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Methods and open-source toolkit for analyzing and visualizing challenge results

Manuel Wiesenfarth, Annika Reinke, Bennett A. Landman, Manuel Jorge Cardoso, Lena Maier-Hein, Annette Kopp-Schneider

arXiv:1910.05121v2cs.CVstat.AP

TL;DR

Biomedical challenges are widely used to benchmark image-analysis algorithms, but uncertainty in challenge results has received little attention. The paper presents methods and an open-source toolkit for analyzing and visualizing single- and multi-task challenges, and applies them to simulated and real examples. The authors report that these methods reveal insights into algorithm performance that common techniques such as ranking tables and boxplots cannot show.

  • Problem

    Uncertainty in challenge results has received little attention despite the use of biomedical challenges to benchmark image-analysis algorithms.

    Source: §I · p. 1, D. Investigating ranking stability · p. 3

  • Method

    The paper proposes analysis and visualization methods for single- and multi-task challenges and implements them in the open-source challengeR toolkit.

    Source: §I · p. 1, §VII · p. 10

  • Results

    Applied to simulated and real challenges, the methods offer intuitive insights into algorithm performance that ranking tables and boxplots cannot reveal.

    Source: §VII · p. 10

  • Takeaways & Limitations

    The toolkit was designed for biomedical image-analysis challenges but may also be applied to validation studies and other fields.

    Source: §VII · p. 10

Abstract

from arXiv · show

Biomedical challenges have become the de facto standard for benchmarking biomedical image analysis algorithms. While the number of challenges is steadily increasing, surprisingly little effort has been invested in ensuring high quality design, execution and reporting for these international competitions. Specifically, results analysis and visualization in the event of uncertainties have been given almost no attention in the literature. Given these shortcomings, the contribution of this paper is two-fold: (1) We present a set of methods to comprehensively analyze and visualize the results of single-task and multi-task challenges and apply them to a number of simulated and real-life challenges to demonstrate their specific strengths and weaknesses; (2) We release the open-source framework challengeR as part of this work to enable fast and wide adoption of the methodology proposed in this paper. Our approach offers an intuitive way to gain important insights into the relative and absolute performance of algorithms, which cannot be revealed by commonly applied visualization techniques. This is demonstrated by the experiments performed within this work. Our framework could thus become an important tool for analyzing and visualizing challenge results in the field of biomedical image analysis and beyond.

I. INTRODUCTION

Biomedical challenges have substantial scientific and clinical stakes, yet their design, reporting, and visualization have received limited attention. The paper proposes systematic methods and open-source software for analyzing single- and multi-task challenge results, with analysis grounded in defined challenge inputs and ranking choices.

I. INTRODUCTION

  • Challenge rankings can affect publication, scientific careers, and clinical uptake, but challenge reporting and design standards are poor and rankings are sensitive to design parameters.Published results often omit visualizations of uncertainty, which can obscure ranking stability.Source: §I · p. 1
  • The paper proposes systematic analysis and visualization methods, alongside the open-source challengeR framework, for single- and multi-task challenge results.The methods address ranking stability and robustness to ranking-method choice.Source: §I · pp. 1–2

II. DATA AND DATA PROCESSING

  • Challenge ranking requires performance metric values, tasks, competing algorithms, test cases per task, and a rule for handling missing values.The paper calls the resulting challenge outcomes “assessment data,” distinguishing them from the imaging data given to participants.Source: §II · p. 2

A. Assessment data

The paper illustrates its analysis with simulated ideal and random challenges and real Medical Segmentation Decathlon results. It describes three ranking approaches and explains how ties are handled.

A. Assessment data

B. Ranking methods

  • Aggregate-then-rank aggregates metric values across test cases before ranking algorithms, whereas rank-then-aggregate combines per-case ranks.Aggregates may use the mean, median, or another quantile; rank aggregation can also use distance-based approaches.Source: B. Ranking methods · p. 2
  • Test-based procedures compare algorithm pairs statistically and rank them from resulting relations or counts of significant tests.Ties in challenge rankings receive the minimum rank; larger algorithm sets generally bring greater ranking instability and more ties in test-based procedures.Source: B. Ranking methods · pp. 2–3

C. Comparison and aggregation of rankings

Rankings can be compared using distance or correlation measures, and multi-task challenges can use a consensus ranking. Ranking stability matters across ranking methods, sampling variability, and tasks.

1) Comparison of rankings:

  • Kendall’s τ measures correlation between ranking lists, while Spearman’s footrule and Spearman’s distance measure rank discrepancies [6, 7, 8].Kendall’s τ ranges from −1 for inverted order to 1 for identical order; footrule sums absolute rank differences and Spearman’s distance sums squared differences.Source: 1) Comparison of rankings · p. 3

2) Consensus Rankings:

  • A consensus ranking can minimize distances from task-specific rankings; using Spearman’s distance yields average ranks, with each task weighted equally unless weights are assigned.Ties use average ranks when averaging across tasks.Source: 2) Consensus Rankings · p. 3

D. Investigating ranking stability

  • Ranking stability across methods, sampling variability, and tasks—reflecting algorithm generalizability—is especially important when test-case counts are small.Source: D. Investigating ranking stability · p. 3

1) Bootstrap approach:

The paper describes bootstrap and significance-testing approaches for assessing ranking uncertainty, then introduces visualizations of assessment data. These methods address variability across samples and make algorithm-level distributions and rankings inspectable.

1) Bootstrap approach:

  • Bootstrap resampling assesses ranking stability under sampling variability by repeatedly applying a ranking strategy to samples drawn with replacement.For a task with n test cases, each bootstrap sample draws n cases; rankings or their correlations and distances from the full-data ranking can then be examined.Source: 1) Bootstrap approach · p. 3

2) Testing approach:

  • Pairwise significance tests can assess differences between algorithms, but multiple comparisons require adjustment such as Holm’s procedure.A nonsignificant result may reflect too few test cases and is not evidence that a difference is absent.Source: 2) Testing approach · p. 3

III. VISUALIZATION FOR SINGLE-TASK CHALLENGES

  • Single-task visualizations are organized around assessment-data distributions and ranking stability, with algorithms ordered by a selected ranking method.The illustrated ordering uses aggregate-then-rank with the mean.Source: §III · p. 3

1) Dot- and boxplots:

  • Dot- and boxplots show per-algorithm metric distributions and individual test-case values, but do not link results from the same case across algorithms.Consequently, a test case on which all methods perform poorly cannot be identified from these plots alone.Source: 1) Dot- and boxplots · p. 3
  • Podium plots connect metric values from the same test case across algorithms, while ranking heatmaps count test cases at each algorithm-rank combination.Podium plots require unique ranks, assigning random ranks to ties, and become difficult to use with many algorithms; heatmaps abstract from metric values.Source: 2) Podium plots · pp. 3–4, Figure 2 · p. 4, Figure 3 · p. 4

3) Ranking heatmap:

The paper proposes visualizations for ranking heatmaps, ranking-method robustness, and ranking stability under a selected method. These views expose agreement, sensitivity, and uncertainty in challenge rankings.

3) Ranking heatmap:

  • Ranking heatmaps contrast test-case rankings with the overall ranking; diagonal concentration indicates concordance, while greater contrast separates algorithms more clearly.They are particularly useful when many test cases make podium plots difficult to interpret.Source: 3) Ranking heatmap · p. 4

B. Ranking robustness with respect to ranking method

C. Ranking stability for a selected ranking method

1) Visualizing bootstrap results:

  • Few blobs suggest greater certainty in bootstrap ranks, while many similarly sized blobs suggest greater uncertainty.Blob area reflects how often an algorithm achieved a rank; the plot also marks median ranks and 95% bootstrap intervals.Source: 1) Visualizing bootstrap results · p. 4, Figure 5 · p. 5
  • Violin plots compare the full-data ranking with bootstrap rankings using Kendall’s τ; identical rankings yield τ=1, while dispersed values indicate instability.The violin combines a boxplot and density plot across bootstrap samples.Source: 1) Visualizing bootstrap results · pp. 4–5

2) Testing approach summarized by significance map:

Significance maps summarize pairwise testing as a view of ranking stability. In multi-task challenges, the analysis also considers whether algorithms perform consistently across tasks.

2) Testing approach summarized by significance map:

  • Significance maps display pairwise test outcomes: yellow marks significant superiority of the x-axis algorithm, while blue marks no significant difference.The map uses one-sided Wilcoxon signed-rank tests at 5% significance, with Holm adjustment for multiple testing.Source: Figure 7 · p. 5, 2) Testing approach summarized by… · p. 5

IV. VISUALIZATION FOR MULTI-TASK CHALLENGES

  • Multi-task challenges address related clinical sub-problems and allow assessment of how algorithms generalize across tasks; algorithms are ordered by average-rank consensus.Source: §IV · p. 6

A. Characterization of algorithms

1) Visualization of ranking variability across tasks:

The paper visualizes rank variability across tasks and compares tasks by ranking stability and similarity. These views support analysis of algorithm performance and task relationships in multi-task challenges.

1) Visualization of ranking variability across tasks:

  • Across tasks, a blob plot shows each algorithm’s ranks and their frequencies; narrow intervals around the diagonal would indicate stable, consistent rankings.Source: 1) Visualization of ranking… · p. 6

2) Visualization of ranking variability based on bootstrapping:

  • Separate task-colored blob plots for each algorithm show its rank variability across tasks and bootstrap samples, supporting individual strength–weakness analysis.Source: 2) Visualization of ranking… · p. 6

B. Characterization of tasks

1) Visualizing bootstrap results:

  • Per-task bootstrap plots indicate stable rankings through narrow blob spreads across algorithms and unstable rankings through wide spreads; violin locations and lengths offer a condensed comparison.Source: 1) Visualizing bootstrap results · p. 6

2) Cluster analysis:

  • Dendrograms and network graphs cluster or position tasks by distances between their algorithm rankings, revealing which tasks have similar or dissimilar rankings.In the network view, each task is a node and edge lengths encode distance; the figure uses Spearman’s footrule.Source: 2) Cluster analysis · p. 6, Figure 8 · p. 6

V. OPEN-SOURCE CHALLENGE VISUALIZATION TOOLKIT

The paper provides challengeR, an open-source R toolkit for challenge-result analysis and visualization. Its multi-task challenge illustration shows clearer ranking patterns for T1 than T2, whose small assessment set leaves rankings uncertain.

V. OPEN-SOURCE CHALLENGE VISUALIZATION TOOLKIT

  • The challengeR toolkit implements the analysis and visualization methods in R and can generate full analysis reports from challenge assessment data.Its input CSV includes metric values, algorithm names, test-case identifiers, and task identifiers for multi-task challenges.Source: §V · p. 6

VI. RESULTS

  • The toolkit was applied to a recently conducted multi-task challenge involving 19 participating algorithms and 17 different (sub-)tasks; 1000 bootstrap samples assessed ranking variability.Single-task visualization tools were illustrated on T1, which has many test cases and a relatively clear ranking, and T2, which has a small number of test cases and a more ambiguous ranking.Source: §VI · pp. 6–7

1) Visualization of assessment data:

  • T1’s raw assessment values suggest a clearer ordering than T2’s, which has only ten test cases and near-perfect metric values for most algorithms.Both tasks show outliers, but the plots do not establish whether the same test cases produced them.Source: 1) Visualization of assessment data · p. 7, Figure 10 · p. 7
  • T1’s podium plot suggests a clear ordering at the top and bottom, while T2’s algorithms often perform similarly and three divergent cases may sway its ranking.In T1, A1 was among the three best performers for almost all test cases.Source: 1) Visualization of assessment data · p. 7, Figure 11 · p. 7
  • The T1 ranking heatmap has a relatively clear diagonal, while T2 shows more varied test-case ranks, though its first and last few algorithms vary less.Source: 1) Visualization of assessment data · p. 7

2) Visualization of ranking stability:

Bootstrap visualizations show relatively clear rankings for T1 but substantially greater ranking variability for T2. Significance testing and alternative ranking methods further qualify how confidently the algorithms can be ordered.

2) Visualization of ranking stability:

  • T1 has a relatively clear ranking, with A1 first in every bootstrap sample, while T2 shows much greater ranking variability.In T2, A5's 95% bootstrap interval spans ranks 4 to 13, and all algorithms reach rank 1 in at least one sample; the authors caution that bootstrapping with few test cases may not estimate the true distribution well.Source: 2) Visualization of ranking stability · pp. 7–8, Figure 13 · p. 8
  • T1's significance map separates the two top-ranked algorithms from the rest, whereas T2's uncertainty prevents a meaningful ranking.Source: Figure 14 · p. 8, 2) Visualization of ranking stability · p. 8
  • T1 rankings are relatively robust across ranking methods, but T2 rankings depend much more on method choice.Mean-then-rank by average DSC produces a considerably different ordering from test-based ranking, which the authors suggest may reflect the impact of outlying test cases.Source: Figure 15 · p. 8, 2) Visualization of ranking stability · p. 8

B. Visualization of cross-task insights

Across nine real-world assessment tasks, the visualizations characterize both algorithm performance and the stability of task rankings. A1 is generally among the leading algorithms, while ranking stability varies across tasks.

B. Visualization of cross-task insights

1) Characterization of algorithms:

  • A1 almost always ranks first across tasks, while other algorithms span wider rank ranges; A1 is almost always among each task's winners and never ranks below fourth.T4 is the exception to A1's near-consistent winner status; A2 also consistently attains top ranks apart from T4, while A3, A4, and A5 vary substantially across tasks.Source: 1) Characterization of algorithms · pp. 8–9, Figure 16 · p. 9

2) Characterization of tasks:

  • Task-similarity visualizations suggest two major task clusters, distinguish T5 from the remaining tasks in the network view, and show A1 as the winner in most tasks.Source: 2) Characterization of tasks · p. 9
  • Task-wise bootstrap plots show stable rankings for T1, though not necessarily in the consensus order, and greater variability for T2 and T9 among medium-ranked algorithms.Source: Figure 17 · p. 9, 2) Characterization of tasks · p. 9
  • Kendall’s τ distributions indicate very stable rankings for T1, T3, and T5, and the least stable rankings for T2, T8, and T9.T4, T6, and T7 are somewhat less stable overall because some algorithms do not separate well.Source: Figure 18 · p. 9, 2) Characterization of tasks · p. 9

VII. DISCUSSION

The discussion presents a systematic methodology and open-source toolkit for analyzing challenge results, with a focus on uncertainty and insights unavailable from common presentation techniques. It also notes a visualization limit when the number of algorithms is large and potential applications beyond challenge data.

VII. DISCUSSION

  • The paper proposes systematic analysis and visualization for challenges, implements it in the open-source R toolkit challengeR, and applies it to simulated and real challenges.The authors report that it reveals performance insights unavailable from ranking tables and boxplots, while emphasizing uncertainty in challenge rankings.Source: §VII · p. 10
  • When there are too many algorithms, analysis can still include all of them, but visualization may need to be limited to a top list.Source: §VII · p. 10
  • The methods may also be applied to validation studies in classical research papers and are designed to transfer beyond biomedical image analysis.Source: §VII · p. 10
  • The authors conclude that the toolkit could become valuable for analyzing and visualizing challenge results, with potential impact beyond biomedical image analysis.Source: §VII · p. 10
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