New turbulence index using TDA detects financial market transitions.
problem Detecting critical transitions in financial markets.
method Persistent homology for identifying topological features.
result Persistent homology-based index captures financial data transitions.
New L0 norm added to TDA for market analysis.
problem Improving TDA tools for market prediction.
method Defined and applied L0 norm in TDA for four markets.
result Enhanced TDA tools for market analysis.
New TDA approach using Finsler metrics.
problem Traditional TDA concepts and methods.
method Introducing Finsler metrics for TDA.
result Relevance of Finsler metrics to TDA.
ASTRA improves TDA by more accurately approximating iHVP.
problem Improving insights into training data attribution.
method ASTRA uses EKFAC-preconditioner on Neumann series iterations to accurately approximate iHVP.
result Improving iHVP approximation significantly improves TDA performance.
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent topological features that can be used for any supervised or unsupervised learning…
TDA improves FX clustering quality over traditional methods.
problem Capturing complex currency co-movements in FX markets.
method Topological Data Analysis (TDA) compared to traditional statistical methods on monthly FX returns.
result TDA-based clustering yields more compact and well-separated clusters.
Python library for integrating TDA with machine learning.
problem Data exploration and interpretability in machine learning.
method Integrates TDA with scikit-learn API, uses C++ for performance.
result Enhanced data exploration and interpretability in machine learning.
Paper proposes MUCS for more reliable TDA in diffusion models.
problem Current TDA approaches lack reliability and robustness.
method Mirrored unlearning and noise-consistent skew (MUCS).
result MUCS outperforms existing methods on three datasets.
Fed-TDA augments federated tabular data to improve performance and privacy.
problem Non-IID data challenges in federated learning.
method Synthesizes tabular data using simple statistics for augmentation.
result Fed-TDA improves test performance and communication efficiency.
This paper introduces TDA and TSI for better business analytics.
problem Nonlinear, multi-scale business datasets under-represented by traditional tools.
method Topological Data Analysis (TDA) and Topological Stability Index (TSI).
result TSI reveals structural variability in business data.
TDA improves cryptocurrency portfolio management.
problem Traditional methods fail to manage cryptocurrencies effectively.
method Topological Data Analysis (TDA) for identifying investment opportunities.
result TDA-based portfolio management outperforms traditional methods.
TDA detects stock market crashes across continents.
problem Detecting extreme events in multiple stock indices simultaneously.
method Topological Data Analysis (TDA) to analyze stock market crashes.
result TDA identifies stock market crashes and their duration.
A new algorithm reduces the size of datasets for TDA.
problem Processing large datasets with high dimensions in TDA is computationally infeasible.
method Introduced Characteristic Lattice Algorithm (CLA) for data reduction.
result CLA reduces dataset size while preserving geometric and topological features.
Study evaluates financial anomaly detection methods on Canadian stock market.
problem Detecting financial anomalies in the Canadian stock market.
method Topological data analysis (TDA), principal component analysis (PCA), and neural network-based approaches.
result Neural network-based methods achieve the strongest performance in detecting financial anomalies.
TDA detects financial bubbles through early warning signals.
problem Detecting financial bubbles early.
method Using Log-Periodic Power Law Singularity (LPPLS) model to fit financial time series data.
result TDA generates early warning signals when LPPLS model fits the data.
Firm financials are well established as return predictors, being the inspiration for a large set of anomalies in the asset pricing literature. Employing topological data analysis we revisit the question of association between seven of the most commonly studied financial ratios and stock returns. Specifically the TDA Ba…
System uses TDA for user segmentation and demand forecasting.
problem User loyalty and demand forecasting challenges.
method TDA-based clustering of time series data with matrix factorization.
result Significantly higher accuracy in clustering and demand forecasting.
We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural grayscale filtration, and different filtrations defined on the binarized image. We…
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.
TDA improves stock portfolio selection by analyzing data structure.
problem Traditional portfolio selection methods fail to handle stock market data complexities.
method Two-stage method involving time series generation and clustering with TDA features.
result TDA-based portfolio outperforms other methods consistently over different time frames.
The fingerprint classification problem is to sort fingerprints into pre-determined groups, such as arch, loop, and whorl. It was asserted in the literature that minutiae points, which are commonly used for fingerprint matching, are not useful for classification. We show that, to the contrary, near state-of-the-art clas…
Paper uses TDA for automated Parkinson's disease classification and severity assessment.
problem Manual diagnosis of neurological diseases is time-consuming and inaccurate.
method Combines Topological Data Analysis (TDA) with machine learning on postural shift data.
result Proposes a stable and accurate method for classifying Parkinson's disease.
TDA-based portfolios show better risk-adjusted returns than classical methods.
problem Traditional portfolio selection methods fail to capture complex asset dynamics.
method Topological Data Analysis (TDA) using persistence landscapes to quantify portfolio risk.
result TDA-based portfolios outperform classical models in excess mean return and financial ratios.
The paper uses TDA to select stocks for a sparse portfolio, improving performance across market scenarios.
problem Sparse portfolio selection in financial markets.
method Topological data analysis (TDA) for clustering stock price movements.
result The TDA-based clustering strategy significantly enhances sparse portfolio performance.
Topological Data Analysis (TDA) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited to the field of financial time series primarily and as a method for feature generation in machine learning applications. In this work, TDA is prese…
Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological summaries, most noticeably the Persistence Diagram, are typically defined in comple…
New method detects dynamical system changes in time series data.
problem Detecting changes in time series data structures.
method Weighted Ordinal Partition Network (OPN) with topological data analysis (TDA).
result Improved accuracy and resilience to noise in dynamic state detection.
This study uses persistent homology to analyze complex transitional networks from time series data.
problem Lack of effective tools to summarize complex topology in transitional networks.
method Persistent homology from topological data analysis applied to coarse-grained state-space networks (CGSSN).
result CGSSN improves dynamic state detection and noise robustness compared to other methods.
Combines geometry and topology for analyzing hierarchical datasets.
problem Analyzing complex, hierarchical datasets with irregular structures.
method Combines manifold learning and topological data analysis.
result Superior classification results compared to state-of-the-art methods.
Study uses TDA to improve OEE forecasting in manufacturing.
problem Volatility and nonlinearity in OEE time series data.
method Topological Data Analysis (TDA) to transform raw data into structured knowledge.
result Improves OEE forecasting accuracy by at least 17%.
PERCEPT detects changes in high-dimensional data streams using topological data analysis.
problem Detecting changes in high-dimensional data streams, especially when embedded in a low-dimensional space.
method Leverages topological data analysis to learn embedded topology as a point cloud via persistence diagrams, then applies non-parametric monitoring for detecting changes.
result Demonstrates efficient detection of online changes from high-dimensional data streams.
Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology. When applying this to two case studies, accuracy exceeds alternative models wit…
Generates random persistence diagrams for data analysis.
problem Generating random persistence diagrams for data analysis.
method Based on pairwise interacting point processes and RJ-MCMC algorithm.
result Demonstrates the efficacy and utility of RPDG in materials science.
This paper extends hypergraph construction to multivariate time series using signature transforms.
problem Constructing hypergraphs from collections of multivariate time series.
method Leveraging signature transforms to introduce controlled randomness and robustness.
result Validated on synthetic datasets, the method enhances robustness in hypergraph construction.
Bayesian approach scores influential training examples for model predictions.
problem Enhance interpretability and safety of machine learning models.
method Formulate TDA as a Bayesian information-theoretic problem, scoring subsets by information loss.
result Method aligns with classical influence scores while promoting diversity for subsets.
This review explores TDA and TDL beyond persistent homology.
problem Limitations of persistent homology in capturing topological invariants and homotopic evolution.
method Spectral representations, sheaf theory, Mayer topology, interaction topology, differential topology, geometric topology.
result Review of topological tools for various data types.
A new landmark sampling method improves TDA performance on biomedical data.
problem Improving landmark samplers for pseudometric spaces with varying density and multiplicities.
method Proposes 'lastfirst' procedure based on ranked distances, proving landmarks have desired properties.
result lastfirst outperforms maxmin on homology detection tasks and comparable on prediction tasks.
A new method uses vectorized summaries of persistence diagrams for efficient hypothesis testing.
problem Efficient hypothesis testing for large and complex persistence diagrams.
method Vectorized summaries of Betti functions and a new shuffling technique.
result The vectorized Betti function leads to competitive results compared to baseline methods.
Paper uses TDA to assess cryptocurrency risk by measuring phase space instability.
problem Traditional risk measures fail to capture market dynamics' geometric structure.
method Applied Takens' Delay Embedding Theorem to generate point cloud, computed persistent homology groups, defined Topological Persistence Norm.
result Proposed leverage calibration heuristic based on persistence of 1-dimensional cycles.
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to basic fundamental and practical aspects of \tda\ for non experts.
Study evaluates clustering methods for Google Trends data.
problem Clustering high-dimensional, noisy time series data.
method Symbolic Aggregate Approximation (SAX), Enhanced SAX (eSAX), and Topological Data Analysis (TDA).
result TDA provides more balanced and meaningful groupings than SAX and eSAX.
New method estimates deep neural network's intrinsic dimension for better generalization.
problem Estimating intrinsic dimension of deep neural networks for generalization.
method Topological data analysis (TDA) and persistent homology (PHD).
result Efficient algorithm to estimate PHD in deep neural networks.
New method predicts model output distributions to improve data attribution.
problem Traditional training data attribution ignores randomness in model training.
method Distributional Training Data Attribution (d-TDA) using influence functions.
result Influence functions are effective and emerge naturally from d-TDA.
A new method detects small holes in noisy data.
problem Detecting small holes in high-density regions from noise.
method Robust Density-Aware Distance (RDAD) filtration, incorporating distance-to-measure concept.
result The RDAD filtration prolongs the persistences of small holes, making them distinguishable from noise.
Paper proposes a method to improve circular coordinate representation for detecting changes in high-dimensional datasets.
problem Detecting changes in high-dimensional datasets with preserved topological structures.
method Adapt circular coordinate framework using a generalized penalty function instead of an L2 penalty.
result Circular coordinates with generalized penalty can detect changes in high-dimensional datasets under different sampling schemes.
Study vineyards linking TDA and knot theory, showing rich topological features.
problem Linking computational topology and knot theory through vineyards.
method Construct periodic functions to study evolution of persistence diagrams.
result Vineyards are as rich as possible in topological terms.
Topological parallax assesses AI models' geometric similarity to datasets for safety.
problem Ensuring AI models' robustness and safety in deep learning applications.
method Topological parallax compares a trained model to a reference dataset using Rips complexes and geodesic distortions.
result Topological parallax indicates whether a model shares similar multiscale geometric features with the dataset.
Paper introduces DP TDA for near-optimal private persistence diagrams.
problem Challenges in privatizing topological data analysis.
method Sensitivity analysis of persistence diagrams, use of exponential mechanism.
result Proposes near-optimal privacy mechanism for TDA.