A chaotic viewpoint-based approach to solve haplotype assembly using hypergraph model

Decreasing the cost of high-throughput DNA sequencing technologies, provides a huge amount of data that enables researchers to determine haplotypes for diploid and polyploid organisms. Although various methods have been developed to reconstruct haplotypes in diploid form, their accuracy is still a challenging task. Also, most of the current methods cannot be applied to polyploid form. In this paper, an iterative method is proposed, which employs hypergraph to reconstruct haplotype. The proposed method by utilizing chaotic viewpoint can enhance the obtained haplotypes. For this purpose, a haplotype set was randomly generated as an initial estimate, and its consistency with the input fragments was described by constructing a weighted hypergraph. Partitioning the hypergraph specifies those positions in the haplotype set that need to be corrected. This procedure is repeated until no further improvement could be achieved. Each element of the finalized haplotype set is mapped to a line by chaos game representation, and a coordinate series is defined based on the position of mapped points. Then, some positions with low qualities can be assessed by applying a local projection. Experimental results on both simulated and real datasets demonstrate that this method outperforms most other approaches, and is promising to perform the haplotype assembly.

Salient Object Detection Based on Weighted Hypergraph and Random Walk

Recently, salient object detection based on the graph model has attracted extensive research interest in computer vision because the graph model can represent the relationship between two regions better. However, it is difficult to capture the high-level relationship between multiple regions. In this algorithm, the input image is segmented into superpixels first. Then, a weighted hypergraph model is established using fuzzy C-means clustering algorithm and a new weighting strategy. Finally, the random walk algorithm is used to sort all superpixels on the weighted hypergraph model to obtain the salient object. The experimental results on three benchmark datasets demonstrate that the proposed method performs better than some other state-of-the-art methods.

A local search algorithm for the constrained max cut problem on hypergraphs.

In the constrained max k-cut problem on hypergraphs, we are given a weighted hypergraph H=(V, E), an integer k and a set c of constraints. The goal is to divide the set V of vertices into k disjoint partitions in such a way that the sum of the weights of the hyperedges having at least two endpoints in different partitions is maximized and the partitions satisfy all the constraints in c. In this paper we present a local search algorithm for the constrained max k-cut problem on hypergraphs and show that it has approximation ratio 1-1/k for a variety of constraints c, such as for the constraints defining the max Steiner k-cut problem, the max multiway cut problem and the max k-cut problem. We also show that our local search algorithm can be used on the max k-cut problem with given sizes of parts and on the capacitated max k-cut problem, and has approximation ratio 1-|Vmax|/|V|, where |Vmax| is the cardinality of the biggest partition. In addition, we present a local search algorithm for the directed max k-cut problem that has approximation ratio (k-1)/(3k-2).

A local search algorithm for the constrained max cut problem on hypergraphs.

In the constrained max k-cut problem on hypergraphs, we are given a weighted hypergraph H=(V, E), an integer k and a set c of constraints. The goal is to divide the set V of vertices into k disjoint partitions in such a way that the sum of the weights of the hyperedges having at least two endpoints in different partitions is maximized and the partitions satisfy all the constraints in c. In this paper we present a local search algorithm for the constrained max k-cut problem on hypergraphs and show that it has approximation ratio 1-1/k for a variety of constraints c, such as for the constraints defining the max Steiner k-cut problem, the max multiway cut problem and the max k-cut problem. We also show that our local search algorithm can be used on the max k-cut problem with given sizes of parts and on the capacitated max k-cut problem, and has approximation ratio 1-|Vmax|/|V|, where |Vmax| is the cardinality of the biggest partition. In addition, we present a local search algorithm for the directed max k-cut problem that has approximation ratio (k-1)/(3k-2).

Vertex-Weighted Hypergraph Learning for Multi-View Object Classification

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 hypergraph structure to formulate the relationship among 3D objects, taking the advantage of hypergraph on high-order correlation modelling. However, traditional hypergraph learning method may suffer from the imbalance data issue. To this end, we propose a vertex-weighted hypergraph learning algorithm for multi-view 3D object classification, introducing an updated hypergraph structure. In our method, the correlation among different objects is formulated in a hypergraph structure and each object (vertex) is associated with a corresponding weight, weighting the importance of each sample in the learning process. The learning process is conducted on the vertex-weighted hypergraph and the estimated object relevance is employed for object classification. The proposed method has been evaluated on two public benchmarks, i.e., the NTU and the PSB datasets. Experimental results and comparison with the state-of-the-art methods and recent deep learning method demonstrate the effectiveness of our proposed method.

Multi-Level Refinement Algorithm of Weighted Hypergraph Partitioning Problem

The formal description of weighted hypergraph partitioning problem is presented. We describe the solution of the weighted hypergraph partitioning problem based on the multi-level method. We propose the multi-level discrete particle swarm optimization refinement algorithm, whose each particle’s position in |V|-dimensional can be considered as the corresponded partitioning. During the refinement process of the uncoarsening phase, the algorithm projects successively each particle’s corresponded partitioning back to the next-level finer hypergraph, and the degree of particle’s freedom increases with the increase in solution space’s dimension. The algorithm also regards the gain of vertex as particle information for the heuristic search and successfully searches the solution space based on the intelligent behavior between individuals’ collaboration. Furthermore, the improved compressed storage format of weighted hypergraph is presented and the two-dimensional auxiliary array is designed for counting the vertices of each hypergraph in different partitions. The rapid method of calculating the vertex’s gain and the cut’s size are proposed to avoid traversing each vertex of hyperedge and reduce the algorithm’s time complexity and space complexity. Experimental results show that the algorithm not only can find the better partitioning of weighted hypergraph than the move-based method but also can improve the search capability of the refinement algorithm.