Related papers: Principal manifold estimation via model complexity…

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…

In this paper, we introduce the concept of principal bundles on statistical manifolds. After necessary preliminaries on information geometry and principal bundles on manifolds, we study the $\alpha$-structure of frame bundles over…

A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

We consider the theory of regression on a manifold using reproducing kernel Hilbert space methods. Manifold models arise in a wide variety of modern machine learning problems, and our goal is to help understand the effectiveness of various…

With the advancement of high-throughput biotechnologies, we increasingly accumulate biomedical data about diseases, especially cancer. There is a need for computational models and methods to sift through, integrate, and extract new…

This paper explores machine learning (ML) models for classifying lung cancer levels to improve diagnostic accuracy and prognosis. Through parameter tuning and rigorous evaluation, we assess various ML algorithms. Techniques like minimum…

Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…

Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…

This study introduces a novel unsupervised medical image feature extraction method that employs spatial stratification techniques. An objective function based on weight is proposed to achieve the purpose of fast image recognition. The…

Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…

Dimensionality reduction (DR) is one of the key tools for the visual exploration of high-dimensional data and uncovering its cluster structure in two- or three-dimensional spaces. The vast majority of DR methods in the literature do not…

Constitutive model discovery refers to the task of identifying an appropriate model structure, usually from a predefined model library, while simultaneously inferring its material parameters. The data used for model discovery are measured…

The deployment of Machine Learning models intraoperatively for tissue characterisation can assist decision making and guide safe tumour resections. For image classification models, pixel attribution methods are popular to infer…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

We propose a new data representation method based on Quantum Cognition Machine Learning and apply it to manifold learning, specifically to the estimation of intrinsic dimension of data sets. The idea is to learn a representation of each…

We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the…

We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computational results from the model, and discuss…

We propose a novel deep neural network methodology for density estimation on product Riemannian manifold domains. In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum…

Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models…