Alternatives to box plots for comparing clustering results

In my research paper, I wish to compare the accuracy of 2 clustering algorithms. I have conducted clustering using these 2 algortihms on 300 proprietary datasets. I use adjusted rand index as the evaluation metric. Since, clustering has been conducted 300 times, I have 300 pairs of adjusted rand indexes to be compared against each other. I need a method to graphically show the performance of both algorithms and compare them. Due to space constraint, I could not use barcharts. Another alternative is to use box plots. I have some apprehension in using box plots to compare clustering algorithms' performances in academic research papers as I have not seen many papers using this approach. My questions:

1. Is it OK to use box plots in this scenario in academic papers?
2. If not, what alternative plots/ techniques could be used to graphically compare the 2 algorithms? (NOTE: I just want to compare the adj. rand indexes and NOT the time consumed or algorithmic complexity of the 2 algorithms)
3. It will be helpful if one could refer papers where similar comparisons are done.

Thanks.

• Using two boxplots comparing the two algorithms might not be sufficient to show the difference. You have paired data, and thus it would be nice to retain that. How about a scatter plot with a line with slope 1 and intercept 0? – ziggystar May 18 '14 at 13:29
• Thanks Ziggystar for the comment. //How about a scatter plot with a line with slope 1 and intercept 0// - could you please elaborate on this? – Annamalai N May 18 '14 at 14:11

Box plots or histograms sound fine for getting an overview, but consider coupling the overview with a scatter plot of the two algorithms' Rand index values, which preserves the pairing (as commenter @ziggystar suggested). Each dot on the scatter plot represents the two scores for a single dataset. With the reference line at slope = 1, dots above the line show where Algorithm B did better and dot below the line show where Algorithm A did better.

Here's an example with semi-random data. Depending on how your scores compare, you might call out clusters of dots in the graph.

The overview plot shows the overall quality of the algorithm, and the scatter plot shows if the overall quality difference holds in general. Or maybe there are particular data sets where the algorithm that's poorer overall does better.

An alternative if there are only a few data sets with much variation is a parallel coordinates or slope graph, which has the advantage of putting both indices in the same dimension and allowing for more regular labeling of individual outliers. Example with a few pairs labeled (and deviations colored): 