scholarly journals Empowering Advanced Driver-Assistance Systems from Topological Data Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 634
Author(s):  
Tarek Frahi ◽  
Francisco Chinesta ◽  
Antonio Falcó ◽  
Alberto Badias ◽  
Elias Cueto ◽  
...  
Keyword(s):  
Data Analysis ◽  
The State ◽  
Sensor Data ◽  
Topological Data Analysis ◽  
Motion Sensors ◽  
Driver Assistance Systems ◽  
The Road ◽  
Topological Features ◽  
Recent Developments ◽  
Topological Data

We are interested in evaluating the state of drivers to determine whether they are attentive to the road or not by using motion sensor data collected from car driving experiments. That is, our goal is to design a predictive model that can estimate the state of drivers given the data collected from motion sensors. For that purpose, we leverage recent developments in topological data analysis (TDA) to analyze and transform the data coming from sensor time series and build a machine learning model based on the topological features extracted with the TDA. We provide some experiments showing that our model proves to be accurate in the identification of the state of the user, predicting whether they are relaxed or tense.

scholarly journals Topological Data Analysis Approaches to Uncovering the Timing of Ring Structure Onset in Filamentous Networks

2021 ◽  
Vol 83 (3) ◽  
Author(s):  
Maria-Veronica Ciocanel ◽  
Riley Juenemann ◽  
Adriana T. Dawes ◽  
Scott A. McKinley
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Actin Filaments ◽  
Time Series Data ◽  
Polymer Networks ◽  
Topological Data Analysis ◽  
Series Data ◽  
Topological Features ◽  
Topological Data

AbstractIn developmental biology as well as in other biological systems, emerging structure and organization can be captured using time-series data of protein locations. In analyzing this time-dependent data, it is a common challenge not only to determine whether topological features emerge, but also to identify the timing of their formation. For instance, in most cells, actin filaments interact with myosin motor proteins and organize into polymer networks and higher-order structures. Ring channels are examples of such structures that maintain constant diameters over time and play key roles in processes such as cell division, development, and wound healing. Given the limitations in studying interactions of actin with myosin in vivo, we generate time-series data of protein polymer interactions in cells using complex agent-based models. Since the data has a filamentous structure, we propose sampling along the actin filaments and analyzing the topological structure of the resulting point cloud at each time. Building on existing tools from persistent homology, we develop a topological data analysis (TDA) method that assesses effective ring generation in this dynamic data. This method connects topological features through time in a path that corresponds to emergence of organization in the data. In this work, we also propose methods for assessing whether the topological features of interest are significant and thus whether they contribute to the formation of an emerging hole (ring channel) in the simulated protein interactions. In particular, we use the MEDYAN simulation platform to show that this technique can distinguish between the actin cytoskeleton organization resulting from distinct motor protein binding parameters.

scholarly journals Using Topological Data Analysis (TDA) and Persistent Homology to Analyze the Stock Markets in Singapore and Taiwan

2021 ◽  
Vol 9 ◽  
Author(s):  
Peter Tsung-Wen Yen ◽  
Siew Ann Cheong
Keyword(s):  
Data Analysis ◽  
Stock Markets ◽  
Persistent Homology ◽  
Betti Numbers ◽  
Stock Index ◽  
Topological Data Analysis ◽  
Series Data ◽  
Topological Features ◽  
Market Crashes ◽  
Topological Data

In recent years, persistent homology (PH) and topological data analysis (TDA) have gained increasing attention in the fields of shape recognition, image analysis, data analysis, machine learning, computer vision, computational biology, brain functional networks, financial networks, haze detection, etc. In this article, we will focus on stock markets and demonstrate how TDA can be useful in this regard. We first explain signatures that can be detected using TDA, for three toy models of topological changes. We then showed how to go beyond network concepts like nodes (0-simplex) and links (1-simplex), and the standard minimal spanning tree or planar maximally filtered graph picture of the cross correlations in stock markets, to work with faces (2-simplex) or any k-dim simplex in TDA. By scanning through a full range of correlation thresholds in a procedure called filtration, we were able to examine robust topological features (i.e. less susceptible to random noise) in higher dimensions. To demonstrate the advantages of TDA, we collected time-series data from the Straits Times Index and Taiwan Capitalization Weighted Stock Index (TAIEX), and then computed barcodes, persistence diagrams, persistent entropy, the bottleneck distance, Betti numbers, and Euler characteristic. We found that during the periods of market crashes, the homology groups become less persistent as we vary the characteristic correlation. For both markets, we found consistent signatures associated with market crashes in the Betti numbers, Euler characteristics, and persistent entropy, in agreement with our theoretical expectations.

scholarly journals Feasibility of topological data analysis for event-related fMRI

2019 ◽  
Vol 3 (3) ◽  
pp. 695-706 ◽  
Author(s):  
Cameron T. Ellis ◽  
Michael Lesnick ◽  
Gregory Henselman-Petrusek ◽  
Bryn Keller ◽  
Jonathan D. Cohen
Keyword(s):  
Data Analysis ◽  
Persistent Homology ◽  
Time Frame ◽  
Topological Data Analysis ◽  
Fmri Data ◽  
Cognitive Representations ◽  
New Approach ◽  
Neural Data ◽  
Topological Features ◽  
Topological Data

Recent fMRI research shows that perceptual and cognitive representations are instantiated in high-dimensional multivoxel patterns in the brain. However, the methods for detecting these representations are limited. Topological data analysis (TDA) is a new approach, based on the mathematical field of topology, that can detect unique types of geometric features in patterns of data. Several recent studies have successfully applied TDA to study various forms of neural data; however, to our knowledge, TDA has not been successfully applied to data from event-related fMRI designs. Event-related fMRI is very common but limited in terms of the number of events that can be run within a practical time frame and the effect size that can be expected. Here, we investigate whether persistent homology—a popular TDA tool that identifies topological features in data and quantifies their robustness—can identify known signals given these constraints. We use fmrisim, a Python-based simulator of realistic fMRI data, to assess the plausibility of recovering a simple topological representation under a variety of conditions. Our results suggest that persistent homology can be used under certain circumstances to recover topological structure embedded in realistic fMRI data simulations.

scholarly journals An algorithm for matching spatial objects of different-scale maps based on topological data analysis

2019 ◽  
Vol 43 (6) ◽  
pp. 1021-1029 ◽  
Author(s):  
S.V. Eremeev ◽  
D.E. Andrianov ◽  
V.S. Titov
Keyword(s):  
Data Analysis ◽  
Spatial Data ◽  
General Structure ◽  
Persistent Homology ◽  
Topological Data Analysis ◽  
Spatial Objects ◽  
Topological Features ◽  
Definition Of ◽  
Topological Data

A problem of automatic comparison of spatial objects on maps with different scales for the same locality is considered in the article. It is proposed that this problem should be solved using methods of topological data analysis. The initial data of the algorithm are spatial objects that can be obtained from maps with different scales and subjected to deformations and distortions. Persistent homology allows us to identify the general structure of such objects in the form of topological features. The main topological features in the study are the connectivity components and holes in objects. The paper gives a mathematical description of the persistent homology method for representing spatial objects. A definition of a barcode for spatial data, which contains a description of the object in the form of topological features is given. An algorithm for comparing feature barcodes was developed. It allows us to find the general structure of objects. The algorithm is based on the analysis of data from the barcode. An index of objects similarity in terms of topological features is introduced. Results of the research of the algorithm for comparing maps of natural and municipal objects with different scales, generalization and deformation are shown. The experiments confirm the high quality of the proposed algorithm. The percentage of similarity in the comparison of natural objects, while taking into account the scale and deformation, is in the range from 85 to 92, and for municipal objects, after stretching and distortion of their parts, was from 74 to 87. Advantages of the proposed approach over analogues for the comparison of objects with significant deformation at different scales and after distortion are demonstrated.

scholarly journals Topological data analysis and machine learning for recognizing atmospheric river patterns in large climate datasets

2019 ◽  
Vol 12 (2) ◽  
pp. 613-628 ◽  
Author(s):  
Grzegorz Muszynski ◽  
Karthik Kashinath ◽  
Vitaliy Kurlin ◽  
Michael Wehner ◽  
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Climate Model ◽  
Topological Data Analysis ◽  
Extreme Weather Events ◽  
Climate Change Scenarios ◽  
Climate Data ◽  
Automated Method ◽  
Topological Features ◽  
Topological Data

Abstract. Identifying weather patterns that frequently lead to extreme weather events is a crucial first step in understanding how they may vary under different climate change scenarios. Here, we propose an automated method for recognizing atmospheric rivers (ARs) in climate data using topological data analysis and machine learning. The method provides useful information about topological features (shape characteristics) and statistics of ARs. We illustrate this method by applying it to outputs of version 5.1 of the Community Atmosphere Model version 5.1 (CAM5.1) and the reanalysis product of the second Modern-Era Retrospective Analysis for Research and Applications (MERRA-2). An advantage of the proposed method is that it is threshold-free – there is no need to determine any threshold criteria for the detection method – when the spatial resolution of the climate model changes. Hence, this method may be useful in evaluating model biases in calculating AR statistics. Further, the method can be applied to different climate scenarios without tuning since it does not rely on threshold conditions. We show that the method is suitable for rapidly analyzing large amounts of climate model and reanalysis output data.

scholarly journals Feasibility of Topological Data Analysis for event-related fMRI

2018 ◽  
Author(s):  
Cameron T. Ellis ◽  
Michael Lesnick ◽  
Gregory Henselman-Petrusek ◽  
Bryn Keller ◽  
Jonathan D. Cohen
Keyword(s):  
Data Analysis ◽  
Persistent Homology ◽  
Time Frame ◽  
Topological Data Analysis ◽  
Fmri Data ◽  
Cognitive Representations ◽  
New Approach ◽  
Neural Data ◽  
Topological Features ◽  
Topological Data

AbstractRecent fMRI research shows that perceptual and cognitive representations are instantiated in high-dimensional multi-voxel patterns in the brain. However, the methods for detecting these representations are limited. Topological Data Analysis (TDA) is a new approach, based on the mathematical field of topology, that can detect unique types of geometric features in patterns of data. Several recent studies have successfully applied TDA to study various forms of neural data; however, to our knowledge, TDA has not been successfully applied to data from event-related fMRI designs. Event-related fMRI is very common but limited in terms of the number of events that can be run within a practical time frame and the effect size that can be expected. Here, we investigate whether persistent homology — a popular TDA tool that identifies topological features in data and quantifies their robustness — can identify known signals given these constraints. We use fmrisim, a Python-based simulator of realistic fMRI data, to assess the plausibility of recovering a simple topological representation under a variety of conditions. Our results suggest that persistent homology can be used under certain circumstances to recover topological structure embedded in realistic fMRI data simulations.

scholarly journals Topological Data Analysis and Machine Learning for Recognizing Atmospheric River Patterns in Large Climate Datasets

2018 ◽  
Author(s):  
Grzegorz Muszynski ◽  
Karthik Kashinath ◽  
Vitaliy Kurlin ◽  
Michael Wehner ◽  
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Climate Model ◽  
Topological Data Analysis ◽  
Extreme Weather Events ◽  
Climate Change Scenarios ◽  
Climate Data ◽  
Automated Method ◽  
Topological Features ◽  
Topological Data

Abstract. Identifying weather patterns that frequently lead to extreme weather events is a crucial first step in understanding how they may vary under different climate change scenarios. Here we propose an automated method for recognizing atmospheric rivers (ARs) in climate data using topological data analysis and machine learning. The method provides useful information about topological features (shape characteristics) and statistics of ARs. We illustrate this method by applying it to outputs of 5 version 5.1 of the Community Atmosphere Model (CAM5.1) and reanalysis product of the second Modern-Era Retrospective Analysis for Research & Applications (MERRA-2). An advantage of the proposed method is that it is threshold-free. Hence this method may be useful in evaluating model biases in calculating AR statistics. Further, the method can be applied to different climate scenarios without tuning since it does not rely on threshold conditions. We show that the method is suitable for rapidly analyzing large amounts of climate model and reanalysis output data.

scholarly journals Assessment of skin barrier function using skin images with topological data analysis

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Keita Koseki ◽  
Hiroshi Kawasaki ◽  
Toru Atsugi ◽  
Miki Nakanishi ◽  
Makoto Mizuno ◽  
...  
Keyword(s):  
Data Analysis ◽  
Barrier Function ◽  
Skin Diseases ◽  
Skin Barrier ◽  
Structural Features ◽  
Transepidermal Water Loss ◽  
Topological Data Analysis ◽  
Skin Barrier Function ◽  
Topological Features ◽  
Topological Data

AbstractRecent developments of molecular biology have revealed diverse mechanisms of skin diseases, and precision medicine considering these mechanisms requires the frequent objective evaluation of skin phenotypes. Transepidermal water loss (TEWL) is commonly used for evaluating skin barrier function; however, direct measurement of TEWL is time-consuming and is not convenient for daily clinical practice. Here, we propose a new skin barrier assessment method using skin images with topological data analysis (TDA). TDA enabled efficient identification of structural features from a skin image taken by a microscope. These features reflected the regularity of the skin texture. We found a significant correlation between the topological features and TEWL. Moreover, using the features as input, we trained machine-learning models to predict TEWL and obtained good accuracy (R2 = 0.524). Our results suggest that assessment of skin barrier function by topological image analysis is promising.

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