Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams

Authors: Tam Le, Makoto Yamada

NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Throughout experiments with many different tasks on various benchmark datasets, we illustrate that the PF kernel compares favorably with other baseline kernels for PDs.
Researcher Affiliation Academia Tam Le RIKEN Center for Advanced Intelligence Project, Japan tam.le@riken.jp Makoto Yamada Kyoto University, Japan RIKEN Center for Advanced Intelligence Project, Japan makoto.yamada@riken.jp
Pseudocode Yes Algorithm 1 Compute d FIM for persistence diagrams
Open Source Code Yes Source code for Algorithm 1 can be obtained in http://github.com/lttam/Persistence Fisher.
Open Datasets Yes It is a synthesized dataset proposed by [Adams et al., 2017] ( 6.4.1) for linked twist map... We consider a 10-class subset7 of MPEG7 object shape dataset [Latecki et al., 2000]. ... granular packing system [Francois et al., 2013] and Si O2 [Nakamura et al., 2015] datasets.
Dataset Splits No The paper mentions training and testing splits, but does not explicitly describe a validation set split. For example, it states "We randomly split 70%/30% for training and test, and repeated 100 times."
Hardware Specification No The paper does not provide specific hardware details used for running its experiments, such as GPU/CPU models or memory amounts.
Software Dependencies No The paper mentions "Libsvm (one-vs-one) [Chang and Lin, 2011]" and "the DIPHA toolbox6" but does not specify their version numbers for reproducibility.
Experiment Setup Yes For hyper-parameters, we typically choose them through cross validation. For baseline kernels, we follow their corresponding authors to form sets of hyper-parameter candidates, and the bandwidth of the Gaussian kernel in (Prob + k G) and (Tang + k G) is chosen from 10{ 3:1:3}. For the Persistence Fisher kernel, there are 2 hyper-parameters: t (Equation (4)) and σ for smoothing measures (Equation (1)). We choose 1/t from {q1, q2, q5, q10, q20, q50} where qs is the s% quantile of a subset of Fisher information metric between PDs, observed on the training set, and σ from 10 3:1:3 . For SVM, we use Libsvm (one-vs-one) [Chang and Lin, 2011] for multi-class classification, and choose a regularization parameter of SVM from 10 2:1:2 .