The joint alignment of multivariate functional data plays an important role
in various fields such as signal processing, neuroscience and medicine,
including the statistical analysis of data from wearable devices. Traditional
methods often ignore the phase variability and instead focus on the variability
in the observed amplitude. We present a novel method for joint alignment of
multivariate quasi-periodic functions using deep neural networks, decomposing,
but retaining all the information in the data by preserving both phase and
amplitude variability. Our proposed neural network uses a special activation of
the output that builds on the unit simplex transformation, and we utilize a
loss function based on the Fisher-Rao metric to train our model. Furthermore,
our method is unsupervised and can provide an optimal common template function
as well as subject-specific templates. We demonstrate our method on two
simulated datasets and one real example, comprising data from 12-lead 10s
electrocardiogram recordings.

使用深度神经网络对多元准周期函数进行联合对齐，既保留相位和振幅的变异性，又使用基于 Fisher-Rao 度量的损失函数进行模型训练，适用于可穿戴设备等多个领域的多元功能数据的统计分析。

使用深度学习进行多元准周期函数数据的联合对齐

Joint Alignment of Multivariate Quasi-Periodic Functional Data Using  Deep Learning

In video analysis, background models have many applications such as
background/foreground separation, change detection, anomaly detection,
tracking, and more. However, while learning such a model in a video captured by
a static camera is a fairly-solved task, in the case of a Moving-camera
Background Model (MCBM), the success has been far more modest due to
algorithmic and scalability challenges that arise due to the camera motion.
Thus, existing MCBMs are limited in their scope and their supported
camera-motion types. These hurdles also impeded the employment, in this
unsupervised task, of end-to-end solutions based on deep learning (DL).
Moreover, existing MCBMs usually model the background either on the domain of a
typically-large panoramic image or in an online fashion. Unfortunately, the
former creates several problems, including poor scalability, while the latter
prevents the recognition and leveraging of cases where the camera revisits
previously-seen parts of the scene. This paper proposes a new method, called
DeepMCBM, that eliminates all the aforementioned issues and achieves
state-of-the-art results. Concretely, first we identify the difficulties
associated with joint alignment of video frames in general and in a DL setting
in particular. Next, we propose a new strategy for joint alignment that lets us
use a spatial transformer net with neither a regularization nor any form of
specialized (and non-differentiable) initialization. Coupled with an
autoencoder conditioned on unwarped robust central moments (obtained from the
joint alignment), this yields an end-to-end regularization-free MCBM that
supports a broad range of camera motions and scales gracefully. We demonstrate
DeepMCBM's utility on a variety of videos, including ones beyond the scope of
other methods. Our code is available at this https URL .

该论文提出了一种新的方法，名为 DeepMCBM，它使用联合对齐的策略和空间变换网络来消除摄像机移动的背景模型领域中的挑战，并实现了最先进的结果。

深度运动相机背景模型

A Deep Moving-camera Background Model

Joint alignment of a collection of functions is the process of independently
transforming the functions so that they appear more similar to each other.
Typically, such unsupervised alignment algorithms fail when presented with
complex data sets arising from multiple modalities or make restrictive
assumptions about the form of the functions or transformations, limiting their
generality. We present a transformed Bayesian infinite mixture model that can
simultaneously align and cluster a data set. Our model and associated learning
scheme offer two key advantages: the optimal number of clusters is determined
in a data-driven fashion through the use of a Dirichlet process prior, and it
can accommodate any transformation function parameterized by a continuous
parameter vector. As a result, it is applicable to a wide range of data types,
and transformation functions. We present positive results on synthetic
two-dimensional data, on a set of one-dimensional curves, and on various image
data sets, showing large improvements over previous work. We discuss several
variations of the model and conclude with directions for future work.

该论文提出了一种基于贝叶斯无限混合模型的转换方法，该方法在不受函数或转换形式限制的情况下可以同时对数据集进行聚类和对齐，并通过使用狄利克雷过程先验来以数据驱动的方式确定聚类的最优数量，并且可适用于多种类型和转换函数的数据，该方法通过在合成数据和各种图像数据集上的实验取得了积极的结果。