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Related papers: A notion of depth for sparse functional data

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We propose a novel framework for sparse functional clustering that also embeds an alignment step. Sparse functional clustering means finding a grouping structure while jointly detecting the parts of the curves' domains where their grouping…

Methodology · Statistics 2019-12-03 Valeria Vitelli

We propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features…

Methodology · Statistics 2020-08-21 Trevor Harris , James Derek Tucker , Bo Li , Lyndsay Shand

We introduce a novel projection depth for data lying in a general Hilbert space, called the regularized projection depth, with a focus on functional data. By regularizing projection directions, the proposed depth does not suffer from the…

Methodology · Statistics 2025-12-24 Filip Bočinec , Stanislav Nagy , Hyemin Yeon

Recovering a dense depth image from sparse LiDAR scans is a challenging task. Despite the popularity of color-guided methods for sparse-to-dense depth completion, they treated pixels equally during optimization, ignoring the uneven…

Computer Vision and Pattern Recognition · Computer Science 2021-12-30 Yufan Zhu , Weisheng Dong , Leida Li , Jinjian Wu , Xin Li , Guangming Shi

Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless,…

Methodology · Statistics 2020-04-02 Tomáš Rubín , Victor M. Panaretos

We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…

Statistics Theory · Mathematics 2023-06-19 Joni Virta

Depth completion aims at predicting dense pixel-wise depth from an extremely sparse map captured from a depth sensor, e.g., LiDARs. It plays an essential role in various applications such as autonomous driving, 3D reconstruction, augmented…

Computer Vision and Pattern Recognition · Computer Science 2022-08-30 Junjie Hu , Chenyu Bao , Mete Ozay , Chenyou Fan , Qing Gao , Honghai Liu , Tin Lun Lam

Laboratory scientists are well equipped with statistical tools for univariate data, yet many phenomena of scientific interest are time-variant or otherwise multidimensional. Functional data analysis is one way of approaching such data: by…

Computation · Statistics 2023-02-28 Julian Lehrer , Mircea Teodorescu , Yohei Rosen

During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and…

Methodology · Statistics 2015-08-18 Peter J. Rousseeuw , Mia Hubert

This paper introduces the sparse functional boxplot and the intensity sparse functional boxplot as practical exploratory tools. Besides being available for complete functional data, they can be used in sparse univariate and multivariate…

Methodology · Statistics 2022-05-30 Zhuo Qu , Marc G. Genton

Existing depth completion methods are often targeted at a specific sparse depth type and generalize poorly across task domains. We present a method to complete sparse/semi-dense, noisy, and potentially low-resolution depth maps obtained by…

Computer Vision and Pattern Recognition · Computer Science 2024-07-23 Guangkai Xu , Wei Yin , Jianming Zhang , Oliver Wang , Simon Niklaus , Simon Chen , Jia-Wang Bian

Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…

Computation · Statistics 2020-07-17 Rainer Dyckerhoff , Pavlo Mozharovskyi , Stanislav Nagy

This paper proposes a depth estimation method using radar-image fusion by addressing the uncertain vertical directions of sparse radar measurements. In prior radar-image fusion work, image features are merged with the uncertain sparse…

Computer Vision and Pattern Recognition · Computer Science 2024-03-26 Masaya Kotani , Takeru Oba , Norimichi Ukita

We consider the problem of clustering functional data while jointly selecting the most relevant features for classification. This problem has never been tackled before in the functional data context, and it requires a proper definition of…

Methodology · Statistics 2015-01-21 Davide Floriello , Valeria Vitelli

Functional data analysis deals with data recorded densely over time (or any other continuum) with one or more observed curves per subject. Conceptually, functional data are continuously defined, but in practice, they are usually observed at…

Methodology · Statistics 2023-01-20 Chengqian Xian , Camila de Souza , John Jewell , Ronaldo Dias

The notion of statistical depth has been extensively studied in multivariate and functional data over the past few decades. In contrast, the depth on temporal point process is still under-explored. The problem is challenging because a point…

Methodology · Statistics 2021-05-24 Zishen Xu , Chenran Wang , Wei Wu

A new depth-based clustering procedure for directional data is proposed. Such method is fully non-parametric and has the advantages to be flexible and applicable even in high dimensions when a suitable notion of depth is adopted. The…

Methodology · Statistics 2022-06-22 Giuseppe Pandolfo , Antonio D'ambrosio

We present a method for inferring dense depth maps from images and sparse depth measurements by leveraging synthetic data to learn the association of sparse point clouds with dense natural shapes, and using the image as evidence to validate…

Computer Vision and Pattern Recognition · Computer Science 2021-08-25 Alex Wong , Safa Cicek , Stefano Soatto

Statistical depth functions are a standard tool in nonparametric statistics to extend order-based univariate methods to the multivariate setting. Since there is no universally accepted total order for fuzzy data (even in the univariate…

Statistics Theory · Mathematics 2024-01-05 Luis González-De La Fuente , Alicia Nieto-Reyes , Pedro Terán

Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…

Machine Learning · Statistics 2024-07-11 Pavlo Mozharovskyi , Romain Valla