We give an approximation algorithm for non-uniform sparsest cut with the following guarantee: For any ε, δ ∈ (0, 1), given cost and demand graphs with edge weights C,D : ( V 2 ) → R+ respectively, we can find a set T ⊆ V with C(T,V \T ) D(T,V \T ) at most 1+ε δ times the optimal non-uniform sparsest cut value, in time 2 poly(n) provided λr ≥ Φ∗/(1 − δ). Here λr is the r’th smallest generalized ...

An exact and fast analytic method based on power series is established to predict the modal field distributions, Petermann-2 spot size, the normalized propagation constant corresponding to fundamental and first higher order mode in graded index fibers with any arbitrary power law profile. The variation of normalized cut-off frequencies of some LPlm modes in graded index fibers with different pr...

In this paper we present a framework for unsupervised segmentation of white matter fiber traces obtained from diffusion weighted MRI data. Fiber traces are compared pairwise to create a weighted undirected graph which is partitioned into coherent sets using the normalized cut (N cut) criterion. A simple and yet effective method for pairwise comparison of fiber traces is presented which in combi...

In this paper we formulate spectral clustering in directed graphs as an optimization problem, the objective being a weighted cut in the directed graph. This objective extends several popular criteria like the normalized cut and the averaged cut to asymmetric affinity data. We show that this problem can be relaxed to a Rayleigh quotient problem for a symmetric matrix obtained from the original a...

This paper is aimed to investigate some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called minimum normalized cuts/isoperimteric numbers defined through taking minimum of the maximum or the mean of the normalized outgoing flows from a set of subdomains of vertices, where these subdomains constitute a ...

An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the recently proposed 1-spectral clustering for the unconstrained problem, our method is based on a tight relaxation of the constrained normalized cut into a continuou...

In image analysis, segmentation is the partitioning of a digital image into multiple regions (sets of pixels), according to some homogeneity criterion. The problem of segmentation is a well-studied one in literature and there are a wide variety of approaches that are used. Different approaches are suited to different types of images and the quality of output of a particular algorithm is difficu...

w e propose Q novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the amage data, our approach aims a t extracting the global impression of an image. We treat image segmentation QS (I graph partitioning problem and propose Q novel global criterion, the normalized cut, for segmenting the graph. The normalized cut...

The Normalized Cut is a widely used measure of separation between clusters in a graph. In this paper we provide a novel probabilistic perspective on this measure. We show that for a partition of a graph into two weakly connected sets, V = A ⊎ B, in fact Ncut(V ) = 1/τA→B + 1/τB→A, where τA→B is the uni-directional characteristic exit time of a random walk from subset A to subset B. Using matrix...