Efficient learning of decomposable models with a bounded clique size

The learning of probability distributions from data is a ubiquitous problem in the fields of Statistics and Artificial Intelligence. During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models due to their advantageous theoretical properties. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k, which controls the complexity of the model. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In this work, we propose a family of algorithms which approximates this problem with a computational complexity of O(k · n^2 log n) in the worst case, where n is the number of implied random variables. The structures of the decomposable models that solve the maximum likelihood problem are called maximal k-order decomposable graphs. Our proposals, called fractal trees, construct a sequence of maximal i-order decomposable graphs, for i = 2, ..., k, in k − 1 steps. At each step, the algorithms follow a divide-and-conquer strategy based on the particular features of this type of structures. Additionally, we propose a prune-and-graft procedure which transforms a maximal k-order decomposable graph into another one, increasing its likelihood. We have implemented two particular fractal tree algorithms called parallel fractal tree and sequential fractal tree. These algorithms can be considered a natural extension of Chow and Liu’s algorithm, from k = 2 to arbitrary values of k. Both algorithms have been compared against other efficient approaches in artificial and real domains, and they have shown a competitive behavior to deal with the maximum likelihood problem. Due to their low computational complexity they are especially recommended to deal with high dimensional domains.

The most persistent soft-clique in a set of sampled graphs

When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques. We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations. Copyright 2012 by the author(s)/owner(s).

On the Performance of Polynomial-time CLIQUE Approximation Algorithms on Very Large Graphs

The performance of a randomized version of the subgraph-exclusion algorithm (called Ramsey) for CLIQUE by Boppana and Halldorsson is studied on very large graphs. We compare the performance of this algorithm with the performance of two common heuristic algorithms, the greedy heuristic and a version of simulated annealing. These algorithms are tested on graphs with up to 10,000 vertices on a workstation and graphs as large as 70,000 vertices on a Connection Machine. Our implementations establish the ability to run clique approximation algorithms on very large graphs. We test our implementations on a variety of different graphs. Our conclusions indicate that on randomly generated graphs minor changes to the distribution can cause dramatic changes in the performance of the heuristic algorithms. The Ramsey algorithm, while not as good as the others for the most common distributions, seems more robust and provides a more even overall performance. In general, and especially on deterministically generated graphs, a combination of simulated annealing with either the Ramsey algorithm or the greedy heuristic seems to perform best. This combined algorithm works particularly well on large Keller and Hamming graphs and has a competitive overall performance on the DIMACS benchmark graphs.

Clique Irreducibility of Some Iterative Classes of Graphs

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.

Clique Irreducibility and Clique Vertex Irreducibility of Graphs

A graphs G is clique irreducible if every clique in G of size at least two,has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irreducibility and clique irreducibility of graphs which are non-complete extended p-sums (NEPS) of two graphs are studied. We prove that if G(c) has at least two non-trivial components then G is clique vertex reducible and if it has at least three non-trivial components then G is clique reducible. The cographs and the distance hereditary graphs which are clique vertex irreducible and clique irreducible are also recursively characterized.

Approximation algorithms and hardness results for the clique packing problem

For a fixed family F of graphs, an F-packing in a graph G is a set of pairwise vertex-disjoint subgraphs of G, each isomorphic to an element of F. Finding an F-packing that maximizes the number of covered edges is a natural generalization of the maximum matching problem, which is just F = {K(2)}. In this paper we provide new approximation algorithms and hardness results for the K(r)-packing problem where K(r) = {K(2), K(3,) . . . , K(r)}. We show that already for r = 3 the K(r)-packing problem is APX-complete, and, in fact, we show that it remains so even for graphs with maximum degree 4. On the positive side, we give an approximation algorithm with approximation ratio at most 2 for every fixed r. For r = 3, 4, 5 we obtain better approximations. For r = 3 we obtain a simple 3/2-approximation, achieving a known ratio that follows from a more involved algorithm of Halldorsson. For r = 4, we obtain a (3/2 + epsilon)-approximation, and for r = 5 we obtain a (25/14 + epsilon)-approximation. (C) 2008 Elsevier B.V. All rights reserved.

Fanfictions na Internet - um clique na construção do leitor-autor

Esta dissertação trata do fenômeno da autoria na internet, tendo como foco de estudo do leitor-autor, mais especificamente, de um autor que foi uma vez leitor de uma história original e que assume a função de continuar a história (do ponto em que a deixou seu primeiro criador) ou de modificá-la de forma a agradar a si mesmo e/ou a outros leitores eventuais. Conforme uma vez afirmou Roland Barthes (2004), o escritor sempre será um imitador de escritos anteriores à sua época, mas nunca original. A partir de análises de trechos das histórias, suas notas de autoria e interação com outros leitores através dos comentários, essas criações de fãs-autores (como são chamados nessa pesquisa os autores que se dedicam à escrita desse tipo de história), estuda-se a modificação do conceito de autoria na atualidade, pois muitas vezes o autor perde seu posto ao manter contato com alguma forma de tecnologia da informação – e agora lida com gêneros chamados híbridos: textos que não são puros, que não possuem uma característica apenas para poderem ser definidos pelos manuais comuns. Desta forma é difícil definir o que é, afinal, o autor na era dos gêneros digitais. Num momento em que a cada dia as pessoas do mundo inteiro aumentam seu número de horas navegando, os gêneros digitais representam uma nova relação entre ser humano e instrumento semiótico, com diversos aspectos a serem observados.

An improved bit parallel exact maximum clique algorithm

This paper describes new improvements for BB-MaxClique (San Segundo et al. in Comput Oper Resour 38(2):571–581, 2011 ), a leading maximum clique algorithm which uses bit strings to efficiently compute basic operations during search by bit masking. Improvements include a recently described recoloring strategy in Tomita et al. (Proceedings of the 4th International Workshop on Algorithms and Computation. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, pp 191–203, 2010 ), which is now integrated in the bit string framework, as well as different optimization strategies for fast bit scanning. Reported results over DIMACS and random graphs show that the new variants improve over previous BB-MaxClique for a vast majority of cases. It is also established that recoloring is mainly useful for graphs with high densities.

Watching subgraphs to improve efficiency in maximum clique search

This paper describes a new technique referred to as watched subgraphs which improves the performance of BBMC, a leading state of the art exact maximum clique solver (MCP). It is based on watched literals employed by modern SAT solvers for boolean constraint propagation. In efficient SAT algorithms, a list of clauses is kept for each literal (it is said that the clauses watch the literal) so that only those in the list are checked for constraint propagation when a (watched) literal is assigned during search. BBMC encodes vertex sets as bit strings, a bit block representing a subset of vertices (and the corresponding induced subgraph) the size of the CPU register word. The paper proposes to watch two subgraphs of critical sets during MCP search to efficiently compute a number of basic operations. Reported results validate the approach as the size and density of problem instances rise, while achieving comparable performance in the general case.

Clustering by clique generation /

Originally presented as the author's thesis (M.A.), University of Illinois at Urbana-Champaign.

Solving Maximum Clique Problem for Protein Structure Similarity

Computing the similarity between two protein structures is a crucial task in molecular biology, and has been extensively investigated. Many protein structure comparison methods can be modeled as maximum weighted clique problems in specific k-partite graphs, referred here as alignment graphs. In this paper we present both a new integer programming formulation for solving such clique problems and a dedicated branch and bound algorithm for solving the maximum cardinality clique problem. Both approaches have been integrated in VAST, a software for aligning protein 3D structures largely used in the National Center for Biotechnology Information, an original clique solver which uses the well known Bron and Kerbosch algorithm (BK). Our computational results on real protein alignment instances show that our branch and bound algorithm is up to 116 times faster than BK.

Fuzzy methods for analysis of microarrays and networks

Bioinformatics involves analyses of biological data such as DNA sequences, microarrays and protein-protein interaction (PPI) networks. Its two main objectives are the identification of genes or proteins and the prediction of their functions. Biological data often contain uncertain and imprecise information. Fuzzy theory provides useful tools to deal with this type of information, hence has played an important role in analyses of biological data. In this thesis, we aim to develop some new fuzzy techniques and apply them on DNA microarrays and PPI networks. We will focus on three problems: (1) clustering of microarrays; (2) identification of disease-associated genes in microarrays; and (3) identification of protein complexes in PPI networks. The first part of the thesis aims to detect, by the fuzzy C-means (FCM) method, clustering structures in DNA microarrays corrupted by noise. Because of the presence of noise, some clustering structures found in random data may not have any biological significance. In this part, we propose to combine the FCM with the empirical mode decomposition (EMD) for clustering microarray data. The purpose of EMD is to reduce, preferably to remove, the effect of noise, resulting in what is known as denoised data. We call this method the fuzzy C-means method with empirical mode decomposition (FCM-EMD). We applied this method on yeast and serum microarrays, and the silhouette values are used for assessment of the quality of clustering. The results indicate that the clustering structures of denoised data are more reasonable, implying that genes have tighter association with their clusters. Furthermore we found that the estimation of the fuzzy parameter m, which is a difficult step, can be avoided to some extent by analysing denoised microarray data. The second part aims to identify disease-associated genes from DNA microarray data which are generated under different conditions, e.g., patients and normal people. We developed a type-2 fuzzy membership (FM) function for identification of diseaseassociated genes. This approach is applied to diabetes and lung cancer data, and a comparison with the original FM test was carried out. Among the ten best-ranked genes of diabetes identified by the type-2 FM test, seven genes have been confirmed as diabetes-associated genes according to gene description information in Gene Bank and the published literature. An additional gene is further identified. Among the ten best-ranked genes identified in lung cancer data, seven are confirmed that they are associated with lung cancer or its treatment. The type-2 FM-d values are significantly different, which makes the identifications more convincing than the original FM test. The third part of the thesis aims to identify protein complexes in large interaction networks. Identification of protein complexes is crucial to understand the principles of cellular organisation and to predict protein functions. In this part, we proposed a novel method which combines the fuzzy clustering method and interaction probability to identify the overlapping and non-overlapping community structures in PPI networks, then to detect protein complexes in these sub-networks. Our method is based on both the fuzzy relation model and the graph model. We applied the method on several PPI networks and compared with a popular protein complex identification method, the clique percolation method. For the same data, we detected more protein complexes. We also applied our method on two social networks. The results showed our method works well for detecting sub-networks and give a reasonable understanding of these communities.