA and is distributed as a native application (wrapper) for MacOS X and Windows. Linux users need to start the jar-file. The latest version can be downloaded here.

If you have any questions or comments, please email mondrian@theusRus.de. Bugs may be submitted to the bug-tracker as well as per email.

News:

• (09/27/22) New versions for Mac added. There are two separate downloads for Intel and M1 both including a full JRE. Download is 50MB(!) now.
  
  
• (12/28/21) Updated the note regarding the Apple Security setting issue to make Mondrian start under Mac OS X 12 again.
  
  
• (08/29/13) New nightly build version 1.5b, fixing performance problems in very large maps and previewing the new universal importer.
  
  
• (07/31/13) Posted some sample demo videos created by Antony Unwin. Once we get some more videos, there will be a video section on this page!
  
  
• (10/03/12) Added new maps for France to the Map Library
  - on departmant level (96 departments), and
  - on regional level (22 regions)
  
  
• (01/11/11) New release: Version 1.2
  The scatterplotsmoother now includes "principle curves", which are one of the nonlinear generalizations of principal components. All smoothers can be plotted for subgroups, which have a color assigned, "smoother by colors".
          The color scheme has been refined once again, to make use of colors as efficiently as possible. The use of alpha-transparency is now consistent between scatterplots and parallel coordinate plots.
          New Transformations: columnwise minimum and maximum. Sorting of levels is now stable, i.e. levels which have the same value for an ordering criterion will keep their previous order.
  The Reference Card speaks Windows now, i.e., Windows users no longer need to translate keyboard shortcuts from the Mac world.
  (Filed bugs fixed since last release: 19, 64, 82, 104, 150, 153, 155, 160, 161, 185, 186)
  
  
• (01/02/11) The web page has been reworked and several issues have been fixed:
  
• A new section with a Quickstart Guide
  
• The order of the plot types now reflects their complexity.
• Technical implementation details are now given where appropriate
• The Map Library has been opened and we hope for many contributions
  
  
• (09/10/09) The slides which go with the book "Interactive Graphics for Data Analysis – Principles and Examples" can now be found on the web.
  They should be a fruitful resource for everybody who wants to learn how to use Mondrian.
  

(10/21/08) Finally "the Book" is out. It covers a 30 page Manual on Mondrian and nine real world case studies in the second part of the book. The first part introduces the most important concepts to get the most out of a tool like Mondrian. See www.interactivegraphics.org for more information.

• (05/24/07) we have a Bugzilla based bug-tracker online. Please submit all bug reports and requests there - feel free to email after submission as well ...
  

Histograms can be weighted. Select two continuous variables (the weights usually should be positive, although Mondrian will not complain about negative weights) and choose weighted Histogram from the plot menu.

   

The example shows a typical situation for weighting in a histogram. The left plot shows the distribution of %blacks for the US Midwest counties. The right plot is weighted with the total population, thus showing us the number of people living in areas with a certain % of blacks.

Some technical definitions of histograms:

Default anchor point: Minimum of sample
     Default binsize: (Maximum - Minimum) / 8.9 -> 9 Bins

R-code for density estimation:
> # no weights
> density(x, bw=bWidth, from=Min, to=Max)
> # weights
> density(x, bw=bWidth, weights=w/sum(w, na.rm=T), from=Min, to=Max)

The density estimate for the selected subsample of size SelN is scaled
by a factor SelN/N. 

The bandwidth bWidth of density estimators is always identical to the 
current binwidth of the histogram itself.

Manual reordering of the classes is possible by reordering the levels in a corresponding barchart.

The context menu offers options to sort the levels by either median or IQ-range (and to reverse a current ordering.)

Boxplots y by x for the cars data set - heavy cars selected.

Parallel boxplots are very similar to parallel coordinate plots, and share most of their functionality.

In contrast to other plots in Mondrian, scatterplots offer axis information, showing the maximum and minimum for orientation.

Query methods for scatterplots operate on three levels. The first level simply gives the position of the cursor, which is displayed as a projection on the x- and y-axes. This query is invoked by  pressing the alt key. Pressing control invokes the second level of querying. A tooltip is presented with the data of the variables in the plot for the points at the cursor. If more than one point is found at the same distance, a list of the cases is presented in the tool tip. Holding shift and control shows the information of any selected variables in the variables list, i.e., an extended query showing data, which are not displayed in the plot.

orientation	objects	extended

         Three levels of queries in a scatterplot

• least square regression (does not need R)
• loess smoother
• regression splines (with confidence intervals)
• principle curves
  

Initial pointsize: 3 points (in-/decrease +/- 2 points)
Initial alpha-transparency: 

  if( n < 400 )
    alpha = 0%
  else if ( n < 800 )
    alpha = 25%
  else if ( n < 1600 )
    alpha = 50%
  else if ( n < 3200 )
    alpha = 62,5%
  else if ( n < 6400 )
    alpha = 75%
  else
    alpha = 87,5%

Definition of Smoothers 
(with "smoother" being a positve integer degree of smoothness, "xf" the
 points where the smoother shall be evaluated.)
>
> # loess
>
> predict(loess(y ~ x, span=3.75/smoother, 
                       degree=1, 
                       family=symmetric, 
                       control = loess.control(iterations=3)), 
                       data.frame(x=xf)
         )     )
>
> # splines
>
> predict(lm(y~ns(x, smoother)), interval="confidence", data.frame(x=xf))
>
> # principle curves
>
> principal.curve(as.matrix(cbind(x,y)), spar=0.3+6*(1/smoother+2))

Besides standard selection and interrogation techniques, interactivity in a barchart includes:

• Reordering of levels via drag & drop (use <alt>-click on a bar or its text to drag)
  (Dropping between categories inserts, dropping on categories exchanges categories)
• Switch between proportional width and height, between barchar and spineplot
  
• Sort levels by 
• frequency
• name 
• absolute highlighting 
• relative highlighting
• Reverse current order 

A barchart for the Titanic dataset. First class passenger are highlighted. 

Use <meta>-+ and <meta>-- to add and delete interactions during the modeling process using the ModelNavigator. During the model process one may want to use the plot option to show the expected values of the model and not the observed values.

The picture below shows an example from the Titanic dataset, which includes information on the class (1,2,3 crew), age (child, adult) and gender (male, female) of the passengers. Surviving passengers are highlighted.

Although there are no labels to decode the cells, the order of the variables is given in the title of the window. Using interactive querying it is easy to check what the cells represent. In this static representation the fact that there are no children and hardly any women in the crew, should be sufficient to decode the plot.

Additionally Mondrian features four variations of mosaicplots. The figures below show the same data from the cars data set, in all five possible variations. Use the pop-up menu for the plot options:

Observed values	Expected values (according to current model)
Same bin size	Fluctuation diagram
These plots show the five different variations of mosaicplots. Whereas the first two options are "real" mosaicplots, the other three versions (same bin size, fluctuation diagram and multiple barchart) are more useful for handling only a few variables with many categories, which is the worst case for a standard mosaicplot. For these three variations, Mondrian plots the category labels for the first two variables, since the categories are equally spaced and so can be easily labelled. By typing shift-up-arrow and shift-down-arrow, the size of boxes can be zoomed. As soon as a box reaches its maximum size, it is red-framed to indicate the incorrect size.
	Multiple barcharts

Besides standard selection and querying, interactivity in a parallel coordinate plot includes:

• Reordering of the variables via drag & drop (use <alt>-drag)
  
• Switch between common and individual scaling (also for selected subsets of axes)
• Adjust α-level of lines via the context-menu or the left and right arrow keys.
• Select Axes by a single click on the axis name and use:
• BACKSPACE to delete this axis from the plot
• <meta>-I to invert the axis
• Type PAGE-UP or PAGE-DOWN repeatedly to cycle through the minimum number of orderings for seeing ALL adjacencies of the variables in the plot.
  (Note: For k variables we need [(k+1)/2] permutations as shown in Ed Wegman's 1991 paper)
  

• HotSelection only shows the currently selected points in PCPs
• Crop Selection removes the currently selected lines from the PCP. Subsequent crop operations allow you to peel a data set. (only works for lines)

A parallel coordinate plot for the olive oil data.

A parallel box plot for the olive oil data.
 

A corresponding data record must be provided for each polygon defined in the dataset. Different polygons might point to the same data record, but multiple records to a set of polygons are ignored.

Maps offer the standard selection and querying tools. Additionally the standard zooming function of Mondrian is available.

All maps have a popup-menu at the top to create a choropleth map of any of the variables.
Further options include:

• Color schemes
• "white to black"
• "red"
• "green"
• "blue"
• "blue to red"
• "blue to white to red"
  
• if R and Rserve are installed
• "heat"
• "terrain"
• "topo"
  
• Invert color scheme
  
• Assign color linearly, normalized, or by rank
• Limit minimum or maximum to a specific value
  

The saturation (more precisely the alpha) of boundaries can now be changed with the right arrow key (more saturation) or left arror key (less saturation).
This can change the perception of the map drastically, so make sure to test it out!

US County Map with full saturation:


US County Map with reduced boundaries:

Note the extreme difference between the maps. (We call this technique map-martinizing…)

Color scheme definition in Maps:

Mappings:

- linear
    intensity = (value-min) / (max-min)

- rank
    intensity = rank(value) / n

- normal
    intensity = (qnorm( rank(value) / n )+3)/6;

Color Schemes:	      

- grayscale
    RBG(1-intensity, 1-intensity, 1-intensity)

- red
    RGB(1-intensity^4/2, 1-intensity, (1-intensity)^3/1.5+0.15)

- green
    RGB( 1-intensity, 1-intensity^4/2, (1-intensity)^3/1.5+0.15)

- blue
    RGB((1-intensity)^3/1.5+0.15, 1-intensity, 1-intensity^4/2)

- blue to red
    RGB(intensity, 0, 1-intensity)

- blue to white to red
    if( intensity < 0.5 )
       RGB(2*intensity, 2*intensity, 1)
    else
       RGB(1, 1-(intensity-0.5)*2, 1-(intensity-0.5)*2)

if R and Rserve are installed

- heat
- terrain      (see R documentation for details)
- topo

• Definition in a barchart or a mosaic plot using <meta>-b assigns a discrete scheme
  

• Definition in a histogram using <meta>-b assigns a continuous "rainbow"-scheme
  

• Individual colors may be assigned using <meta>-1 to <meta>-9

	LEFT: The map of the German electoral districts is colored according to the party winning the most votes in 2009. TOP: The barchart shows the same coloring for the different states.

• Permanently defined colors always interfere with the highlighing color and may cause confusion
• Whereas overplotting is no problem for highlighting (highlighted cases are alway plotted on top) the overplotting issue with multiple colors can not be resolved satisfactorily (α-transparency won't work well here).

Qualitative (i.e., discrete colors)

// Color Brewer: 12, qualitative, Set3

   Color[1]  = RGB(128, 177, 211)
   Color[2]  = RGB(188, 128, 189)
   Color[3]  = RGB(179, 222, 105)
   Color[4]  = RGB(253, 180, 98)
   Color[5]  = RGB(252, 205, 229)
   Color[6]  = RGB(141, 211, 199)
   Color[7]  = RGB(251, 128, 114)
   Color[8]  = RGB(204, 235, 197)
   Color[9]  = RGB(255, 237, 111)
   Color[10] = RGB(190, 186, 218)

   Color[11..20] = Color[1..10].darker()
   Color[21..30] = Color[1..10].darker().darker()
   Color[31..  ] = Color[1..10].darker().darker()


Quantitative (i.e., continuous colors)

   for(i=1..k) 
     brushColor[i] = HSB(0.225 + i/k*0.8, 0.5, 1.0);

In an interactive graphical system, possible interactions can be carried out with mouse and keyboard. Since JAVA programs are not bound to a specific platform, Mondrian tries to only makes use of features, which can be found on all platforms. There are some restrictions like the one-button-mouse for most MAC-users (Steve give us the right button!!). The most commonly found modifier keys are SHIFT, CONTROL, ALT and META. CONTROL is blocked as the popup-trigger on the Macintosh, META misused under Windows and ALT blocked by many window-managers under Linux.

The interactions in Mondrian are assigned as follows:

• click -> select a single object
• click and drag -> create a selection (rectangle)
• META-click and drag -> zoom in/out (middle-click (wheel) and drag on Windows & Linux)
  
• CTRL and mouse-over -> query object (use CTRL-SHIFT to get extended query)
• ALT and mouse-over -> query coordinates in plot
  
• popup-trigger on background -> alter the plot setting
• ALT-click and drag -> reorder objects

The figures below show an application using the well known "pollen" dataset.

The so-called ModelNavigator allows a stepwise graphical modeling of loglinear models.

The ModelNavigator basically inverts the use of graphs and models. Whereas packages like R or S-Plus usually assume a model, for which diagnostic plots can be plotted, the approach in Mondrian starts with a graph, then sets up a model, and uses the statistical measures as diagnostics, to check the graphical conclusions.

For a more precise description of this technique see the paper on Visualization of Loglinear Models.
 

Numerical and alphanumerical data are both allowed. See example below:

Double click (or use <meta>-T if you need to change more than one variable) a continuous variable () to change it to be categorical (). Vice versa double click  to change to . Alphanumerical variables are tagged as  and cannot be changed to another type. To get a fast and effective overview of which variables have missings, there are 'white'-versions of the icons of all three types, i.e. , and indicating at least one missing in the particular variable. When working with very many variables, just type the prefix of a variable name to search for a particular variable and to make the variable window select all those variables and also scroll to the first hit.

numCases <- Number of instances in the dataset
numCat <- Number of distinct cases in a variables

if( not is.numerical(x) ) then
    mode(x) <- "alphanumerical"
else 
    if ( numCases > 800 ) then
        if( numCat < 15 * log( numCases )/log(10) - 1 )
             mode(x) <- "categorical"
	else
             mode(x) <- "continuous"
    else
        if( numCat < 1.5 * sqrt( numCases )
             mode(x) <- "categorical"
	else
             mode(x) <- "continuous"

The threshold as R code snippet:
>
> i <- 1:1500
> 
> plot(i, (i>800)*(15 * log(i)/log(10) - 1) + (i<=800)*(1.5 * sqrt(i)),
       type='l')
> 

The format for map-data

The dataset must include one variable of references, which the polygons refer to. This variable must start with '/P'. If a dataset is asociated with polygons, there must be an empty line after the data matrix followed by the relative path+filename to the file containing the map data.

In the map file, each polygon must be defined as follows:

It must start with a header like
id \t name \t n
where id is the matching id from the reference variable. Name can be any arbitrary string naming the polygon. n is the number of points in the polygon.
This header is followed by x and y coordinates defining the polygon - separated by tabs, one pair per line. The first and last coordinates must match, i.e. the polygon must be closed.

An example for Union county:
...
-1.3050 0.7141

1761 /Pnew jersey,union 25
-1.2981 0.7112
-1.2997 0.7100
-1.2995 0.7097
-1.2990 0.7099
-1.2988 0.7098
-1.2991 0.7094
-1.2992 0.7090
-1.2999 0.7086
-1.2985 0.7088
-1.2969 0.7089
-1.2969 0.7088
-1.2964 0.7087
-1.2954 0.7088
-1.2951 0.7090
-1.2947 0.7095
-1.2945 0.7095
-1.2942 0.7100
-1.2942 0.7102
-1.2945 0.7103
-1.2949 0.7103
-1.2956 0.7106
-1.2965 0.7108
-1.2970 0.7107
-1.2976 0.7108
-1.2981 0.7112

1762 /Pnew jersey,warren 33
-1.3112 0.7149
...

> write.table(rDataSetToDump, 
              "<WhereYourWorkspaceSits>/.MondrianTmpImport.txt", 
              quote=FALSE, 
              sep="\t", 
              row.names = FALSE)

Currently this type of connection, which leaves the data entirely inside the database, is under further development and is thus not available in the latest releases.

The figure below shows the database connection dialog: 

- +, -, *, /
- -x, 1/x
- log(x), exp(x)
- min(x1, ..., xk), max(x1, ..., xk)
  (creates two new variables, one with the value, 
                              one with the variable label)

MDS (multidimensional scaling)
creates a scatterplot of the 2-d scaling:
>
> tempD <- dist(scale(tempData))
> is.na(tempD)[tempD==0] <- T
> startConf <- cmdscale(dist(scale(tempData)), k=2)
> sMds <- sammon(tempD, y=startConf, k=2, trace=F)
>

PCA (principal component analysis)
creates k principal components out of k input variables
>
> pca <- predict(princomp("+call+" , 
                          data = tempData, 
                          cor = [FALSE|TRUE], 
                          na.action = na.exclude))
>

Here are the color definitions in RGB HEX

		Background   Objects      Text/Lines   Highlighting
RoSuDa classic	(ff,ff,99)   (c0,c0,c0)   (00,00,00)   (00,ff,00)
Terra di Siena	(df,b8,60)   (c0,c0,c0)   (00,00,00)   (b4,60,87)
Xtra red	(ff,ff,B3)   (c0,c0,c0)   (00,00,00)   (ff,00,00)
DataDesk	(00,00,00)   (00,00,00)   (ff,ff,ff)   (ff,00,00)
Daltonian	(00,99,99)   (c0,c0,c0)   (00,00,00)   (ff,74,00)

Changes in Version 0.99 as of 11/18/2003
- Three new variations of Mosaic plots (same bin size, fluctuation diagram and multiple barcharts)
- Automatic sorting of axes in a parallel coordinate plot
- Use meta-R to switch the splitting direction of the last variable in a Mosaic plots
- Inverse color scheme for density highlighting in scatterplots
- Preference box to set highlight color and background color
- Zooming under Windows is still delayed because of a yet to be finalized major update on the interface

Changes in Version 0.98 as of 03/22/2003:
- Boxplots y by x. Just select a continuous variable and a categorical variable and choose 'parallel boxplots' in the plot menu.
- Regression lines in scatterplots (can be queried)
- Highlight color is now red!
- Add lines in scatterplots by third variables to visualize paths and other relationships.

Changes in Version 0.97a as of 11/21/2002:
- oneClick selection is introduced, i.e. a selection rectangle of size 0 will only select the clicked object, but NOT create a corresponding selection rectangle (selection is only temporary as with the select all feature (META-a))
- Bug fix in Scatterplots
- Update on selection rectangle appearance

Changes in Version 0.97 as of 7/12/2002:
- META-a will select all points in any plot now
- alpha-channel works in scatterplots (use arrow keys to change) and parallel coordinates (via pop-up).
- scatterplot are automatically binned, if the dataset is really large (can be overridden)
- interrogation in maps added

First public release 0.96 as of 4/9/2002

Note: The JAR-file can be started by a simple double click. Within Windows, Sun's JRE or JDK must be installed (make sure that .jar files are not associated with any decompression application), Mac OS X users just smile.

This is quite misleading and actually complete nonsense (no matter which language you are running macOSX in). The application is NOT damaged or whatsoever corrupted. 

Once you copied Mondrian to your Applications folder you may simply fix this problem by opening Terminal and typing:

> xattr -d com.apple.quarantine /Applications/Mondrian.app

This takes Mondrian out of quarantine (an awkward naming choice in COVID-19 times!), where all downloaded apps end up, if they do not adhere to Apple's certificates.

> install.packages("Rserve")

> Rserve()

• all variables have a name in the header, i.e. the first row/line
  (When saving data from R without omitting the row names, the "row.name" column has no header name!)
  
• there are empty cells in the file. Mondrian currently does not tolerate empty entries, you have to use "NA".
  

1. There is no application associated with the suffix .jar. To change this, follow these instructions.
2. Another application "grabbed" the responsibility for .jar-files - usually "WinRAR" - after the installation of the JRE. To change this, you must:

• Launch the WinRAR application
  (Start -> Programs -> WinRAR -> WinRAR)
• Once the application has been started, select "Options", "Settings".
• Select the "Integration" tab.
• This tab lists all associated file types for the WinRAR application. De-select the "JAR" type and click "Ok".
• Close the WinRAR application.