相关论文: A New Construction of the Vietoris-Rips Complex

Given an undirected, weighted $n$-vertex graph $G = (V, E, w)$, a Gomory-Hu tree $T$ is a weighted tree on $V$ such that for any pair of distinct vertices $s, t \in V$, the Min-$s$-$t$-Cut on $T$ is also a Min-$s$-$t$-Cut on $G$. Computing…

While the robustness of vision models is often measured, their dependence on specific architectural design choices is rarely dissected. We investigate why certain vision architectures are inherently more robust to additive Gaussian noise…

Achieving invariance to nuisance transformations is a fundamental challenge in the construction of robust and reliable vision systems. Existing approaches to invariance scale exponentially with the dimension of the family of…

The total effective resistance, also called the Kirchhoff index, provides a robustness measure for a graph $G$. We consider two optimization problems of adding $k$ new edges to $G$ such that the resulting graph has minimal total effective…

The robust estimator presented in this paper processes each structure independently. The scales of the structures are estimated adaptively and no threshold is involved in spite of different objective functions. The user has to specify only…

This paper presents a new algorithm KIOPS for computing linear combinations of $\varphi$-functions that appear in exponential integrators. This algorithm is suitable for large-scale problems in computational physics where little or no…

A cut tree (or Gomory-Hu tree) of an undirected weighted graph G=(V,E) encodes a minimum s-t-cut for each vertex pair {s,t} \subseteq V and can be iteratively constructed by n-1 maximum flow computations. They solve the multiterminal…

In this paper we represent a new framework for integrated distributed systems. In the proposed framework we have used three parts to increase Satisfaction and Performance of this framework. At first we analyse integrated systems and their…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

Revealing hidden geometry and topology in noisy data sets is a challenging task. Elastic principal graph is a computationally efficient and flexible data approximator based on embedding a graph into the data space and minimizing the energy…

Subgraph discovery in a single data graph---finding subsets of vertices and edges satisfying a user-specified criteria---is an essential and general graph analytics operation with a wide spectrum of applications. Depending on the criteria,…

Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition…

We determine the homotopy type of the Vietoris-Rips complexes of the (vertex sets of the) platonic solids. The most interesting case is that the Vietoris-Rips complex of the dodecahedron is a wedge of nine 3-spheres when the parameter is…

In this report paper we first present a report of the Advanced Machine Learning Course Project on the provided data set and then present a novel heuristic algorithm for exact Bayesian network (BN) structure discovery that uses decomposable…

Finding maximum cliques in large networks is a challenging combinatorial problem with many real-world applications. We present a fast algorithm to achieve the exact solution for the maximum clique problem in large sparse networks based on…

Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for…

We describe a new method to accelerate neighbor searches on GRAPE, i.e. a special purpose hardware that efficiently calculates gravitational forces and potentials in $N$-body simulations. In addition to the gravitational calculations, GRAPE…

We propose a novel and flexible roof modeling approach that can be used for constructing planar 3D polygon roof meshes. Our method uses a graph structure to encode roof topology and enforces the roof validity by optimizing a simple but…

In the field of compressed sensing, a key problem remains open: to explicitly construct matrices with the restricted isometry property (RIP) whose performance rivals those generated using random matrix theory. In short, RIP involves…

A multigraph $G = (V, E)$ is $(k, \ell)$-sparse if every subset $X \subseteq V$ induces at most $\max\{k|X| - \ell, 0\}$ edges. Finding a maximum-size $(k, \ell)$-sparse subgraph is a classical problem in rigidity theory and combinatorial…