let $g=(v,e)$ be a connected graph. the eccentric connectivity index of $g$, $xi^{c}(g)$, is defined as $xi^{c}(g)=sum_{vin v(g)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. the eccentric distance sum of $g$ is defined as $xi^{d}(g)=sum_{vin v(g)}ec(v)d(v)$, where $d(v)=sum_{uin v(g)}d_{g}(u,v)$ and $d_{g}(u,v)$ is the distance between $u$ and $v$ ...

Generalized maps are widely used to model the topology of nD objects (such as 2D or 3D images) by means of incidence and adjacency relationships between cells (0D vertices, 1D edges, 2D faces, 3D volumes, ...). We have introduced in [1] a map edit distance. This distance compares maps by means of a minimum cost sequence of edit operations that should be performed to transform a map into another...

Dempster-Shafer theory of evidence (D-S theory) is widely used in uncertain information process. The basic probability assignment(BPA) is a key element in D-S theory. How to measure the distance between two BPAs is an open issue. In this paper, a new method to measure the distance of two BPAs is proposed. The proposed method is a generalized of existing evidence distance. Numerical examples are...

We study the r-th generalized minimum distance function (gmd function for short) and the corresponding generalized footprint function of a graded ideal in a polynomial ring over a field. If X is a set of projective points over a finite field and I(X) is its vanishing ideal, we show that the gmd function and the Vasconcelos function of I(X) are equal to the r-th generalized Hamming weight of the...

In this paper, we obtain a generalized version of the wellknown distance function family Lp norm. We prove that the new functions satisfy distance function properties. By using these functions, convex symmetric shapes can be described as loci, the set of points which are in equal distance from a given point. We also show that these symmetric convex shapes can be easily parameterized. We also sh...

Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.

Fuzzy c-means (FCM) has been considered as an effective algorithm for image segmentation. However, it still suffers from two problems: one is insufficient robustness to image noise, and the other is the Euclidean distance in FCM, which is sensitive to outliers. In this paper, we propose two new algorithms, generalized FCM (GFCM) and hierarchical FCM (HFCM), to solve these two problems. Traditio...