CONTEST: A Controllable Test Matrix Toolbox for MATLAB
ACM Transactions on Mathematical Software (TOMS)
Estimating node similarity from co-citation in a spatial graph model
Proceedings of the 2010 ACM Symposium on Applied Computing
Spatial models for virtual networks
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Diameter and broadcast time of random geometric graphs in arbitrary dimensions
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Tutorial on biological networks
Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery
Some typical properties of the spatial preferred attachment model
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
A novel approach to modelling protein-protein interaction networks
ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part II
Increasing reliability of protein interactome by fast manifold embedding
Pattern Recognition Letters
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Motivation: Finding a good network null model for protein–protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between network structure and biological function as well as into evolution. Also, network (graph) models are used to guide biological experiments and discover new biological features. It has been proposed that geometric random graphs are a good model for PPI networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space and edges (links) exist between pairs of nodes for which the corresponding points in the metric space are close enough according to some distance norm. Computational experiments have revealed close matches between key topological properties of PPI networks and geometric random graph models. In this work, we push the comparison further by exploiting the fact that the geometric property can be tested for directly. To this end, we develop an algorithm that takes PPI interaction data and embeds proteins into a low-dimensional Euclidean space, under the premise that connectivity information corresponds to Euclidean proximity, as in geometric-random graphs. We judge the sensitivity and specificity of the fit by computing the area under the Receiver Operator Characteristic (ROC) curve. The network embedding algorithm is based on multi-dimensional scaling, with the square root of the path length in a network playing the role of the Euclidean distance in the Euclidean space. The algorithm exploits sparsity for computational efficiency, and requires only a few sparse matrix multiplications, giving a complexity of O(N2) where N is the number of proteins. Results: The algorithm has been verified in the sense that it successfully rediscovers the geometric structure in artificially constructed geometric networks, even when noise is added by re-wiring some links. Applying the algorithm to 19 publicly available PPI networks of various organisms indicated that: (a) geometric effects are present and (b) two-dimensional Euclidean space is generally as effective as higher dimensional Euclidean space for explaining the connectivity. Testing on a high-confidence yeast data set produced a very strong indication of geometric structure (area under the ROC curve of 0.89), with this network being essentially indistinguishable from a noisy geometric network. Overall, the results add support to the hypothesis that PPI networks have a geometric structure. Availability: MATLAB code implementing the algorithm is available upon request. Contact: natasha@ics.uci.edu