Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Learning Representations of Persistence Barcodes
Authors: Christoph D. Hofer, Roland Kwitt, Marc Niethammer
JMLR 2019 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we present experiments on a variety of problems, including graph classification, eigenvalue prediction of (normalized) graph Laplacian matrices, 2D/3D shape recognition and the classification of EEG signals. ... We present a diverse set of experiments for supervised learning with different types of data objects. In particular, we show results for 2D/3D shape recognition and the classification of social network graphs, evaluated on standard benchmark data sets. Additionally, we present two exploratory experiments for the problems of predicting the eigenvalue distribution of normalized graph Laplacian matrices and activity recognition from EEG signals. |
| Researcher Affiliation | Academia | Christoph D. Hofer EMAIL Department of Computer Science University of Salzburg Salzburg, Austria; Roland Kwitt EMAIL Department of Computer Science University of Salzburg Salzburg, Austria; Marc Niethammer EMAIL Department of Computer Science University of North Carolina Chapel Hill, NC, USA |
| Pseudocode | No | The paper does not contain any clearly labeled pseudocode or algorithm blocks. The methods are described using mathematical formulations and textual explanations. |
| Open Source Code | Yes | Source code to fully reproduce the experiments is publicly-available10. 10. https://github.com/c-hofer/jmlr_2019.git |
| Open Datasets | Yes | Animal dataset, introduced by Bai et al. (2009)... MPEG-7 dataset ... see Latecki et al. (2000)... SHREC14 benchmark and replicate the evaluation setup of Reininghaus et al. (2015)... reddit-5k (5 classes, 5k graphs) and reddit-12k (11 classes, 12k graphs)... Pokec (Takak and Zabovsky, 2012) social network graph that is part of the SNAP repository14. 14. https://snap.stanford.edu/data/soc-pokec.html |
| Dataset Splits | Yes | Table 1 lists the average cross-validation accuracies over 10 random 90/10 splits. ... all other results (using persistent homology) are averaged over 10 random 90/10 splits. ... When training on S2 and testing on S2 in a 90/10 cross-validation setup... Table 4 lists the average cross-validation accuracies for 10 random 90/10 splits of the dataset. |
| Hardware Specification | No | Also, we were unable to handle 1-dimensional features, due to the vast number of cycles produced and the memory limitations of our GPU(s). No specific GPU models, CPU models, or detailed hardware specifications are provided. |
| Software Dependencies | No | All experiments were implemented in Py Torch7, using DIPHA8 (Bauer et al., 2014) and Perseus9 (Mischaikow and Nanda, 2013) for persistent homology computations. ... No specific version numbers for PyTorch, DIPHA, or Perseus are given. |
| Experiment Setup | Yes | For optimization, we use stochastic gradient descent (SGD) with momentum and cross-entropy loss (if not mentioned otherwise). We additionally include a non-linearity φ : R R (in our case φ = tanh) after the input layer(s)... The parameter ν for the birth-lifetime transform of Definition 16 is fixed to 0.01 over all experiments. ... Regarding initialization of the structure elements, we run k-means++ (Arthur and Vassilvitskii, 2007) clustering on all points from diagrams in the training portion of each dataset with k = N. The N cluster centers are then used to initialize the position of the structure elements. The parameter r is set to 1/4 of the maximum lifetime of barcode elements in the training corpus. ... We use the architecture of Figure 6 with φ = id and train with an initial learning rate of 0.01, a momentum of 0.9 and a batch size of 100 for 200 epochs. The learning rate is halved every 40-th epoch. ... The network is trained for 300 epochs with a batch size of 20 and an initial learning rate of 0.5. The learning rate is halved every 20-th epoch. |