Mapper and Ball Mapper tools for complex data analysis.
problem Exploring and visualizing high-dimensional data and scalar functions.
method Combining Mapper and Ball Mapper, adding new features for encoding structure and symmetries.
result A new hybrid algorithm, Mapper on Ball Mapper, for comparing high-dimensional data descriptors.
Parallel Mapper algorithm for efficient topological data analysis.
problem Efficient parallel processing of Mapper for topological data analysis.
method Provable correct parallel algorithm for Mapper execution on multiple processors.
result Demonstrates the efficiency of parallel Mapper compared to sequential implementations.
Mapper instability quantified for robust graph construction.
problem Variability in Mapper output due to parameter selection.
method Defined an intrinsic instability measure for Mapper outputs.
result Identified local minima of instability for reliable outputs.
Optimizes cover parameter in Mapper algorithm for better visualization.
problem Tuning the cover parameter in Mapper algorithm to generate a ``nice'' graph.
method Optimizes cover by repeatedly splitting using statistical tests and Gaussian mixture model.
result Algorithm generates covers that retain dataset essence while being faster.
Mapper classifier improves robustness over CNNs.
problem Improving robustness of classifiers against attacks.
method Mapper algorithm applied to PCA or autoencoders projected data.
result Mapper classifier is immune to gradient-based attacks.
Mapper-GIN simplifies 3D point cloud classification with lightweight structure.
problem Robust 3D point cloud classification under corruption.
method Mapper algorithm for structural decomposition, GIN for graph classification.
result Mapper-GIN achieves competitive accuracy with minimal parameters.
Improved Mapper algorithm for datasets with varying density.
problem Difficulty in tuning resolution for datasets with varying density.
method Generalized cover type and incorporated lens-space density into the cover.
result Graph produced by Mapper converges to Reeb graph of Rips complex.
Bi-filtration stabilizes TDA mapper results under noise.
problem Stability issues in TDA mapper results under data perturbation.
method Introduced bi-filtration approach to stabilize mapper graphs.
result Persistent homology of perturbed data set is 2δ-interleaved with original.
A new Mapper algorithm optimizes data visualization through automatic parameter tuning.
problem Manual parameter tuning and fixed intervals limit the performance of the standard Mapper algorithm.
method Introduces a soft Mapper framework based on Gaussian mixture models for automatic interval construction and optimization via stochastic gradient descent.
result Demonstrates effectiveness in capturing underlying topological structures and identifying distinct subgroups.
New statistical method for estimating Reeb spaces from multivariate data.
problem Stability and convergence of Mapper to Reeb spaces in multivariate and metric spaces.
method Modified Mapper construction with risk bounds for Gromov-Hausdorff distance.
result Risk bounds for estimating Reeb spaces using the modified Mapper.
Mapper tool preserves graph structures for better visualization.
problem Graphs can be hard to visualize for large datasets.
method Developed a variation of mapper for weighted, undirected graphs.
result Homology-preserving skeletons enable multi-scale visualization.
New tool helps analyze complex financial data.
problem Difficulty in comprehending high-dimensional financial data.
method Topological Data Analysis Ball Mapper algorithm.
result Shows new way to see detail in financial data.
Mapper merges GNNs with TDA for graph visualisation.
problem Visualising complex graphs for understanding model structure.
method Combining Mapper, GNNs, and PageRank for graph pooling.
result Hierarchical visualisations reveal graph structure and model application.
ShapeVis visualizes high-dimensional data efficiently.
problem Scalability issues with Mapper in high-dimensional data.
method Landmarks, weighted witness-graph, induced maps, modularity-based pruning.
result ShapeVis scales to millions of data points while preserving visualization quality.
AuToMATo clusters data without tuning parameters, outperforming others.
problem Clustering data efficiently and without manual tuning.
method Combines ToMATo with bootstrapping for density estimation.
result Performs well across various clustering algorithms and applications.
This paper proposes a new method for learning covers of geometric datasets to improve topological inference and visualization.
problem Improving topological inference and visualization of large-scale geometric datasets.
method Proposes a method for learning topologically-faithful covers of geometric datasets using optimization.
result Simplicial complexes obtained from learned covers outperform standard methods in terms of size and representation of large-scale topology.
THD technique identifies loan applicants at risk.
problem Lack of explainable machine learning in finance.
method Topological Hierarchical Decomposition (THD) algorithm.
result THD identifies groups of loan applicants at risk.
New algorithm explains neural network extrema for better model generalization.
problem Understanding and improving neural network generalization.
method Dynamic extremum mapping and solving linear equations.
result Number of extrema correlates with model parameters, and new algorithm simplifies gradient issues.
Topological data analysis reveals complex financial-ratio-stock return relationships.
problem Understanding the complex associations between financial ratios and stock returns.
method Topological data analysis (TDA) using the Ball Mapper algorithm.
result Interdependencies between financial ratios are often non-monotonic, offering new insights.
Survey of techniques for diagnosing pediatric sleep apnea from inexpensive data.
problem Diagnosing pediatric sleep apnea from limited and variable data.
method Exploratory data analysis using correlation networks, Mapper, SVD; supervised and unsupervised learning techniques.
result Analysis of various learning techniques applied to pediatric sleep apnea data.
DCoM uses deep neural networks to detect semantic data types from raw column values.
problem Detecting semantic data types from dirty and unseen data.
method DCoM employs multi-input NLP-based deep neural networks trained on 686,765 data columns.
result DCoM outperforms existing methods significantly on 78 different semantic data types.
This study uses TDA to map corporate failure, revealing distinct regions of risk.
problem Understanding and predicting corporate default risk.
method Topological Data Analysis (TDA) applied to Altman's Z-score model.
result Firms do not cluster neatly along default predictors, suggesting complex risk landscapes.
A new encoding framework predicts brain activity from visual stimuli and intrinsic brain connections.
problem Traditional encoding models ignore brain inner states, limiting their performance in natural image identification.
method Proposes a novel encoding framework combining external stimuli and brain inner states, using a forward encoding model and an inner state model.
result The framework achieves better performance on natural image identification from fMRI responses than traditional models.
NM-VQTSG improves synthetic time series fidelity by aligning distributions.
problem Fidelity challenges in VQ-based time series generation.
method Neural mapping model using U-Net to refine synthetic data.
result Significant improvements in FID, IS, and conditional FID metrics.
Survey of embedding methods for high-dimensional and network data.
problem Embedding high-dimensional and nonlinear data structures in a lower-dimensional space.
method Survey of various embedding methods including principal curves, multidimensional scaling, graph-based methods, and topological embeddings.
result Discussion of the pros and cons of algorithmic machine learning and statistical modeling approaches.
VDTW improves cross-year crop mapping accuracy.
problem Cross-year crop mapping accuracy is poor with existing methods.
method Vector Dynamic Time Warping (VDTW) for multi-year classification.
result VDTW achieves 99.85% and 99.74% overall accuracies for same and cross years, respectively.
Metagenomics characterizes the taxonomic diversity of microbial communities by sequencing DNA directly from an environmental sample. One of the main challenges in metagenomics data analysis is the binning step, where each sequenced read is assigned to a taxonomic clade. Due to the large volume of metagenomics datasets,…