Related papers: The Normalized Edit Distance with Uniform Operatio…
We introduce a manifold analysis technique for neural network representations. Normalized Space Alignment (NSA) compares pairwise distances between two point clouds derived from the same source and having the same size, while potentially…
Given a set of points in the Euclidean space $\mathbb{R}^\ell$ with $\ell>1$, the pairwise distances between the points are determined by their spatial location and the metric $d$ that we endow $\mathbb{R}^\ell$ with. Hence, the distance…
The Escherization problem involves finding a closed figure that tiles the plane that is most similar to a given goal figure. In Koizumi and Sugihara's formulation of the Escherization problem, the tile and goal figures are represented as…
Given two distributions $P$ and $S$ of equal total mass, the Earth Mover's Distance measures the cost of transforming one distribution into the other, where the cost of moving a unit of mass is equal to the distance over which it is moved.…
The graph edit distance (GED) measures the dissimilarity between two graphs as the minimal cost of a sequence of elementary operations transforming one graph into another. This measure is fundamental in many areas such as structural pattern…
Graph Edit Distance (GED) is a widely used measure of graph similarity, valued for its flexibility in encoding domain knowledge through operation costs. However, existing learning-based approximation methods follow a modeling paradigm that…
We introduce a new distance and we use it to parameter estimation purposes. We observe how it operates and we use in its place the usual methods of estimation which we call the methods of the new approach. We realize that we obtain a…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
The general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at…
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…
Persistence diagrams (PDs) are used as signatures of point cloud data. Two clouds of points can be compared using the bottleneck distance d_B between their PDs. A potential drawback of this pipeline is that point clouds sampled from…
The standardized mean difference (SMD) is a widely used measure of effect size, particularly common in psychology, clinical trials, and meta-analysis involving continuous outcomes. Traditionally, under the equal variance assumption, the SMD…
Graph Edit Distance (GED) is a popular similarity measurement for pairwise graphs and it also refers to the recovery of the edit path from the source graph to the target graph. Traditional A* algorithm suffers scalability issues due to its…
The emergence of geometric deep learning as a novel framework to deal with graph-based representations has faded away traditional approaches in favor of completely new methodologies. In this paper, we propose a new framework able to combine…
An edge-operation on a graph $G$ is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs $\mathcal{G}$, the editing distance from $G$ to $\mathcal{G}$ is the smallest number…
Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
The Pearson distance between a pair of random variables $X,Y$ with correlation $\rho_{xy}$, namely, 1-$\rho_{xy}$, has gained widespread use, particularly for clustering, in areas such as gene expression analysis, brain imaging and cyber…
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
Meaning Representation (AMR; Banarescu et al., 2013) encodes the meaning of sentences as a directed graph and Smatch (Cai and Knight, 2013) is the primary metric for evaluating AMR graphs. Smatch, however, is unaware of some…