Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine lea…
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48 results for “Persistent Characteristics”
The conventional formal tool to detect effects of the financial persistence is in terms of the Hurst exponent. A typical corresponding result is that its value comes out close to 0.5, as characteristic for geometric Brownian motion, with at most small departures from this value in either direction depending on the mark…
Develops persistent Khovanov homology for tangles.
problem Lack of local topological features in evolutionary Khovanov homology for knots and links.
method Introduces a new mathematical framework using persistent Khovanov homology of tangles, employing functor and planar algebra.
result Provides a new method to characterize local features in curve-type data.
This work characterizes topological descriptors of graph products and their expressive power.
problem Capturing multiscale structural information in graph products using topological descriptors.
method Analysis of various filtrations on graph products, including Euler characteristic and persistent homology.
result Persistent homology of graph products contains more information than individual graphs.
Wavelet analysis reveals non-linear dynamics in cryptocurrency prices.
problem Understanding non-linear dynamics in high-frequency cryptocurrency prices.
method Wavelet analysis of frequency and time variables.
result Cyclical persistence at different frequencies in cryptocurrency prices.
We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in the tensor algebra of that vector space. The composition of these two operations …
Hypernetworks are simplified simplicial complexes with curvature.
problem Representing hypernetworks geometrically for analysis.
method Hypernetworks are interpreted as posets, which are simplicial complexes with Forman Ricci curvature.
result Hypernetworks have intrinsic curvature that correlates with their Euler characteristic.
Quantum circuits predict volatility dynamics preserving asymmetry.
problem Modeling volatility time series with asymmetry.
method Single-qubit quantum circuit learning (QCL) applied to synthetic data generated by Rational GARCH model.
result QCL-based predictions preserve negative return-volatility correlation and anti-persistent behavior.
Unbiased Gradient Estimation in Unrolled Computation Graphs with Persistent Evolution Strategiescs.LG
PES method reduces bias in gradient estimation for unrolled graphs.
problem High variance and bias in gradient estimation for unrolled computation graphs.
method Divide graph into unrolls, apply ES update, accumulate correction terms.
result PES provides unbiased, low-variance gradient estimates.
Study forecasts U.S. bond index using deep learning, finding persistence is key.
problem Forecasting U.S. aggregate bond index with deep learning methods.
method Constructed a stationary but maximally persistent representation of the bond index, evaluated using MLPs and CNNs.
result Deep learning models outperform traditional methods in short-horizon forecasting of bond indices.
Neural networks approximate Calabi-Yau metrics and curvature.
problem Finding Ricci-flat metrics for Calabi-Yau manifolds.
method Use neural networks to approximate metrics within a Kähler class.
result Neural networks can approximate topological characteristics of Calabi-Yau manifolds.
Nonlinear Evidence of Investor Heterogeneity: Retail Cash Flows as Drivers of Market Dynamicsq-fin.GN
Study reveals investor heterogeneity in Korean equity market cash flows.
problem Investor heterogeneity and its impact on market dynamics.
method Detrended fluctuation analysis (DFA) on aggregated cash flows.
result Persistence in cash flows varies by investor type, with retail flows showing strong persistence.
Robust Topological Feature Extraction for Mapping of Environments using Bio-Inspired Sensor Networkscs.RO
In this paper, we exploit minimal sensing information gathered from biologically inspired sensor networks to perform exploration and mapping in an unknown environment. A probabilistic motion model of mobile sensing nodes, inspired by motion characteristics of cockroaches, is utilized to extract weak encounter informati…
RCLA reduces noise in topological data analysis, preserving essential structure.
problem Noise in large datasets obscures topological features in persistent homology.
method Grid-based RCLA integrates data reduction and denoising with a threshold parameter.
result RCLA provides a theoretical guarantee and automatic parameter selection.
Study on price fluctuations and persistence in European electricity spot markets.
problem Analyzing variability and persistence of electricity prices in European spot markets.
method Analysis of hourly, intraday, and 15-min intraday market prices; quantification of fluctuations, correlations, and extreme events; classification into circulation weather types.
result Different time scales in market dynamics; multifractal behavior below 12 hours; anti-correlation and mean reversion above 12 hours; long-term behavior influenced by four-day weather patterns; -Gaussian distributions as best fit.
The study uses a multi-armed bandit model to analyze and mitigate hiring discrimination.
problem Hiring discrimination due to insufficient data on worker skill and characteristics.
method Multi-armed bandit model to simulate firms' learning process and policy solutions.
result Temporary affirmative actions effectively alleviate discrimination caused by data insufficiency.
Study examines how industrial emissions evolve over time in response to various factors.
problem Understanding how firm-level emissions change over time in response to environmental regulation, economic conditions, and organizational constraints.
method Used a time-varying mean-group estimator to link emissions data with firm characteristics and macroeconomic indicators over 1992-2023.
result Firm-level characteristics and aggregate conditions have different impacts on emissions growth at different times.
Approaches for approximating persistent homology for large datasets.
problem Inability to compute persistent homology for large datasets.
method Multiple subsampling framework for statistical approximation of persistent homology.
result Derivation of finite sample convergence rates for empirical means of persistent homology.
Proposes deep graph persistence to address neural persistence issues in deep learning.
problem Variance of weights and lack of spatial structure in deep neural networks impact neural persistence.
method Extends neural persistence to the whole network, considering interactions between layers.
result Deep graph persistence alleviates variance-related issues and captures persistent paths through the network.
Paper proves -means clustering works on persistence diagrams.
problem Complex geometry of persistence diagram space.
method Proves convergence of -means on persistence diagram space.
result Performance of -means on persistence diagrams and measures is superior.
Formula for interleaving distance of rectangle persistence modules.
problem Calculating distances between rectangle persistence modules.
method Formulas based on rectangle geometry, extended to decomposable modules.
result Closed formulas for interleaving and bottleneck distances.
New method uses topological features for chatter detection in turning processes.
problem Chatter detection in turning processes using complex dynamical systems.
method Embedding time series as point clouds, using persistence diagrams, and applying machine learning classifiers.
result TDA-based features yield high accuracy (97%) for two out of four cutting configurations.
This paper demonstrates the flaws of co-persistence theory proposed by Bollerslev and Engle (1993) which cause the theory can hardly be applied. With the introduction of the half-life of decay coefficient as the measure of the persistence, and both the weak definition of persistence and co-persistence in variance, this…
New methods found persistent tangles in knots.
problem Persistent tangles in knot diagrams.
method Non-trivial colorings for tangles.
result Any knot with non-trivial coloring has persistent tangles.
Optimizes wavelets for graph classification using spectral wavelet signatures and persistence diagrams.
problem Graph classification with geometric properties encoded in persistence diagrams.
method Optimizes spectral wavelets for graph datasets to capture best-suited features for classification.
result Competitive performance in graph classification problems compared to other persistence-based architectures.
New method for analyzing multiparameter persistence modules from smooth functions.
problem Analyzing multiparameter persistence modules from smooth functions.
method Generalized Morse theory applied to cobordism and Cerf theory.
result Complete description of persistence modules as direct sums of indecomposables.
Develops robust persistence diagrams using kernel methods.
problem Persistence diagrams are sensitive to data perturbations.
method Constructs robust persistence diagrams from superlevel filtrations of robust density estimators using reproducing kernels.
result Robust persistence diagrams are consistent estimators in bottleneck distance.
We analyze the market efficiency of 25 commodity futures across various groups -- metals, energies, softs, grains and other agricultural commodities. To do so, we utilize recently proposed Efficiency Index to find that the most efficient of all the analyzed commodities is heating oil, closely followed by WTI crude oil,…
This paper interprets critical scales in persistent homology for compact metric spaces.
problem Understanding critical scales in persistent homology for general compact metric spaces.
method Analyzing local minima of the distance function and their impact on persistence.
result Each decrease in zero-dimensional persistence and increase in one-dimensional persistence is induced by local minima of the distance function.
MuRiT efficiently computes multi-parameter persistence barcodes.
problem Efficient computation of multi-parameter persistent homology.
method Vietoris-Rips transformation to reduce multi-parameter to single-parameter computation.
result MuRiT computes pathwise persistence barcodes for multi-filtered flag complexes.
Persistent homology can recognize knotting in curves.
problem Recognizing knotting in curves
method Compute one-dimensional persistent homology, extract cycle representatives, and assign a hypergraph curvature-based score.
result Systematic differences between knotted and unknotted structures are revealed.
This article analyzes the relationship between co-persistence and hedging which indicates co-persistence ratio is just the long-term hedging ratio. The new method of exhaustive search algorithm for deriving co-persistence ratio is derived in the article. And we also develop a new hedging strategy of combining co-persis…
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come. In this article, by considering the space of persistence diagrams as a space of d…
Persistent homology detects curvature from sampled points.
problem Understanding the geometric information encoded in short intervals of persistent homology.
method Persistent homology computations and average persistence landscapes.
result Persistent homology detects curvature of disks from sampled points.
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams in machine learning have been done through kernel methods, i.e., embeddings of …
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a …
Study evaluates predictive models for blended courses, analyzing performance across different offerings.
problem Limited success in predicting student performance in blended courses.
method Used data from two offerings of two different undergraduate courses to train and evaluate models.
result Models perform better on the same offering and less well on different offerings of the same course.
A new approach to reinforcement learning improves policy performance by adjusting control frequency.
problem Improving reinforcement learning performance by optimizing control frequency.
method Introducing action persistence and a novel algorithm, PFQI, to learn optimal value function at a given persistence.
result PFQI effectively learns optimal value function with action persistence, improving reinforcement learning performance.
This paper explores how different audio signal representations affect topological signatures and their predictive power.
problem The impact of different signal representations on topological signatures and their predictive power.
method The study compares three different signal representations (embedding, spectrogram, and spectrogram zeroes) and evaluates their topological signatures for speaker gender, vowel type, and individual prediction.
result Topological signatures from spectrogram zeroes offer the best improvement for gender prediction, and different representations are complementary.
Given a compact geodesic space we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or Čech filtration of to obtain what we call a persistence. This paper contains the theory describing such persistence: properties of the set of critical points, their preci…
A new method compares persistent cycles in topological data.
problem Comparing persistent homology representations of two spaces.
method Direct comparison of individual persistent cycles based on persistence intervals and spatial placement.
result Demonstrated the effectiveness of the method in topological inference.
Persistence Spheres: a Bi-continuous Linear Representation of Measures for Partial Optimal Transportstat.ML
Improved persistence spheres map measures to functions, stable under partial transport.
problem Representing and comparing measures in topological machine learning.
method Persistence spheres map measures to continuous functions on the sphere, stable under 1-Wasserstein partial transport.
result Persistence spheres provide a stable, parameter-free representation of measures, improving upon existing methods.
New model predicts persistent weather patterns better than persistence model.
problem Improving weather forecasting accuracy for persistent patterns.
method Mixture of experts model using ordinal neural network.
result The model outperforms persistence and other models for longer time horizon predictions.
Embeds persistence diagrams into Hilbert spaces to use kernel methods.
problem No inner product structure on persistence diagrams.
method Shows non-embeddability of persistence diagrams into Hilbert spaces.
result Persistence diagrams with bottleneck distance do not coarse embed into Hilbert spaces.
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the "life span" or "persistence" of a homology class. As a case study, …
A Stochastic Cascade Model for FX Dynamicscond-mat.stat-mech
A time series model for the FX dynamics is presented which takes into account structural peculiarities of the market, namely its heterogeneity and an information flow from long to short time horizons. The model emerges from an analogy between FX dynamics and hydrodynamic turbulence. The heterogeneity of the market is m…
Detecting Consumers' Financial Vulnerability using Open Banking Data: Evidence from UK Payday Loansstat.AP
Study identifies two borrowing patterns in UK payday loan users.
problem Financial vulnerability of payday loan users.
method Two-state hidden Markov model (HMM) using Open Banking data.
result 36.4% of borrowers experience high-intensity exposure for 12 weeks or more.
Study cosmic structures using Topological Data Analysis and Persistence Energy.
problem Investigate cosmic web evolution in CDM cosmologies.
method Apply LITE method to embed persistence diagrams into vector spaces and analyze cosmic structures.
result Discover a correlation between Persistence Energy and redshift values.