Pub Date : 2024-09-17DOI: 10.1186/s13362-024-00161-w
Giulia Elena Aliffi, Giovanni Nastasi, Vittorio Romano, Dario Pitocco, Alessandro Rizzi, Elvin J. Moore, Andrea De Gaetano
Diabetes Mellitus is a metabolic disorder which may result in severe and potentially fatal complications if not well-treated and monitored. In this study, a quantitative analysis of the data collected using CGM (Continuous Glucose Monitoring) devices from eight subjects with type 2 diabetes in good metabolic control at the University Polyclinic Agostino Gemelli, Catholic University of the Sacred Heart, was carried out. In particular, a system of ordinary differential equations whose state variables are affected by a sequence of stochastic perturbations was proposed and used to extract more informative inferences from the patients’ data. For this work, Matlab and R programs were used to find the most appropriate values of the parameters (according to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)) for each patient. Fitting was carried out by Particle Swarm Optimization to minimize the ordinary least squares error between the observed CGM data and the data from the ODE model. Goodness of fit tests were made in order to assess which probability distribution was best suitable for representing the waiting times computed from the model parameters. Finally, both parametric and non-parametric density estimation of the frequency histograms associated with the variability of the glucose elimination rate from blood were conducted and their representative parameters assessed from the data. The results show that the chosen models succeed in capturing most of the glucose fluctuations for almost every patient.
{"title":"A system of ODEs for representing trends of CGM signals","authors":"Giulia Elena Aliffi, Giovanni Nastasi, Vittorio Romano, Dario Pitocco, Alessandro Rizzi, Elvin J. Moore, Andrea De Gaetano","doi":"10.1186/s13362-024-00161-w","DOIUrl":"https://doi.org/10.1186/s13362-024-00161-w","url":null,"abstract":"Diabetes Mellitus is a metabolic disorder which may result in severe and potentially fatal complications if not well-treated and monitored. In this study, a quantitative analysis of the data collected using CGM (Continuous Glucose Monitoring) devices from eight subjects with type 2 diabetes in good metabolic control at the University Polyclinic Agostino Gemelli, Catholic University of the Sacred Heart, was carried out. In particular, a system of ordinary differential equations whose state variables are affected by a sequence of stochastic perturbations was proposed and used to extract more informative inferences from the patients’ data. For this work, Matlab and R programs were used to find the most appropriate values of the parameters (according to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)) for each patient. Fitting was carried out by Particle Swarm Optimization to minimize the ordinary least squares error between the observed CGM data and the data from the ODE model. Goodness of fit tests were made in order to assess which probability distribution was best suitable for representing the waiting times computed from the model parameters. Finally, both parametric and non-parametric density estimation of the frequency histograms associated with the variability of the glucose elimination rate from blood were conducted and their representative parameters assessed from the data. The results show that the chosen models succeed in capturing most of the glucose fluctuations for almost every patient.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"16 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-16DOI: 10.1186/s13362-024-00160-x
Stefan Gavranovic, Zain Hassan, Lukas Failer, Dirk Hartmann
While interactive simulations have been mostly limited to Computer Graphics applications, new generations of Graphics Processing Units (GPUs) allow the realization of industrial-grade interactive 3D physics simulations. By combining an immersed boundary method with efficient GPU-based MINRES and CG solvers using a GPU-based geometric multigrid preconditioner, we demonstrate a fast industrial 3D computational mechanics solver. The various implementation aspects - specifically how they differ from similar concepts used in the Computer Graphics community - are discussed in detail. The proposed concept opens up new classes of industrial simulation applications allowing a democratization beyond today’s expert users, from designer centric simulation to operational and service decisions based on 3D simulations. To support this, we provide various benchmark cases including a real-world study of a simulation-based service decision for a damaged gear-box mount.
{"title":"Fast 3D solvers for interactive computational mechanics","authors":"Stefan Gavranovic, Zain Hassan, Lukas Failer, Dirk Hartmann","doi":"10.1186/s13362-024-00160-x","DOIUrl":"https://doi.org/10.1186/s13362-024-00160-x","url":null,"abstract":"While interactive simulations have been mostly limited to Computer Graphics applications, new generations of Graphics Processing Units (GPUs) allow the realization of industrial-grade interactive 3D physics simulations. By combining an immersed boundary method with efficient GPU-based MINRES and CG solvers using a GPU-based geometric multigrid preconditioner, we demonstrate a fast industrial 3D computational mechanics solver. The various implementation aspects - specifically how they differ from similar concepts used in the Computer Graphics community - are discussed in detail. The proposed concept opens up new classes of industrial simulation applications allowing a democratization beyond today’s expert users, from designer centric simulation to operational and service decisions based on 3D simulations. To support this, we provide various benchmark cases including a real-world study of a simulation-based service decision for a damaged gear-box mount.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"118 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-10DOI: 10.1186/s13362-024-00159-4
Matei Hanu, Jürgen Hesser, Guido Kanschat, Javier Moviglia, Claudia Schillings, Jan Stallkamp
This paper addresses the challenging task of guide wire navigation in cardiovascular interventions, focusing on the parameter estimation of a guide wire system using Ensemble Kalman Inversion (EKI) with a subsampling technique. The EKI uses an ensemble of particles to estimate the unknown quantities. However, since the data misfit has to be computed for each particle in each iteration, the EKI may become computationally infeasible in the case of high-dimensional data, e.g. high-resolution images. This issue can been addressed by randomised algorithms that utilize only a random subset of the data in each iteration. We introduce and analyse a subsampling technique for the EKI, which is based on a continuous-time representation of stochastic gradient methods and apply it to on the parameter estimation of our guide wire system. Numerical experiments with real data from a simplified test setting demonstrate the potential of the method.
{"title":"Ensemble Kalman inversion for image guided guide wire navigation in vascular systems","authors":"Matei Hanu, Jürgen Hesser, Guido Kanschat, Javier Moviglia, Claudia Schillings, Jan Stallkamp","doi":"10.1186/s13362-024-00159-4","DOIUrl":"https://doi.org/10.1186/s13362-024-00159-4","url":null,"abstract":"This paper addresses the challenging task of guide wire navigation in cardiovascular interventions, focusing on the parameter estimation of a guide wire system using Ensemble Kalman Inversion (EKI) with a subsampling technique. The EKI uses an ensemble of particles to estimate the unknown quantities. However, since the data misfit has to be computed for each particle in each iteration, the EKI may become computationally infeasible in the case of high-dimensional data, e.g. high-resolution images. This issue can been addressed by randomised algorithms that utilize only a random subset of the data in each iteration. We introduce and analyse a subsampling technique for the EKI, which is based on a continuous-time representation of stochastic gradient methods and apply it to on the parameter estimation of our guide wire system. Numerical experiments with real data from a simplified test setting demonstrate the potential of the method.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"34 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-27DOI: 10.1186/s13362-024-00157-6
Katarzyna Skowronek, Radosław Zimroz, Agnieszka Wyłomańska
In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains.
{"title":"Testing for finite variance with applications to vibration signals from rotating machines","authors":"Katarzyna Skowronek, Radosław Zimroz, Agnieszka Wyłomańska","doi":"10.1186/s13362-024-00157-6","DOIUrl":"https://doi.org/10.1186/s13362-024-00157-6","url":null,"abstract":"In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"269 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-19DOI: 10.1186/s13362-024-00156-7
Sílvia Barbeiro, Rafael Henriques, José Luis Santos
In this work we focus on the development of a numerical algorithm for the inverse elastography problem. The goal is to perform an efficient material parameter identification knowing the elastic displacement field induced by a mechanical load. We propose to define the inverse problem through a quadratic optimization program which uses the direct problem formulation to define the objective function. In this way, we end up with a convex minimization problem which attains its minimum at the solution of a linear system. The effectiveness of our method is illustrated through numeral examples.
{"title":"A quadratic optimization program for the inverse elastography problem","authors":"Sílvia Barbeiro, Rafael Henriques, José Luis Santos","doi":"10.1186/s13362-024-00156-7","DOIUrl":"https://doi.org/10.1186/s13362-024-00156-7","url":null,"abstract":"In this work we focus on the development of a numerical algorithm for the inverse elastography problem. The goal is to perform an efficient material parameter identification knowing the elastic displacement field induced by a mechanical load. We propose to define the inverse problem through a quadratic optimization program which uses the direct problem formulation to define the objective function. In this way, we end up with a convex minimization problem which attains its minimum at the solution of a linear system. The effectiveness of our method is illustrated through numeral examples.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"49 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-16DOI: 10.1186/s13362-024-00155-8
Natascha Jeziorski, Claudia Redenbach
Training defect detection algorithms for visual surface inspection systems requires a large and representative set of training data. Often there is not enough real data available which additionally cannot cover the variety of possible defects. Synthetic data generated by a synthetic visual surface inspection environment can overcome this problem. Therefore, a digital twin of the object is needed, whose micro-scale surface topography is modeled by texture synthesis models. We develop stochastic texture models for sandblasted and milled surfaces based on topography measurements of such surfaces. As the surface patterns differ significantly, we use separate modeling approaches for the two cases. Sandblasted surfaces are modeled by a combination of data-based texture synthesis methods that rely entirely on the measurements. In contrast, the model for milled surfaces is procedural and includes all process-related parameters known from the machine settings.
{"title":"Stochastic geometry models for texture synthesis of machined metallic surfaces: sandblasting and milling","authors":"Natascha Jeziorski, Claudia Redenbach","doi":"10.1186/s13362-024-00155-8","DOIUrl":"https://doi.org/10.1186/s13362-024-00155-8","url":null,"abstract":"Training defect detection algorithms for visual surface inspection systems requires a large and representative set of training data. Often there is not enough real data available which additionally cannot cover the variety of possible defects. Synthetic data generated by a synthetic visual surface inspection environment can overcome this problem. Therefore, a digital twin of the object is needed, whose micro-scale surface topography is modeled by texture synthesis models. We develop stochastic texture models for sandblasted and milled surfaces based on topography measurements of such surfaces. As the surface patterns differ significantly, we use separate modeling approaches for the two cases. Sandblasted surfaces are modeled by a combination of data-based texture synthesis methods that rely entirely on the measurements. In contrast, the model for milled surfaces is procedural and includes all process-related parameters known from the machine settings.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"11 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-14DOI: 10.1186/s13362-024-00151-y
Aleksander A. Stanislavsky, Aleksander Weron
The molecular movement in single particle tracking (SPT) experiments shows a crucial role of diffusion in many biological processes such as signaling, cellular organization, transport mechanisms, and more. The SPT analysis detects not only classical Brownian motion but diffusion with other features. These include directed diffusion and confined motion. The behavior remains a challenging problem for several reasons. Due to the action of many physical processes, random trajectories of cellular molecules are segmented in different diffusive modes. Often their study requires sophisticated algorithms for the analysis of statistical properties. In this paper we consider the segment analysis for trajectories of G proteins and coupled-receptors in living cells. Their movement is often transient and switches among free diffusion, confined diffusion, directed diffusion, and immobility. Moreover, the confined segments can have both Gaussian and non-Gaussian statistics. The types of alternation of diffusive modes along the trajectories of G proteins and coupled-receptors are analyzed.
单粒子追踪（SPT）实验中的分子运动表明，扩散在信号传递、细胞组织、运输机制等许多生物过程中都起着至关重要的作用。SPT 分析不仅能检测到经典的布朗运动，还能检测到具有其他特征的扩散。这些特征包括定向扩散和封闭运动。由于多种原因，这种行为仍然是一个具有挑战性的问题。由于许多物理过程的作用，细胞分子的随机轨迹被分割成不同的扩散模式。对它们的研究通常需要复杂的统计特性分析算法。在本文中，我们考虑对活细胞中的 G 蛋白和耦合受体的轨迹进行分段分析。它们的运动通常是瞬时的，并在自由扩散、封闭扩散、定向扩散和不动之间切换。此外，受限段可能具有高斯和非高斯统计量。本文分析了 G 蛋白和耦合受体轨迹上的扩散模式交替类型。
{"title":"Transient motion classification and segment analysis of diffusive trajectories of G proteins and coupled-receptors in a living cell","authors":"Aleksander A. Stanislavsky, Aleksander Weron","doi":"10.1186/s13362-024-00151-y","DOIUrl":"https://doi.org/10.1186/s13362-024-00151-y","url":null,"abstract":"The molecular movement in single particle tracking (SPT) experiments shows a crucial role of diffusion in many biological processes such as signaling, cellular organization, transport mechanisms, and more. The SPT analysis detects not only classical Brownian motion but diffusion with other features. These include directed diffusion and confined motion. The behavior remains a challenging problem for several reasons. Due to the action of many physical processes, random trajectories of cellular molecules are segmented in different diffusive modes. Often their study requires sophisticated algorithms for the analysis of statistical properties. In this paper we consider the segment analysis for trajectories of G proteins and coupled-receptors in living cells. Their movement is often transient and switches among free diffusion, confined diffusion, directed diffusion, and immobility. Moreover, the confined segments can have both Gaussian and non-Gaussian statistics. The types of alternation of diffusive modes along the trajectories of G proteins and coupled-receptors are analyzed.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"68 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-02DOI: 10.1186/s13362-024-00143-y
Stephan Scholz, Lothar Berger
The chain rule is a standard tool in differential calculus to find derivatives of composite functions. Faà di Bruno’s formula is a generalization of the chain rule and states a method to find high-order derivatives. In this contribution, we propose an algorithm based on Faà di Bruno’s formula and Bell polynomials (Bell in Ann Math 29:38–46, 1927; Parks and Krantz in A primer of real analytic functions, 2012) to compute the structure of derivatives of function compositions. The application of our method is showcased using trajectory planning for the heat equation (Laroche et al. in Int J Robust Nonlinear Control 10(8):629–643, 2000).
链式法则是微分学中求复合函数导数的标准工具。Faà di Bruno 公式是对链式法则的概括，提出了一种求高阶导数的方法。在这篇论文中，我们提出了一种基于 Faà di Bruno 公式和贝尔多项式（Bell，发表于 Ann Math 29:38-46, 1927 年；Parks 和 Krantz，发表于 A primer of real analytic functions, 2012 年）的算法，用于计算函数合成导数的结构。我们的方法在热方程的轨迹规划中得到了应用（Laroche 等人，载于 Int J Robust Nonlinear Control 10(8):629-643, 2000）。
{"title":"Fast computation of function composition derivatives for flatness-based control of diffusion problems","authors":"Stephan Scholz, Lothar Berger","doi":"10.1186/s13362-024-00143-y","DOIUrl":"https://doi.org/10.1186/s13362-024-00143-y","url":null,"abstract":"The chain rule is a standard tool in differential calculus to find derivatives of composite functions. Faà di Bruno’s formula is a generalization of the chain rule and states a method to find high-order derivatives. In this contribution, we propose an algorithm based on Faà di Bruno’s formula and Bell polynomials (Bell in Ann Math 29:38–46, 1927; Parks and Krantz in A primer of real analytic functions, 2012) to compute the structure of derivatives of function compositions. The application of our method is showcased using trajectory planning for the heat equation (Laroche et al. in Int J Robust Nonlinear Control 10(8):629–643, 2000).","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"44 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-31DOI: 10.1186/s13362-024-00154-9
Krzysztof Burnecki, Marek A. Teuerle, Martyna Zdeb
In this paper we build a methodology for pricing of insurance-linked securities which are tied to multiple natural catastrophe perils. As a representative example, we construct a multi-peril catastrophe (CAT) bond which can be linked to the industry loss indices or actual losses incurred by an insurer. We provide pricing formulas for such CAT bonds. We illustrate the introduced methodology on the US natural catastrophe data obtained from Property Claim Services (PCS). Within this dataset, we specifically examine two types of risks: losses associated with wind and thunderstorm events, and those linked to winter storm events. Then, we fit and validate the underlying compound non-homogeneous Poisson processes taking into account the fact that the data are left-truncated. The best fitted loss distributions appear to be Burr and Generalised Extreme Value and for the first peril and log-normal for the second. Finally, we visualise the zero-coupon CAT bond prices for the selected best-fitted models.
{"title":"Pricing of insurance-linked securities: a multi-peril approach","authors":"Krzysztof Burnecki, Marek A. Teuerle, Martyna Zdeb","doi":"10.1186/s13362-024-00154-9","DOIUrl":"https://doi.org/10.1186/s13362-024-00154-9","url":null,"abstract":"In this paper we build a methodology for pricing of insurance-linked securities which are tied to multiple natural catastrophe perils. As a representative example, we construct a multi-peril catastrophe (CAT) bond which can be linked to the industry loss indices or actual losses incurred by an insurer. We provide pricing formulas for such CAT bonds. We illustrate the introduced methodology on the US natural catastrophe data obtained from Property Claim Services (PCS). Within this dataset, we specifically examine two types of risks: losses associated with wind and thunderstorm events, and those linked to winter storm events. Then, we fit and validate the underlying compound non-homogeneous Poisson processes taking into account the fact that the data are left-truncated. The best fitted loss distributions appear to be Burr and Generalised Extreme Value and for the first peril and log-normal for the second. Finally, we visualise the zero-coupon CAT bond prices for the selected best-fitted models.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"75 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-30DOI: 10.1186/s13362-024-00153-w
Rani Basna, Hiba Nassar, Krzysztof Podgórski
Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods.
{"title":"Spline-based methods for functional data on multivariate domains","authors":"Rani Basna, Hiba Nassar, Krzysztof Podgórski","doi":"10.1186/s13362-024-00153-w","DOIUrl":"https://doi.org/10.1186/s13362-024-00153-w","url":null,"abstract":"Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"211 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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