Related papers: Local Regularization of Noisy Point Clouds: Improv…
We proposed a new criterion \textit{noise-stability}, which revised the classical rigidity theory, for evaluation of MDS algorithms which can truthfully represent the fidelity of global structure reconstruction; then we proved the…
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…
Many efforts have been made for revealing the decision-making process of black-box learning machines such as deep neural networks, resulting in useful local and global explanation methods. For local explanation, stochasticity is known to…
One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn…
This paper deals with the geometric multi-model fitting from noisy, unstructured point set data (e.g., laser scanned point clouds). We formulate multi-model fitting problem as a sequential decision making process. We then use a deep…
In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic…
A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix…
Some prominent discretisation methods such as finite elements provide a way to approximate a function of $d$ variables from $n$ values it takes on the nodes $x_i$ of the corresponding mesh. The accuracy is $n^{-s_a/d}$ in $L^2$-norm, where…
Recent progress of semantic point clouds analysis is largely driven by synthetic data (e.g., the ModelNet and the ShapeNet), which are typically complete, well-aligned and noisy free. Therefore, representations of those ideal synthetic…
This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…
To better understand the dynamics of human settlements, thorough knowledge of the uncertainty in geospatial built-up surface datasets is critical. While frameworks for localized accuracy assessments of categorical gridded data have been…
Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit…
Despite impressive performance on numerous visual tasks, Convolutional Neural Networks (CNNs) --- unlike brains --- are often highly sensitive to small perturbations of their input, e.g. adversarial noise leading to erroneous decisions. We…
The low-dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately) on low-dimensional manifolds embedded in a high-dimensional Euclidean space. In this…
In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be obtained via replacing the Laplacian regulariser with a…
The paper discusses regularization properties of artificial data for deep learning. Artificial datasets allow to train neural networks in the case of a real data shortage. It is demonstrated that the artificial data generation process,…
Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
This paper presents a novel self-supervised approach to reconstruct human shape and pose from noisy point cloud data. Relying on large amount of dataset with ground-truth annotations, recent learning-based approaches predict correspondences…
The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are…