Related papers: Analyzing Midpoint Subdivision
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
Tsukamoto (2022) introduced the notion of Bedford-McMullen carpet system, a subsystem of $([0,1]^{\mathbb{N}}\times[0,1]^{\mathbb{N}},shift)$ whose metric mean dimension and mean Hausdorff dimension does not coincide in general. The aim of…
We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasi-isometric information for a group. We show how these tilings detect…
Deep supervision, or known as 'intermediate supervision' or 'auxiliary supervision', is to add supervision at hidden layers of a neural network. This technique has been increasingly applied in deep neural network learning systems for…
Co-Clustering, the problem of simultaneously identifying clusters across multiple aspects of a data set, is a natural generalization of clustering to higher-order structured data. Recent convex formulations of bi-clustering and tensor…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
The purpose of this article is to show a second main theorem with the explicit truncation level for holomorphic mappings of $ \mathbb{C} $ (or of a compact Riemann surface) into a compact complex manifold sharing divisors in subgeneral…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…
Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…
Machine learning (ML) models that achieve high average accuracy can still underperform on semantically coherent subsets ("slices") of data. This behavior can have significant societal consequences for the safety or bias of the model in…
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
With the development of deep learning, many state-of-the-art natural image scene classification methods have demonstrated impressive performance. While the current convolution neural network tends to extract global features and global…
Several methods for triclustering three-dimensional data require the cluster size or the number of clusters in each dimension to be specified. To address this issue, the Multi-Slice Clustering (MSC) for 3-order tensor finds signal slices…
Although the field of distributed optimization is well-developed, relevant literature focused on the application of distributed optimization to multi-robot problems is limited. This survey constitutes the second part of a two-part series on…
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…
Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying…
This work establishes $H^1$-norm stability and convergence for an L2 method on general nonuniform meshes when applied to the subdiffusion equation. Under mild constraints on the time step ratio $\rho_k$, such as $0.4573328\leq \rho_k\leq…
Many statistical learning problems can be posed as minimization of a sum of two convex functions, one typically a composition of non-smooth and linear functions. Examples include regression under structured sparsity assumptions. Popular…