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Big Data and Transcriptomics
Published in Shampa Sen, Leonid Datta, Sayak Mitra, Machine Learning and IoT, 2018
Sudharsana Sundarrajan, Sajitha Lulu, Mohanapriya Arumugam
Clustering is the process of grouping objects into a set of disjoint classes, namely clusters. The objects within a class are highly similar with each other and the objects in other classes are more dissimilar. Clustering is the first step of gene expression matrix analysis. One of the major characteristics of gene expression data is that it can be clustered to both genes and samples. The coexpressed genes can be grouped into clusters based on the expression patterns. In gene-based clustering, the genes are considered as objects and the samples are considered as features. In addition, the samples can be partitioned into homogenous groups. The groups correspond to particular macroscopic phenotypes, which may include clinical syndromes or disease types. On the other hand, sample-based clustering considers samples as objects and genes as features. Clustering algorithms such as K-means, Self-organizing map (SOM), hierarchical clustering, graph-based methods such as Cluster Identification via Connectivity Kernels (CLICK), Corrupted clique graph (CAST), and model-based clustering approaches are used to group genes and partition samples.5 Other clustering algorithms are summarized in Table 5.2.
Partitioning and Clustering
Published in Charles J. Alpert, Dinesh P. Mehta, Sachin S. Sapatnekar, Handbook of Algorithms for Physical Design Automation, 2008
Lengauer [Len90] proves that no matter what weighting scheme is selected, there will always exist an exact graph bipartition with a deviation of Ω(|e|) from the cost of cutting a single net. Additionally, Ihler et al. [IWW93] conjecture that a clique graph model is the best in terms of deviation from the true cost of cutting one net.
Graphs from Subgraphs
Published in N. P. Shrimali, Nita H. Shah, Recent Advancements in Graph Theory, 2020
Joseph Varghese Kureethara, Johan Kok
The idea of entire graph is believed to be originated from the problem of entire colouring (vertices, edges, faces) of a planar graph.[20] k-overlap Clique Graph[34] The k-overlap clique graph of a graph G has all maximal cliques of G as vertices. Two vertices are adjacent if their intersection contains at most k vertices.Block Graph[19] Let G be a graph and let B be the collection of all blocks in G. Then the block graph G(B) has B as the vertex set. Two vertices, i. e., the blocks B, C∈B are adjacent if and only if B and C have a cut-vertex in common.Full Graph[23] The full graph F(G) of a graph G is the graph whose vertex set is the union of the set of vertices, edges and blocks of G in which two vertices are adjacent if the corresponding members of G are adjacent or incident.
Bearing-only formation control of multi-agent systems in local reference frames
Published in International Journal of Control, 2021
Xiaoyuan Luo, Xianluo Li, Xiaolei Li, Xinping Guan
The maximal clique is important in the bearing-only controller design and global stability analysis throughout this paper. One of the characteristics of the maximal clique is that a node in a group is associated with any node in the same maximal clique. The p-clique graph, with , of , denoted as is a graph whose nodes represent the maximal clique of , and where two nodes are adjacent if the intersection of their associated cliques contains at least p nodes (Mckee & Mcmorris, 1999). The graph theory of the tree and the induced subgraph are used. The loop without a circle becomes a tree. When any two nodes in a loop have a connected path, it is called a tree. If the nodes of an induced subgraph of are a subset of its nodes, the induced subgraph includes all those edges of that join two nodes in the subset.
Domain decomposition of finite element models utilizing eight meta-heuristic algorithms: A comparative study
Published in Mechanics Based Design of Structures and Machines, 2020
A clique graph G of a FEM mesh contains its nodes in one-to-one correspondence with the elements of the considered FEM mesh, and two nodes of G are connected by an edge if the corresponding elements have at least one common node. Ten other graphs are defined by Kaveh (2006, 2013, 2014) for transforming the connectivity properties of finite element models into the connectivity of graphs. In this paper the skeletal graphs are used to decompose the finite element models into sub-domains.