Introduction | Computing and Comparing Persistence Diagrams | Computing Diagrams and TDApplied's PyH Function | Determining the Radius Threshold with TDApplied's enclosing_radius Function | Converting Diagrams to DataFrames with TDApplied's diagram_to_df Function | Comparing Persistence Diagrams and TDApplied's diagram_distance and diagram_kernel Functions | Visualizing and Interpreting Persistence Diagrams | TDApplied's Function plot_diagram | Filtering Topological Features and TDApplied's universal_null Function | Bootstrapping Topological Features and TDApplied's bootstrap_persistence_thresholds Function | Representative (Co)Cycles | VR Graphs and TDApplied's vr_graphs and plot_vr_graph Functions | Hypothesis Testing | Detecting Group Differences and TDApplied's permutation_test Function | Independence Between Two Groups of Paired Diagrams and TDApplied's independence_test Function | Model Inference and TDApplied's permutation_model_inference Function | Finding Latent Structure | Kernel k-means and TDApplied's diagram_kkmeans Function | Multidimensional Scaling and TDApplied's diagram_mds Function | Kernel Principal Components Analysis, and TDApplied's diagram_kpca Function | Predicting Labels of Persistence Diagrams | Support Vector Machines and TDApplied's diagram_ksvm Function | Limitations of TDApplied Functionality | Conclusion | References

Introduction | Speedups | Parallelization | Fisher Information Metric Approximation | Using Pre-Computed Matrices | Storing Calculations in permutation_test | Benchmarking Against Similar Packages | Benchmarking PyH Against TDAstats' calculate_homology Function and rgudhi's compute_persistence Function | Benchmarking the TDApplied diagram_distance and TDA wasserstein Functions | Benchmarking the TDApplied diagram_distance Function against persim's wasserstein Functions | Benchmarking the TDApplied diagram_distance and rgudhi PersistenceFisherDistance Functions | Conclusions | References

Abstract | Introduction | A task-related spatial loop | Linking the secondary loop to raw data | Linking topology to behavior | Conclusion | Appendix: Converting Correlations to Distances | References

Introduction | TDAstats' phom.dist Function | Examples | Comparisons | Proof of Correctness for TDApplied's diagram_distance Function | Conclusion | References

Introduction | Classification with Extreme Gradient Boosting (XGBoost) | Conclusion | References