Weighted median filters (smoothers) have been shown to be analogous to normalized FIR linear filters constrained to have only positive weights. In this paper, it is shown that much like the mean is generalized to the rich class of linear FIR filters, the median can be generalized to a richer class of weighted median (WM) filters admitting positive and negative weights. The generalization follow...

The median graph is a useful tool to cluster a set of graphs and obtain a prototype of them. The spectral graph theory is another approach to represent graphs and find “good” approximate solutions for the graph-matching problem. Recently, both approaches have been put together and a new representation has emerged, which is called Spectral-Median Graphs. In this paper, we summarize and compare t...

Quasi-median graphs are a tool commonly used by evolutionary biologists to visualise the evolution of molecular sequences. As with any graph, a quasi-median graph can contain cut vertices, that is, vertices whose removal disconnect the graph. These vertices induce a decomposition of the graph into blocks, that is, maximal subgraphs which do not contain any cut vertices. Here we show that the sp...

We propose proximity graph depth as a class of depth functions, based on the minimum path length along proximity graph edges to the convex hull of a point set. We analyze the characteristics of several proximity graph depth functions both theoretically and experimentally, define depth contours enclosing regions of increasing depth, and present algorithms for calculating depth values in a point ...

Résumé : Graphs have very interesting properties for object representation in pattern recognition. However, graph matching algorithms are usually computationally complex. In addition, graphs are harder to manipulate and operate than feature vectors. In the last years, some attempts have been made to combine the best of the graph and the vector domains in order to get the advantages of both worl...

For any vertex v and any edge e in a non-trivial connected graph G, the distance sum d(v) of v is d(v) = ∑ u∈V d(v, u), the vertex-to-edge distance sum d1(v) of v is d1(v) = ∑ e∈E d(v, e), the edge-to-vertex distance sum d2(e) of e is d2(e) = ∑ v∈V d(e, v) and the edge-to-edge distance sum d3(e) of e is d3(e) = ∑ f∈E d(e, f). The set M(G) of all vertices v for which d(v) is minimum is the media...

The median graph has been shown to be a good choice to infer a representative of a set of graphs. It has been successfully applied to graph-based classification and clustering. Nevertheless, its computation is extremely complex. Several approaches have been presented up to now based on different strategies. In this paper we present a new approximate recursive algorithm for median graph computat...

For a commutative semigroup S with 0, the zero-divisor graph of S denoted by Γ(S) is the graph whose vertices are nonzero zero-divisor of S, and two vertices x, y are adjacent in case xy = 0 in S. In this paper we study median and center of this graph. Also we show that if Ass(S) has more than two elements, then the girth of Γ(S) is three.

In this paper, we study different classes of intersection graphs of maximal hypercubes of median graphs. For a median graph G and k ≥ 0, the intersection graph Qk(G) is defined as the graph whose vertices are maximal hypercubes (by inclusion) in G, and two vertices Hx and Hy in Qk(G) are adjacent whenever the intersection Hx ∩ Hy contains a subgraph isomorphic to Qk. Characterizations of clique...

In this paper we study group actions on quasi-median graphs, or 'CAT(0) prism complexes', generalising the notion of CAT(0) cube complexes. We consider hyperplanes in a graph $X$ and define contact $\mathcal{C}X$ for these hyperplanes. show that is always quasi-isometric to tree, result Hagen, under certain conditions action $G \curvearrowright X$ induces an acylindrical \mathcal{C}X$, giving a...