Article
Computer Science, Artificial Intelligence
Darshan Bryner, Anuj Srivastava
Summary: Elastic Riemannian metrics have been successfully used for statistical treatments of functional and curve shape data. However, this usage is limited by the assumption of fixed and matched function boundaries. In this study, a new Riemannian framework is developed to allow for partial matching, comparing, and clustering of functions with phase variability and uncertain boundaries. The framework introduces a new diffeomorphism group and metric that are invariant to the action of the group, and imposes a Riemannian Lie group structure to enable efficient gradient-based optimization. The framework is illustrated by registering and clustering COVID-19 rate curves, demonstrating improved pattern identification, reduced mismatch errors, and decreased variability within clusters compared to previous methods.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2022)
Article
Computer Science, Information Systems
Tie Li, Gang Kou, Yi Peng
Summary: This study proposes a new representation learning approach called Nystro center dot mNet for credit evaluation and sub-pattern analysis. The Nystro center dot mNet overcomes the limitations of the Nystro center dot m method in credit evaluation and utilizes the advantages of distance metric learning. Experimental results on real-life credit data show that the newly generated distributions improve the performance of distance-based classifiers and linear classifiers.
INFORMATION SCIENCES
(2023)
Article
Computer Science, Information Systems
Atreyee Mondal, Nilanjan Dey, Simon Fong, Amira S. Ashour
Summary: A novel shape-based image clustering approach using time-series analysis was proposed, extracting shapes of objects based on mean structural similarity index and converting them into one-dimensional time-series data for hierarchical divisive clustering. Experimental results demonstrated the superiority of using Pearson correlation measure in clustering performance.
MULTIMEDIA TOOLS AND APPLICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
Fang Bai, Adrien Bartoli
Summary: This paper introduces the problem of deformable Generalized Procrustes Analysis (GPA) and resolves fundamental ambiguities using shape constraints requiring eigenvalues of shape covariance. A closed-form and optimal solution based on eigenvalue decomposition is provided, handling regularization and favoring smooth deformation fields. This method is applicable to most common transformation models, offering a fast, globally optimal and widely applicable solution.
INTERNATIONAL JOURNAL OF COMPUTER VISION
(2022)
Article
Biochemical Research Methods
Adam B. Olshen, Mark R. Segal
Summary: This study investigated the impact of weighting schemes on 3D genome reconstruction using SPRITE multi-way contact data. The results showed that the conversion of multi-way interactions to pairwise distances had limited influence on the reconstruction, possibly due to the abundance of pairwise contacts.
BMC BIOINFORMATICS
(2023)
Article
Computer Science, Artificial Intelligence
Jian Zheng, Hongchun Qu, Zhaoni Li, Lin Li, Xiaoming Tang, Fei Guo
Summary: This article proposes a novel autoencoder method using Mahalanobis distance metric of rescaling transformation to improve feature extraction ability. Experimental results demonstrate its superiority in terms of feature extraction accuracy and linear separabilities over existing methods.
PEERJ COMPUTER SCIENCE
(2022)
Article
Multidisciplinary Sciences
Anders Karlsson
Summary: This article introduces the beginning of metric functional analysis, focusing on the concept of metric functionals and their applications in various subjects. It discusses cases where linear notions fail to describe linear phenomena captured by metric concepts, and proves a general mean ergodic theorem and a metric fixed-point theorem.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2021)
Article
Automation & Control Systems
Agnieszka Kaliszewska, Monika Syga
Summary: The paper focuses on clustering analysis based on the shape and size of 2D contours, which are boundaries of cross-sections of 3D objects of revolution. The proposed similarity measures utilize combined disparate Procrustes analysis (PA) and dynamic time warping (DTW) distances. The study finds its motivation and primary application in archaeology, specifically in the clustering of archaeological pottery.
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE
(2022)
Article
Statistics & Probability
Valentina Masarotto, Guido Masarotto
Summary: This paper addresses the problem of clustering functional data based on their covariance structure. A soft clustering methodology is proposed, using the Wasserstein-Procrustes distance and penalizing the in-between cluster variability by a term proportional to the entropy of the partition matrix. This allows for partial classification of covariance operators into multiple groups and is suitable for situations where clusters can overlap or have unclear separation.
SCANDINAVIAN JOURNAL OF STATISTICS
(2023)
Article
Computer Science, Artificial Intelligence
Juan Luis Suarez, Salvador Garcia, Francisco Herrera
Summary: Distance metric learning is a branch of machine learning that focuses on learning distances from data to improve the performance of similarity-based algorithms. This tutorial covers theoretical background, foundations, and popular methods of distance metric learning, evaluating their capabilities through exhaustive testing. Results highlighted outstanding algorithms, with discussion on future prospects and challenges.
Article
Computer Science, Theory & Methods
Ilsuk Kang, Hosik Choi, Young Joo Yoon, Junyoung Park, Soon-Sun Kwon, Cheolwoo Park
Summary: Multi-dimensional functional data analysis is an important research topic in medical research. Two clustering methods using the Frechet distance for multi-dimensional functional data are proposed. The methods extend an existing approach and enforce sparsity on functional variables. They demonstrate effectiveness through simulation examples and are applied to thyroid cancer data in South Korea.
STATISTICS AND COMPUTING
(2023)
Article
Health Care Sciences & Services
Ronald Wihal Oei, Hao Sen Andrew Fang, Wei-Ying Tan, Wynne Hsu, Mong-Li Lee, Ngiap-Chuan Tan
Summary: Patient similarity analytics with the D3K measure incorporating domain knowledge and data-driven insights performed well in identifying patient cohorts with similar clinical characteristics, showing potential for enhancing shared decision making in personalized healthcare.
JOURNAL OF PERSONALIZED MEDICINE
(2021)
Article
Computer Science, Artificial Intelligence
Abdul Atif Khan, Amaresh Chandra Mishra, Sraban Kumar Mohanty
Summary: Suitable selection of a proximity measure is crucial for clustering, especially for complex high-dimensional datasets. This study proposes a new measure that considers the absolute differences between features, the inhomogeneity of features, and a continuous version of Boltzmann's entropy. Experimental results demonstrate the superiority of this measure in clustering synthetic, real, and gene expression datasets.
KNOWLEDGE-BASED SYSTEMS
(2023)
Article
Statistics & Probability
Yuexuan Wu, Chao Huang, Anuj Srivastava
Summary: Functional data analysis (FDA) is a fast-growing area of research and development in statistics. This paper reviews and develops fundamental geometrical concepts for analyzing functional data based on shape. It discusses tasks such as shape fitting, shape fPCA, and shape regression models, and presents examples using simulated and real data.
Article
Radiology, Nuclear Medicine & Medical Imaging
Farshad Sobhani, Amirfarhang Miresmaeili, Hossein Mahjub, Maryam Farhadian
Summary: This study compared the palatal morphology between individuals with palatal and labially displaced canines and control subjects using statistical shape analysis. The results showed a significant difference in palatal shape between the palatally displaced canines group and the control group, while the difference between the labially displaced canines group and the control group was not significant.
BMC MEDICAL IMAGING
(2023)
Article
Engineering, Biomedical
Valerio Varano, Paolo Piras, Stefano Gabriele, Luciano Teresi, Paola Nardinocchi, Ian L. Dryden, Concetta Torromeo, Michele Schiariti, Paolo E. Puddu
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
(2020)
Editorial Material
Operations Research & Management Science
Piercesare Secchi
APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY
(2020)
Article
Statistics & Probability
Ian L. Dryden, Alfred Kume, Phillip J. Paine, Andrew T. A. Wood
Summary: This article proposes a regression model for size-and-shape response data, with the regression structure entering through the landmark means. Two approaches to parameter estimation are considered, one based on marginal likelihood and the other using the EM algorithm for model-consistent estimation. The article explains how to deal with challenging computational issues and demonstrates the usefulness of the regression modeling framework with real-data examples.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2021)
Article
Statistics & Probability
Kwang-Rae Kim, Ian L. Dryden, Huiling Le, Katie E. Severn
Summary: This paper generalizes a smoothing spline fitting method to Riemannian manifold data and develops such a fitting procedure for shapes of configurations in general m-dimensional Euclidean space. The parallel transport along a geodesic on Kendall shape space is linked to the solution of a homogeneous first-order differential equation, enabling the approximation of unrolling and unwrapping procedures for numerical solutions for higher dimensional shape data. The fitting method is applied to analyze dynamic 3D peptide data.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
(2021)
Article
Geosciences, Multidisciplinary
Alessandra Menafoglio, Laura Guadagnini, Alberto Guadagnini, Piercesare Secchi
Summary: This study addresses the characterization of spatially variable Natural Background Levels (NBLs) of concentrations of chemical species in a large-scale groundwater body. By modeling concentration PDFs as random points in a Bayes Hilbert space, the study enables spatial prediction and uncertainty quantification using Object Oriented Data Analysis. The use of depth measures for distributional data helps in detecting central and outlying NBL distributions and building prediction regions for NBL distribution at unsampled locations.
SPATIAL STATISTICS
(2021)
Article
Statistics & Probability
Katie E. Severn, Ian L. Dryden, Simon P. Preston
Summary: This study focuses on developing a suitable methodology for statistical analysis of network data using graph Laplacian matrices, with applications in areas such as communication networks and corpus linguistics. An adapted Nadaraya-Watson estimator is developed for estimating regression curves in dynamic networks, with uniform weak consistency for both Euclidean and power Euclidean metrics. The methodology is applied to the Enron email corpus to model trends in monthly networks and detect anomalous patterns, as well as in corpus linguistics to explore changes in writing style over time based on word co-occurrence networks.
Article
Engineering, Biomedical
Laurence Burroughs, Mahetab H. Amer, Matthew Vassey, Britta Koch, Grazziela P. Figueredo, Blessing Mukonoweshuro, Paulius Mikulskis, Aliaksei Vasilevich, Steven Vermeulen, Ian L. Dryden, David A. Winkler, Amir M. Ghaemmaghami, Felicity R. A. J. Rose, Jan de Boer, Morgan R. Alexander
Summary: In this study, a novel combinatorial chemistry-topography screening platform, the ChemoTopoChip, was used to identify materials suitable for bone regeneration by screening for human mesenchymal stem cell (hiMSCs) and human macrophage response. The results show that the materials selected through this platform can induce osteoinduction in hiMSCs and modulate macrophage phenotype, providing a materials-induced alternative to osteo-inductive supplements in bone-regeneration.
Article
Social Sciences, Mathematical Methods
Oleksandr Didkovskyi, Giovanni Azzone, Alessandra Menafoglio, Piercesare Secchi
Summary: The study evaluates the vulnerability of Italian municipalities exposed to seismic hazard by analyzing open data provided by ISTAT, in addition to considering factors such as demographic dynamics and the age of building stock. It offers a tentative ranking of social and material vulnerability, along with differential profiles of dominant fragilities, to aid in planning precision policies aimed at seismic risk prevention and reduction.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY
(2021)
Article
Statistics & Probability
Tobia Boschi, Francesca Chiaromonte, Piercesare Secchi, Bing Li
Summary: The study introduces a new low-dimensional registration procedure that utilizes functional covariance components to capture meaningful modes of dependency between two sets of curves. The procedure aligns the curves simultaneously to optimize subsequent regression analysis, implemented using continuous registration algorithm and a novel parallel algorithm in R, and compared to other common registration approaches through simulations and application to the AneuRisk data.
Article
Chemistry, Physical
Keverne A. Louison, Ian L. Dryden, Charles A. Laughton
Summary: This approach uses machine learning to transform molecular models between different levels of resolution, requiring only particle coordinates for training, and enabling bidirectional transformation.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2021)
Article
Statistics & Probability
Rowland G. Seymour, David Sirl, Simon P. Preston, Ian L. Dryden, Madeleine J. A. Ellis, Bertrand Perrat, James Goulding
Summary: Identifying the most deprived regions in developing countries can be challenging due to logistical issues with traditional household surveys. The Bradley-Terry model, utilizing comparisons of affluence in different areas, provides a promising solution to simplify logistics and avoid biases. A novel Bayesian Spatial Bradley-Terry model has been developed to effectively decrease the number of comparisons required for inference, demonstrating practical effectiveness in a data set collected in Dar es Salaam, Tanzania.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS
(2022)
Article
Statistics & Probability
Katie E. Severn, Ian L. Dryden, Simon P. Preston
Summary: This study proposes a general framework for extrinsic statistical analysis of network samples in various applications, such as text documents, social interactions, and brain activity. By defining the graph Laplacian matrices of networks and corresponding metrics, embeddings, tangent spaces, the framework enables computing means, performing principal component analysis, regression, and hypothesis tests.
ANNALS OF APPLIED STATISTICS
(2022)
Article
Computer Science, Artificial Intelligence
Agostino Torti, Marta Galvani, Alessandra Menafoglio, Piercesare Secchi, Simone Vantini
Summary: This article presents a general and flexible bi-clustering algorithm for the analysis of Hilbert data. The algorithm, named HC2, is applied to analyze the regional railway service in the Lombardy region, aiming to identify recurrent patterns in passengers' daily access. By modeling the data as multivariate functional data and time series, this approach enables the measurement of both overcrowding and travel demand, providing useful insights for optimizing the service.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2022)
Article
Geosciences, Multidisciplinary
Riccardo Scimone, Alessandra Menafoglio, Laura M. Sangalli, Piercesare Secchi
Summary: Using the tools and perspective of Object Oriented Spatial Statistics, we analyze mortality data in the provinces and municipalities of Italy for the year 2020 and assess the impact of the COVID-19 pandemic on the local death process. We use functional data and linear models to predict expected mortality based on previous years' data and compare predictions with actual observations. Spatial clustering of mortality densities is used to identify anomalous areas. This analysis pipeline can be applied to other granular spatio-temporal data to quantify the disruption caused by the pandemic.
SPATIAL STATISTICS
(2022)
Article
Environmental Sciences
Ning Sun, Zoran Bursac, Ian Dryden, Roberto Lucchini, Sophie Dabo-Niang, Boubakari Ibrahimou
Summary: This study utilizes disease mapping models to estimate the spatiotemporal patterns of disease risks and identifies high-risk clusters for preeclampsia and gestational diabetes in Florida. It also shows that exposure to PM2.5 increases the risk of these diseases, although to a lesser extent compared to previous studies.
ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH
(2023)