[I found a typo and updated the MDS_visualization.Rmd script on 10/8/26]

The long awaited script for MDS visualization is finally here!  It took so long in part because I'm not great at math, and rotating the dimension scores is matrix multiplication.  Thankfully, with Ryan Lidster's help on that part, you can now plot your MDS output and rotate the points to your heart's content.

The R Markdown file is available here, and an example of its output is available in this pdf.  As you can see, MDS_visualization.Rmd takes the output files created by MDS_Analysis_new.Rmd as input, such as MDS_3D_AllContexts.txt.  It works with both 2D and 3D solutions, but make sure you pay attention to which you are choosing because there are different chunks you should run based on 2D versus 3D. 

After reading in your file, the script creates new columns from the row names.  You want columns for however you want to group your dimension scores in the figure.  In this example, we want each length template to have the same color (one color for CVCV, another for CVVCV, etc.) and each speaker to have the same shape (square for speaker N, circle for speaker L, etc.).  Since our row names are typically condition_speaker, the script separates the two based on the underscore delimiter.  If you've used another way of naming your rows, the stringr package has a lot of options for string manipulation.  Also, since the script pulls the labels from the "condition" column, you'll want to make sure your condition names are the ones you want to have in your figure (e.g., IPA symbols).  The script has an example of using stringr to find and replace condition names.

The script then uses the ggplot2 package to create the scatterplots.  This package is very versatile, and you can change essentially any part of the plot to look how you want (title, axes, colors, sizes, labels, etc.).  For example, because dimension scores are not inherently meaningful on their own, I've removed the numerical tick marks from the axes.  Here is what our first plots look like.  Since this is a 3D solution, we have both Dimension 1 by Dimension 2 and Dimension 1 by Dimension 3 (the second plot basically looking at the first plot from above).

If you don't like the orientation of the coordinates, this is where matrix rotation comes into play.  If you think of a 2D solution as dots on a flat piece of paper, if you spin the paper around, you can see them from different angles, but the distances between the dots don't change.  We can do the same in three dimensions, like turning a cube all around in your hand.  The only important thing is that we don't change the distances between points, since figuring out distances is the purpose of an MDS analysis.  

In order to do rotation, we can spin the coordinates around the x-axis, y-axis, or z-axis.  Here is a great visual example of rotating around each of these axes from ​jsfiddle.net/greggman/Lqg93y1v/. 

We tell the script to do this by inputting how much of a rotation we want in radians.  Below is a handy guide for converting angles to radians from this site.

You can put π into R as "pi", so pi/2 is a 90º rotation, pi is a 180º rotation, and (3 * pi)/2 is a 270º degree rotation.  Let's say we want to rotate our solution 90º around the z-axis.  Below is what this would look like.  As you can see in the first plot, the points have moved counterclockwise a fourth of the way around.  If you look at the updated dimension scores in the new dataframe MDS_points_rotated, you'll notice that because we're rotating around the z-axis, none of the D3 scores have changed.  In the second plot below, this means that all of the points are at the same height as in the original plot.

If you want to rotate around more than one axis, change the input of the relevant rotation chunk to the output of the previous rotation (MDS_points to MDS_rotated_points).  Here is what it would look like if we also rotated the already rotated solution 90º around the y-axis.

Use the rotations to help you understand how listeners were grouping the stimuli.  In this case, the original dimension scores are clearer, since for Dimension 1 at least, we can also see a divide with points with short V1 on the left and those with long V1 on the right.  Perhaps we would want to rotate -45º along the z-axis to make this distinction sharper.  You can also think about what makes most sense visually for your audience, such as putting /i/ in the top left corner in a study looking at vowels. 

​Once you're happy with your rotation, be sure to save the image(s) with the ggsave chunk at the bottom of the script.  There is also a chunk for saving the new dimension scores, which you can use later if you want to correlate acoustic/phonological properties with the dimension scores to find out what cues listeners were using to group the stimuli.

This script will save text files of the dimension scores for 1, 2, 3, 4, and 5 dimensional solutions.  The dimension scores are the points in space of each stimulus. In the image below, we see the 3 dimensional solution of our Finnish length data, combined across contexts.  You can think of D1, D2, and D3 as (x, y, z) coordinates.  For example, in row 7, we see that the average CVCCVV token for speaker N (averaged across pata, tiki, and kupu contexts) is placed by the MDS solution at x = 0.00527, y = -0.59382, z = -0.41867.  

When Dimension 1 x Dimension 2 (i.e. x and y coordinates) and Dimension 1 x Dimension 3 (i.e. x and z coordinates) are plotted , we see where CVCCVV_N is placed relative to other stimuli.  You can think of the second graph (Dim1 x Dim3) as viewing the first graph from above. 

In these plots, you can somewhat see that the stimuli are grouping together mainly by vowel length rather than consonant length (e.g. Dim 1 has mostly short V1 on the left and long V1 on the right), but it's still difficult to interpret.  For this reason, we recommend rotating the solution (i.e. moving all of the points in a certain way by a specific amount) to provide a better visualization.  This doesn't change the position of the points relative to each other, which is the important part in an MDS solution.  My colleague Ryan Lidster did this in Excel, but since that was rather clunky, I'm working with him on creating an R script to aid in rotating MDS solutions and plotting them.  Stay tuned!  [Edit 4/13/26: We finally have a script for visualization that includes rotation!  See the next blog entry.]

Added 4/13/26:
Finally, this new version of the script outputs matrices of Euclidean distances between stimuli.  These are useful if you want to compare MDS distances for contrasts to their accuracy in a discrimination task, as we did in our 2023 paper.  I'll have more information about this in a later blog entry.

To analyze your data with the R script below, you'll need 2 files: 

• Your Lookup Matrix file, which details which stimulus corresponds to which number on which slide.  How to create this file is explained in the blog post here.  This file should be saved as a tab-separated text file.  The example Lookup Matrix from our Finnish length experiment is available here.
• Your Coded FC Results file, which codes the results from each participant's free classification PowerPoint task.  How to create this file is explain in the blog post here.  This should also be saved as a tab-separated text file.  Make sure your stimuli are in the same order across contexts, since the R script outputs results in alphabetical order, and the combined contexts results will be inaccurate if the orders are different across contexts.  The example Coded FC Results file from our Finnish length experiment is available here.

You'll use this R Markdown file to analyze your results (if you don't have R and RStudio, download those first).  The comments in the script show what you should get if you analyze the example files above.  Don't forget to set your working directory to the file path where your files are located and to change the file names to match your Lookup Matrix and Coded FC Results files.

The R code will create various similarity and dissimilarity matrices (by counts,  by percentages, by contexts individually and combined, etc.) that can be used to visualize your results and analyze them with multi-dimensional scaling.  These will be saved to your working directory as text files with the name as specified in each code block.  Note that when you open these files, the headers will be one column off, since they'll start at the very left.  Let's look at one file as an example.  Below we have a screenshot of the tab-separated text file for similarity in percentages for Context 1 (in this case "upu") with all speakers combined.

As you can see, the header cVccV_upu at the top left should be the header for the first column of numbers.  If you want to make a table with these results, I recommend opening this file in Excel and moving all of the headers one column to the right.  (Note that you do NOT need to do this to use the R script for multi-dimensional scaling described in the following blog post.)  The file will now look like this:

This file shows us that, for example, [kuppu] tokens and [kuuppu] tokens were grouped together 19.7% of the time (column B, row 6).  Since this is the similarities for all speakers combined, the numbers along the diagonal show how often the sound files of the same stimulus spoken by different speakers were grouped together (not very often; English speakers are bad at length).

​The R code can handle up to 4 different contexts.  If you have more than 4 contexts, have more than 2 versions (i.e. Version A and Version B for counterbalanced order of presentation), or find any errors with the code, let me know at daidoned AT uncw.edu and I can modify/fix the script.

Once you have results for your free classification task, you'll need to code what stimuli participants grouped together.  We recommend having around 30 participants or more for your eventual analysis.  If you use the format pictured below, you will then be able to use an R script that creates similarity matrices from your data.

Make sure you label your columns this way so that the R script will work correctly.
Subject: The participant's ID 
Version: The version of the task that the participant did

• For example, in our Finnish length task we had two versions for the different orders of slides that we counterbalanced.  In version A, the "ata" context (pata, paata, patta, etc.) was on slide 1, the "iki" context (tiki, tiiki, tikki, etc.) was on slide 2, and the "upu" context (kupu, kuupu, kuppu, etc.) was on slide 3.  In version B, the "upu" context was first, the "iki" context was second, and the "ata" context was third.  Be sure to use the letters "A" and "B" for your coding instead of numbers.  If you only have one version, label them all version A.  You'll still need this column for the R code.  If you have more than 2 versions, the R code won't work.  Send me an email and I can modify the script for you.

Slide: The slide that you are coding
Context: The context for that slide
Group: Which group on that slide you are coding
Tokens: Which tokens were grouped together in that group

Let's use the following participant's results as a model.  Here is their first slide:  ​

This participant's ID is B50.  They did version A of our task.  This is slide 1, and in Version A, the context on the first slide is "ata".  They made 5 groups of stimuli on this slide, so let's choose a group at random and code it, for instance the group at the left containing 19, 14, 23, 20, and 24.  Since this is the first group we're coding on this slide, we can label it group 1 under Group and put in the token numbers under Tokens.  For the token numbers, we want to separate them with commas and no spaces.  It doesn't matter what order the token numbers are in within that cell.  So now we have:

If we code the rest of the groups on this slide, we have:

Here is B50's second slide:

And below is the coding for this slide added to the spreadsheet.  Since B50 made 4 groups on this slide, we only have 1-4 under Group:

Here is B50's slide 3:

This participant's results are finished being coded!  Do this for all your participants and you'll be ready to analyze your data.  You'll need to save this spreadsheet as a tab-separated text file for use with the R script to create similarity matrices.

In this post I'll discuss how to create a free classification task, also known as a free sort task, which we apply to non-native perception in Daidone, Kruger, and Lidster (2015).  This task is useful for determining the perceptual similarity of non-native sounds and examining what acoustic, phonological, or indexical dimensions of the stimuli matter for listeners.  It can be used to examine segmental or suprasegmental phenomena and can be used to predict their discriminability (check out our slides from New Sounds 2019).  Here is an example of what our Finnish length free classification task looks like in PowerPoint.  The numbers on the slide are sound files that participants click on and listen to and then group by which seem similar to them.