Related papers: Shamap: Shape-based Manifold Learning

Anomalies are samples that significantly deviate from the rest of the data and their detection plays a major role in building machine learning models that can be reliably used in applications such as data-driven design and novelty…

Metric learning methods for dimensionality reduction in combination with k-Nearest Neighbors (kNN) have been extensively deployed in many classification, data embedding, and information retrieval applications. However, most of these…

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…

Point cloud is a principal data structure adopted for 3D geometric information encoding. Unlike other conventional visual data, such as images and videos, these irregular points describe the complex shape features of 3D objects, which makes…

An unsupervised shape analysis is proposed to learn concepts reflecting shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects is used in which constellations are…

Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup…

The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale…

Recent advancements in medical image segmentation techniques have achieved compelling results. However, most of the widely used approaches do not take into account any prior knowledge about the shape of the biomedical structures being…

Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…

spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…

Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…

Manifold learning is a fundamental problem in machine learning with numerous applications. Most of the existing methods directly learn the low-dimensional embedding of the data in some high-dimensional space, and usually lack the…

In this paper, we present SIMAP, a novel layer integrated into deep learning models, aimed at enhancing the interpretability of the output. The SIMAP layer is an enhanced version of Simplicial-Map Neural Networks (SMNNs), an explainable…

Metric learning aims at finding a suitable distance metric over the input space, to improve the performance of distance-based learning algorithms. In high-dimensional settings, it can also serve as dimensionality reduction by imposing a…

In this paper, we revisit the classical representation of 3D point clouds as linear shape models. Our key insight is to leverage deep learning to represent a collection of shapes as affine transformations of low-dimensional linear shape…

Driven by the increasing demand for accurate and efficient representation of 3D data in various domains, point cloud sampling has emerged as a pivotal research topic in 3D computer vision. Recently, learning-to-sample methods have garnered…

Despite the popularity of the manifold hypothesis, current manifold-learning methods do not support machine learning directly on the latent $d$-dimensional data manifold, as they primarily aim to perform dimensionality reduction into…

Non-linear dimensionality reduction can be performed by \textit{manifold learning} approaches, such as Stochastic Neighbour Embedding (SNE), Locally Linear Embedding (LLE) and Isometric Feature Mapping (ISOMAP). These methods aim to produce…

As datasets used in scientific applications become more complex, studying the geometry and topology of data has become an increasingly prevalent part of the data analysis process. This can be seen for example with the growing interest in…

Shapley values are model-agnostic methods for explaining model predictions. Many commonly used methods of computing Shapley values, known as off-manifold methods, rely on model evaluations on out-of-distribution input samples. Consequently,…