Network Topology Mapping from Partial Virtual Coordinates and Graph Geodesics

For many important network types (e.g., sensor networks in complex harsh environments and social networks) physical coordinate systems (e.g., Cartesian), and physical distances (e.g., Euclidean), are either difficult to discern or inapplicable. Accordingly, coordinate systems and characterizations based on hop-distance measurements, such as Topology Preserving Maps (TPMs) and Virtual-Coordinate (VC) systems are attractive alternatives to Cartesian coordinates for many network algorithms. Herein, we present an approach to recover geometric and topological properties of a network with a small set of distance measurements. In particular, our approach is a combination of shortest path (often called geodesic) recovery concepts and low-rank matrix completion, generalized to the case of hop-distances in graphs. Results for sensor networks embedded in 2-D and 3-D spaces, as well as a social networks, indicates that the method can accurately capture the network connectivity with a small set of measurements. TPM generation can now also be based on various context appropriate measurements or VC systems, as long as they characterize different nodes by distances to small sets of random nodes (instead of a set of global anchors). The proposed method is a significant generalization that allows the topology to be extracted from a random set of graph shortest paths, making it applicable in contexts such as social networks where VC generation may not be possible.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1712.1006

Identifying networks with common organizational principles

Many complex systems can be represented as networks, and the problem of network comparison is becoming increasingly relevant. There are many techniques for network comparison, from simply comparing network summary statistics to sophisticated but computationally costly alignment-based approaches. Yet it remains challenging to accurately cluster networks that are of a different size and density, but hypothesized to be structurally similar. In this paper, we address this problem by introducing a new network comparison methodology that is aimed at identifying common organizational principles in networks. The methodology is simple, intuitive and applicable in a wide variety of settings ranging from the functional classification of proteins to tracking the evolution of a world trade network.Comment: 26 pages, 7 figure

Photometric redshifts with Quasi Newton Algorithm (MLPQNA). Results in the PHAT1 contest

Context. Since the advent of modern multiband digital sky surveys, photometric redshifts (photo-z's) have become relevant if not crucial to many fields of observational cosmology, from the characterization of cosmic structures, to weak and strong lensing. Aims. We describe an application to an astrophysical context, namely the evaluation of photometric redshifts, of MLPQNA, a machine learning method based on Quasi Newton Algorithm. Methods. Theoretical methods for photo-z's evaluation are based on the interpolation of a priori knowledge (spectroscopic redshifts or SED templates) and represent an ideal comparison ground for neural networks based methods. The MultiLayer Perceptron with Quasi Newton learning rule (MLPQNA) described here is a computing effective implementation of Neural Networks for the first time exploited to solve regression problems in the astrophysical context and is offered to the community through the DAMEWARE (DAta Mining & ExplorationWeb Application REsource) infrastructure. Results. The PHAT contest (Hildebrandt et al. 2010) provides a standard dataset to test old and new methods for photometric redshift evaluation and with a set of statistical indicators which allow a straightforward comparison among different methods. The MLPQNA model has been applied on the whole PHAT1 dataset of 1984 objects after an optimization of the model performed by using as training set the 515 available spectroscopic redshifts. When applied to the PHAT1 dataset, MLPQNA obtains the best bias accuracy (0.0006) and very competitive accuracies in terms of scatter (0.056) and outlier percentage (16.3%), scoring as the second most effective empirical method among those which have so far participated to the contest. MLPQNA shows better generalization capabilities than most other empirical methods especially in presence of underpopulated regions of the Knowledge Base.Comment: Accepted for publication in Astronomy & Astrophysics; 9 pages, 2 figure