Reproducing Famous Papers

The preceding chapters introduced the methods and applied them to examples. In this part, we return to published experiments and ask whether JuliaTDA can recover their results using the original data and the reported analysis.

A reproduction begins with a concrete target: a figure, a numerical result, or a structural feature of the data. We identify the dataset, translate the published procedure into Julia, and compare the result with that target. When a paper leaves an implementation choice unspecified, we record our choice and investigate how much it affects the answer.

Each chapter follows the same sequence:

1. Target and data. Identify the published experiment and verify the source, measurements, sample order, and checksum of the data.
2. Analysis. Explain the transformations and parameters, with Julia code that reproduces the computation.
3. Comparison. Show the observed result, including differences from the paper.
4. Sensitivity and verification. Check the implementation and expose the effects of choices that are not fully specified in the publication.

We distinguish an exact numerical match from a qualitative recovery of a pattern. An unsuccessful match is also useful: it can reveal a missing variable, an undocumented parameter, or an implementation convention that changes the analysis.

The first experiment

We begin with Mapper on the Reaven–Miller diabetes data, targeting Figure 5 of Singh et al. (2007). The outcome is a partial qualitative reproduction. Some configurations recover the two low-density flares, while the automatic bandwidth produces a chain. The chapter includes both outcomes.

The data, scripts, parameter grid, recorded results, and resolved environment are included in reproductions/experiments/mapper2007/. The chapter uses saved figures, so building the book does not rerun the experiment; instructions explain how to run it separately.

Further papers

Four additional chapters compare JuliaTDA computations with published targets:

• Lum et al. (2013): a partial reconstruction of Mapper on the public GSE2034 breast cancer cohort, with verified clinical alignment and explicit preprocessing assumptions.
• Chazal et al. (2013): the full author-released ToMATo twin-spirals benchmark, including an independent merge audit.
• Perea and Harer (2015): the specified sliding-window signals and coefficient-field comparison from Figure 3, with the remaining numerical mismatch documented.
• Cohen-Steiner et al. (2007): a numerical verification of the stability theorem on a new cubical example. This target is a mathematical bound, rather than a published empirical figure.

Each chapter includes executed analyses, saved results, figures, verification and commands for rerunning its private experiment. The PAD/Mapper analysis of Nicolau et al. (2011) remains a future target.

Nicolau, Monica, Arnold J. Levine, and Gunnar Carlsson. 2011. “Topology Based Data Analysis Identifies a Subgroup of Breast Cancers with a Unique Mutational Profile and Excellent Survival.” Proceedings of the National Academy of Sciences 108 (17): 7265–70. https://doi.org/10.1073/pnas.1102826108.

Singh, Gurjeet, Facundo Mémoli, and Gunnar Carlsson. 2007. “Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition.” Eurographics Symposium on Point-Based Graphics, 91–100. https://doi.org/10.2312/SPBG/SPBG07/091-100.