1,334 research outputs found
Guaranteed clustering and biclustering via semidefinite programming
Identifying clusters of similar objects in data plays a significant role in a
wide range of applications. As a model problem for clustering, we consider the
densest k-disjoint-clique problem, whose goal is to identify the collection of
k disjoint cliques of a given weighted complete graph maximizing the sum of the
densities of the complete subgraphs induced by these cliques. In this paper, we
establish conditions ensuring exact recovery of the densest k cliques of a
given graph from the optimal solution of a particular semidefinite program. In
particular, the semidefinite relaxation is exact for input graphs corresponding
to data consisting of k large, distinct clusters and a smaller number of
outliers. This approach also yields a semidefinite relaxation for the
biclustering problem with similar recovery guarantees. Given a set of objects
and a set of features exhibited by these objects, biclustering seeks to
simultaneously group the objects and features according to their expression
levels. This problem may be posed as partitioning the nodes of a weighted
bipartite complete graph such that the sum of the densities of the resulting
bipartite complete subgraphs is maximized. As in our analysis of the densest
k-disjoint-clique problem, we show that the correct partition of the objects
and features can be recovered from the optimal solution of a semidefinite
program in the case that the given data consists of several disjoint sets of
objects exhibiting similar features. Empirical evidence from numerical
experiments supporting these theoretical guarantees is also provided
Non-negative Matrix Factorization: A Survey
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Multi-objective community detection applied to social and COVID-19 constructed networks
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University LondonCommunity Detection plays an integral part in network analysis, as it facilitates understanding the structures and functional characteristics of the network. Communities organize real-world networks into densely connected groups of nodes. This thesis provides a critical analysis of the Community Detection and highlights the main areas including algorithms, evaluation metrics, applications, and datasets in social networks.
After defining the research gap, this thesis proposes two Attribute-Based Label Propagation algorithms that maximizes both Modularity and homogeneity. Homogeneity is considered as an objective function one time, and as a constraint another time. To better capture the homogeneity of real-world networks, a new Penalized Homogeneity degree (PHd) is proposed, that can be easily personalized based on the network characteristics.
For the first time, COVID-19 tracing data are utilized to form two dataset networks: one is based on the virus transition between the world countries. While the second dataset is an attributed network based on the virus transition among the contact-tracing in the Kingdom of Bahrain. This type of networks that is concerned in tracking a disease was not formed based on COVID-19 virus and has never been studied as a community detection problem. The proposed datasets are validated and tested in several experiments. The proposed Penalized Homogeneity measure is personalized and used to evaluate the proposed attributed network.
Extensive experiments and analysis are carried out to evaluate the proposed methods and benchmark the results with other well-known algorithms. The results are compared in terms of Modularity, proposed PHd, and accuracy measures. The proposed methods have achieved maximum performance among other methods, with 26.6% better performance in Modularity, and 33.96% in PHd on the proposed dataset, as well as noteworthy results on benchmarking datasets with improvement in Modularity measures of 7.24%, and 4.96% respectively, and proposed PHd values 27% and 81.9%
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
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