3D object classification with multi-view representation has become very popular, thanks to the progress on computer techniques and graphic hardware, and attracted much research attention in recent years. Regarding this task, there are mainly two challenging issues, i.e., the complex correlation among multiple views and the possible imbalance data issue. In this work, we propose to employ the hy...

Multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging from scientific computing to data science. In this paper we introduce the concept of algebraic distance on hypergraphs and demonstrate its use as an algorithmic component in the coars...

The quality of the image plays a vital role in image processing technique. It can be determined by the removal of the noisy pixels in the images. In this paper, we designed the hypergraph model for the representation of images. We use noise removal algorithm for digital images.This algorithm is based on the hypergraph model of images. This is used to detect the noisy pixels and thus can be remo...

In this paper, we present a new hypergraph partitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the original hypergraph by successively projecting and refining the bisection to the next level finer hyper...

The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. While independent sets in graphs are defined as sets of vertices containing no edges, hypergraphs have different types of independent sets depending on the number of vertices from an independent set allowed in an edge. We say that a subset of vertices is jindependent if its i...

A hypergraph G = (X,W ) is called d-uniform if each hyperedge w is a set of d vertices. A 1-factor of a hypergraph G is a set of hyperedges such that every vertex of the hypergraph is incident to exactly one hyperedge from the set. A 1factorization of G is a partition of all hyperedges of the hypergraph into disjoint 1-factors. The adjacency matrix of a d-uniform hypergraph G is the d-dimension...

In this work we propose a representation of the web as a directed hypergraph, instead of a graph, where links can connect not only pairs of pages, but also pairs of disjoint sets of pages. In our model, the web hypergraph is derived from the web graph by dividing the set of pages into non-overlapping blocks and using the links between pages of distinct blocks to create hyperarcs. Each hyperarc ...

We generalize the notion of an Euler tour in a graph in the following way. An Euler family in a hypergraph is a family of closed walks that jointly traverse each edge of the hypergraph exactly once. An Euler tour thus corresponds to an Euler family with a single component. We provide necessary and sufficient conditions for the existence of an Euler family in an arbitrary hypergraph, and in part...

K-way hypergraph partitioning has an ever-growing use in parallelization of scientific computing applications. We claim that hypergraph partitioning with multiple constraints and fixed vertices should be implemented using direct K-way refinement, instead of the widely adopted recursive bisection paradigm. Our arguments are based on the fact that recursive-bisection-based partitioning algorithms...