Joint Curve Registration and Classification with Two-level Functional Models

Functional Registration and Local Variations: Identifiability, Rank, and Tuning

We develop theory and methodology for the problem of nonparametric registration of functional data that have been subjected to random deformation (warping) of their time scale. The separation of this phase variation ("horizontal" variation) from the amplitude variation ("vertical" variation) is crucial in order to properly conduct further analyses, which otherwise can be severely distorted. We determine precise nonparametric conditions under which the two forms of variation are identifiable. These show that the identifiability delicately depends on the underlying rank. By means of several coun…

面向函数型数据的序贯贝叶斯配准方法

Sequential Bayesian Registration for Functional Data

针对函数型数据序贯采集、现有配准方法需全量重拟合的问题，提出基于序贯蒙特卡洛采样的贝叶斯序贯配准框架，可递归更新函数对齐并兼顾不确定性，结合分布式计算降低成本，在模拟与三类真实数据上验证了有效性。

Model-based curve registration via stochastic approximation EM algorithm

Functional data often exhibit both amplitude and phase variation around a common base shape, with phase variation represented by a so called warping function. The process removing phase variation by curve alignment and inference of the warping functions is referred to as curve registration. When functional data are observed with substantial noise, model-based methods can be employed for simultaneous smoothing and curve registration. However, the nonlinearity of the model often renders the inference computationally challenging. In this paper, we propose an alternative method for model-based cur…

Improved fMRI-based Pain Prediction using Bayesian Group-wise Functional Registration

In recent years, neuroimaging has undergone a paradigm shift, moving away from the traditional brain mapping approach toward developing integrated, multivariate brain models that can predict categories of mental events. However, large interindividual differences in brain anatomy and functional localization after standard anatomical alignment remain a major limitation in performing this analysis, as it leads to feature misalignment across subjects in subsequent predictive models.

Registration-free localization of defects in 3-D parts from mesh metrology data using functional maps

Spectral Laplacian methods, widely used in computer graphics and manifold learning, have been recently proposed for the Statistical Process Control (SPC) of a sequence of manufactured parts, whose 3-dimensional metrology is acquired with non-contact sensors. These techniques provide an {\em intrinsic} solution to the SPC problem, that is, a solution exclusively based on measurements on the scanned surfaces or 2-manifolds without making reference to their ambient space. These methods, therefore, avoid the computationally expensive, non-convex registration step needed to align the parts, as requ…

Spatially Penalised Registration of Multivariate Functional Data

Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we focus on the hitherto unconsidered setting where phase variation of the component functions are spatially correlated. We propose an algorithm to optimize a metric-based objective function for registration with a novel penalty term that incorporates the spatial correlation between the component phase variations through a kriging estimate of an appropriate phase r…

部分观测函数型数据的联合配准与保形预测

Joint Registration and Conformal Prediction for Partially Observed Functional Data

针对部分观测函数型数据缺失段预测的挑战，提出联合配准与保形预测方法，分离振幅和相位变异，整合配准与预测，生成可靠预测带，且实现简单、计算高效。

Feature Sensitive and Automated Curve Registration

Given two sets of functional data having a common underlying mean function but different degrees of distortion in time measurements, we provide a method of estimating the time transformation necessary to align (or `register') them. We prove that the proposed method is consistent under fairly general conditions. Simulation results show superiority of the performance of the proposed method over two existing methods. The proposed method is illustrated through the analysis of three paleoclimatic data sets.

探索Covid-19时空动力学：非欧几里得空间感知函数配准

Exploring Covid-19 Spatiotemporal Dynamics: Non-Euclidean Spatially Aware Functional Registration

本文提出一种非欧几里得空间感知函数配准方法，通过多维标度近似驾驶时间以解决传统空间框架失效问题，定量分析了英国380个地区Covid-19疫情波次的时空相位变化。

Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse and Fragmented Functional Data

In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense, sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and estimating the individual underlying functions from discrete observations has thus far been mainly approached sequentially without formal uncertainty propagation, or in an application-specific manner. We propose a unified Bayesian framework for simultaneous registration and estimation, which is flexible enough to accommodate inference on individual functions …

Multimodal Bayesian Registration of Noisy Functions using Hamiltonian Monte Carlo

Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty, which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account…

Feature Sensitive Curve Registration by Kernel Matching

In this paper, we argue that the problem of registering two sets of functional data, where the underlying mean function has sharp features, is not properly addressed by methods designed to align a bunch of growth curves data. We provide a new method, which is able to pool local information without smoothing and to match sharp landmarks without manual identification. This method, which we refer to as kernel-matched registration, is based on maximizing a kernel-based measure of alignment. We prove that the proposed method is consistent under fairly general conditions. Simulation results show sup…

Registration of Functional Data Using Fisher-Rao Metric

We introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This framework uses the Fisher-Rao Riemannian metric to derive a proper distance on the quotient space of functions modulo the time-warping group. A convenient square-root velocity function (SRVF) representation transforms the Fisher-Rao metric into the standard $\ltwo$ metric, simplifying the computations. This distance is then used to define a Karcher mean template and warp the individual functions to align them with the K…