Xingqin Qi

A Novel Model for DNA Sequence Similarity Analysis Based on Graph Theory

Determination of sequence similarity is one of the major steps in computational phylogenetic studies. As we know, during evolutionary history, not only DNA mutations for individual nucleotide but also subsequent rearrangements occurred. It has been one of major tasks of computational biologists to develop novel mathematical descriptors for similarity analysis such that various mutation phenomena information would be involved simultaneously. In this paper, different from traditional methods (eg, nucleotide frequency, geometric representations) as bases for construction of mathematical descriptors, we construct novel mathematical descriptors based on graph theory. In particular, for each DNA sequence, we will set up a weighted directed graph. The adjacency matrix of the directed graph will be used to induce a representative vector for DNA sequence. This new approach measures similarity based on both ordering and frequency of nucleotides so that much more information is involved. As an application, the method is tested on a set of 0.9-kb mtDNA sequences of twelve different primate species. All output phylogenetic trees with various distance estimations have the same topology, and are generally consistent with the reported results from early studies, which proves the new methods efficiency; we also test the new method on a simulated data set, which shows our new method performs better than traditional global alignment method when subsequent rearrangements happen frequently during evolutionary history.

Optimal local community detection in social networks based on density drop of subgraphs

The determination of community structures within social networks is a significant problem in the area of data mining. A proper community is usually defined as a subgraph with a higher internal density and a lower crossing density with others subgraphs. Hierarchical clustering algorithms produce a set of nested clusters, sometimes called dense subgraphs, organized as a hierarchical system and the output is always referred as a dendrogram. However, determining which of clusters in the dendrogram will be selected to form communities in the final output is a difficult problem. Most implementations of data mining algorithms require expert guidance in the implementation of the algorithm in order to establish the appropriate selection of such communities, and ultimately the output may not be optimized as with fixed height tree-cutting algorithms. In this paper, a novel algorithm for community selection is proposed. The intuition of our approach is based on drops of densities between each pair of parent and child nodes on the dendrogram - the higher the drop in density, the higher probability the child should form an independent community. Based on the Max-Flow Min-Cut theorem, we propose a novel algorithm which can output an optimal set of local communities automatically. In addition, a faster algorithm running in linear time is also presented for the case that the dendrogram is a tree. Finally, we validate this approach through a variety of data sets ranging from synthetic graphs to real world benchmark data sets.

A Hierarchical Algorithm for Clustering Extremist Web Pages

Extremist political movements have proliferated on the web in recent years due to the advent of minimal publication costs coupled with near universal access, resulting in what appears to be an abundance of groups that hover on the fringe of many socially divisive issues. Whether white-supremacist, neo- Nazi, anti-abortion, black separatist, radical Christian, animal rights, or violent environmentalists, all have found a home (and voice) on the Web. These groups form social networks whose ties are predicated primarily on shared political goals. Little is known about these groups, their interconnections, their animosities, and most importantly, their growth and development and studies such as the Dark Web Project, while considering domestic extremists, have focused primarily on international terrorist groups. Yet here in the US, there has been a complex social dynamic unfolding as well. While left-wing radicalism declined throughout the 80s and 90s, right wing hate groups began to flourish. Today, the web offers a place for any brand of extremism, but little is understood about their current growth and development. While there is much to gain from in-depth studies of the content provided by these sites, there is also a surprising amount of information contained in their online network structure as manifested in links between and among these web sites. Our research follows the idea that much can be known about you by the company you keep. In this paper, we propose an approach to measure the intrinsic relationships (i.e., similarities) of a set of extremist web pages. In this model, the web presence of a group is thought of as a node in a social network and the links between these pages are the ties between groups. This approach takes the bi-directional hyperlink structure of web pages and, based on similarity scores, applies an effective multi-membership clustering algorithm known as the quasi clique merger method to cluster these web pages using a derived hierarchical tree. The experimental results show that this new similarity measurement and hierarchical clustering algorithm gives an improvement over traditional link based clustering methods.

“Follow the Leader”: A Centrality Guided Clustering and Its Application to Social Network Analysis

Within graph theory and network analysis, centrality of a vertex measures the relative importance of a vertex within a graph. The centrality plays key role in network analysis and has been widely studied using different methods. Inspired by the idea of vertex centrality, a novel centrality guided clustering (CGC) is proposed in this paper. Different from traditional clustering methods which usually choose the initial center of a cluster randomly, the CGC clustering algorithm starts from a “LEADER”—a vertex with the highest centrality score—and a new “member” is added into the same cluster as the “LEADER” when some criterion is satisfied. The CGC algorithm also supports overlapping membership. Experiments on three benchmark social network data sets are presented and the results indicate that the proposed CGC algorithm works well in social network clustering.

Signed Quasi-Clique Merger: A New Clustering Method for Signed Networks with Positive and Negative Edges

Signed networks with both positive and negative links have gained considerable attention over the past several years. Community detection is among the main challenges for signed network analysis. It aims to find mutually antagonistic groups such that entities within the same group have as many positive relationships as possible and entities between different groups have as many negative relationships as possible. Most existing algorithms for community detection in signed networks aim to provide a hard partition of the network where any node should belong to a single community. However, overlapping communities, where a node is allowed to belong to multiple communities, widely exist in many real-world networks. Another disadvantage of some existing algorithms is that the number of final clusters k should be an input of the clustering process. It may however be the case that we do not know k in advance. In this paper, to offer improvements to existing algorithms, we propose a new clustering method for signed networks, the Signed Quasi-clique Merger (SQCM) algorithm. This algorithm detects the meaningful clusters (i.e. subgraphs with high friendly density) from the networks directly, where the friendly density of a subgraph C=(V(C),E(C)) is defined as d(C)=2∑e∈E(C)w(e)|V(C)|(|V(C)|−1). We construct a hierarchically nested system to illustrate their inclusion relationships. The output of SQCM is a smaller hierarchical tree, which clearly highlights meaningful clusters. During the clustering process, we do not need to know the number of final clusters k in advance; the algorithm is able to detect it on its own. Another important feature of SQCM is overlapping clustering or multi-membership. Its effectiveness is demonstrated through rigorous experiments involving both benchmark and randomly generated signed networks.

Numerical Characterization of DNA Sequence Based on Dinucleotides

Sequence comparison is a primary technique for the analysis of DNA sequences. In order to make quantitative comparisons, one devises mathematical descriptors that capture the essence of the base composition and distribution of the sequence. Alignment methods and graphical techniques (where each sequence is represented by a curve in high-dimension Euclidean space) have been used popularly for a long time. In this contribution we will introduce a new nongraphical and nonalignment approach based on the frequencies of the dinucleotide XY in DNA sequences. The most important feature of this method is that it not only identifies adjacent XY pairs but also nonadjacent XY ones where X and Y are separated by some number of nucleotides. This methodology preserves information in DNA sequence that is ignored by other methods. We test our method on the coding regions of exon-1 of β–globin for 11 species, and the utility of this new method is demonstrated.

Laplacian Energy of Digraphs and a Minimum Laplacian Energy Algorithm

In spectral graph theory, the Laplacian energy of undirected graphs has been studied extensively. However, there has been little work yet for digraphs. Recently, Perera and Mizoguchi (2010) introduced the directed Laplacian matrix L=D−A and directed Laplacian energy LE(G)=∑i=1nλi2 using the second spectral moment of L for a digraph G with n vertices, where D is the diagonal out-degree matrix, and A=(aij) with aij=1 whenever there is an arc (i,j ) from the vertex i to the vertex j and 0 otherwise. They studied the directed Laplacian energies of two special families of digraphs (simple digraphs and symmetric digraphs). In this paper, we extend the study of Laplacian energy for digraphs which allow both simple and symmetric arcs. We present lower and upper bounds for the Laplacian energy for such digraphs and also characterize the extremal graphs that attain the lower and upper bounds. We also present a polynomial algorithm to find an optimal orientation of a simple undirected graph such that the resulting oriented graph has the minimum Laplacian energy among all orientations. This solves an open problem proposed by Perera and Mizoguchi at 2010.

Modeling Network Changes: Systemic Centrality in Foreign Policy Interaction Analysis

The complex network of relationships between countries provides an abundance of data from which intelligence analysts must synthesize useful interpretations that effectively inform foreign policy and security decision making. In this work, a network of foreign policy event interactions is developed and then used to describe the state of the international system by estimating the behavioral distances from all relevant actors to the US. Using a graph theoretic approach, we develop a tool for estimating behavioral distances through direct network links when behavior is present, and indirect network paths when direct behavior is unobserved. The international system is examined in temporal aggregations of 60 and 30 days prior to and following the 1991 Gulf War and the 2003 invasion of Iraq. Both periods see distancing from the US as the wars approach, and a partial return to the prior state by 60 days after the initiation of conflict. The overall position of the US and the response of other nations towards the US indicates that the systemic leadership role of the US is diminished in behavioral relationships with a moderate number of actors.