Graphs in machine learning: an introduction

Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper, we give an introduction to some methods relying on graphs for learning. This includes both unsupervised and supervised methods. Unsupervised learning algorithms usually aim at visualising graphs in latent spaces and/or clustering the nodes. Both focus on extracting knowledge from graph topologies. While most existing techniques are only applicable to static graphs, where edges do not evolve through time, recent developments have shown that they could be extended to deal with evolving networks. In a supervised context, one generally aims at inferring labels or numerical values attached to nodes using both the graph and, when they are available, node characteristics. Balancing the two sources of information can be challenging, especially as they can disagree locally or globally. In both contexts, supervised and un-supervised, data can be relational (augmented with one or several global graphs) as described above, or graph valued. In this latter case, each object of interest is given as a full graph (possibly completed by other characteristics). In this context, natural tasks include graph clustering (as in producing clusters of graphs rather than clusters of nodes in a single graph), graph classification, etc. 1 Real networks One of the first practical studies on graphs can be dated back to the original work of Moreno [51] in the 30s. Since then, there has been a growing interest in graph analysis associated with strong developments in the modelling and the processing of these data. Graphs are now used in many scientific fields. In Biology [54, 2, 7], for instance, metabolic networks can describe pathways of biochemical reactions [41], while in social sciences networks are used to represent relation ties between actors [66, 56, 36, 34]. Other examples include powergrids [71] and the web [75]. Recently, networks have also been considered in other areas such as geography [22] and history [59, 39]. In machine learning, networks are seen as powerful tools to model problems in order to extract information from data and for prediction purposes. This is the object of this paper. For more complete surveys, we refer to [28, 62, 49, 45]. In this section, we introduce notations and highlight properties shared by most real networks. In Section 2, we then consider methods aiming at extracting information from a unique network. We will particularly focus on clustering methods where the goal is to find clusters of vertices. Finally, in Section 3, techniques that take a series of networks into account, where each network i

Exact ICL maximization in a non-stationary temporal extension of the stochastic block model for dynamic networks

The stochastic block model (SBM) is a flexible probabilistic tool that can be used to model interactions between clusters of nodes in a network. However, it does not account for interactions of time varying intensity between clusters. The extension of the SBM developed in this paper addresses this shortcoming through a temporal partition: assuming interactions between nodes are recorded on fixed-length time intervals, the inference procedure associated with the model we propose allows to cluster simultaneously the nodes of the network and the time intervals. The number of clusters of nodes and of time intervals, as well as the memberships to clusters, are obtained by maximizing an exact integrated complete-data likelihood, relying on a greedy search approach. Experiments on simulated and real data are carried out in order to assess the proposed methodology

Exact ICL maximization in a non-stationary time extension of the latent block model for dynamic networks

The latent block model (LBM) is a flexible probabilistic tool to describe interactions between node sets in bipartite networks, but it does not account for interactions of time varying intensity between nodes in unknown classes. In this paper we propose a non stationary temporal extension of the LBM that clusters simultaneously the two node sets of a bipartite network and constructs classes of time intervals on which interactions are stationary. The number of clusters as well as the membership to classes are obtained by maximizing the exact complete-data integrated likelihood relying on a greedy search approach. Experiments on simulated and real data are carried out in order to assess the proposed methodology.Comment: European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN), Apr 2015, Bruges, Belgium. pp.225-230, 2015, Proceedings of the 23-th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2015

Block modelling in dynamic networks with non-homogeneous Poisson processes and exact ICL

We develop a model in which interactions between nodes of a dynamic network are counted by non homogeneous Poisson processes. In a block modelling perspective, nodes belong to hidden clusters (whose number is unknown) and the intensity functions of the counting processes only depend on the clusters of nodes. In order to make inference tractable we move to discrete time by partitioning the entire time horizon in which interactions are observed in fixed-length time sub-intervals. First, we derive an exact integrated classification likelihood criterion and maximize it relying on a greedy search approach. This allows to estimate the memberships to clusters and the number of clusters simultaneously. Then a maximum-likelihood estimator is developed to estimate non parametrically the integrated intensities. We discuss the over-fitting problems of the model and propose a regularized version solving these issues. Experiments on real and simulated data are carried out in order to assess the proposed methodology

Synthesis of NiO nanowalls by thermal treatment of Ni film deposited onto a stainless steel substrate

Two-dimensional nanostructures have a variety of applications due to their large surface areas. In this study, the authors present a simple and convenient method to realize two-dimensional NiO nanowalls by thermal treatment of a Ni thin film deposited by sputtering onto a stainless steel substrate. The substrate surface area is supposed to be significantly increased by creating nanowalls. The effects on the nanowall morphology of the thermal treatment temperature and duration are investigated. A mechanism based on the surface diffusion of Ni2+ ions from the Ni base film is then proposed for the growth of the NiO nanowalls. The as-synthesized NiO nanowalls are characterized by scanning electron microscopy, energy-dispersive x-ray analysis, x-ray diffraction, transmission electron microscopy and high resolution transmission electron microscopy

State Dependence and Alternative Explanations for Consumer Inertia

For many consumer packaged goods products, researchers have documented a form of state dependence whereby consumers become "loyal" to products they have consumed in the past. That is, consumers behave as though there is a utility premium from continuing to purchase the same product as they have purchased in the past or, equivalently, there is a psychological cost to switching products. However, it has not been established that this form of state dependence can be identified in the presence of consumer heterogeneity of an unknown form. Most importantly, before this inertia can be given a structural interpretation and used in policy experiments such as counterfactual pricing exercises,alternative explanations which might give rise to similar consumer behavior must be ruled out. We develop a flexible model of heterogeneity which can be given a semi-parametric interpretation and rule out alternative explanations for positive state dependence such as autocorrelated choice errors, consumer search, or consumer learning.

Nanoenergetic Materials for MEMS: A Review

New energetic materials (EMs) are the key to great advances in microscale energy-demanding systems as actuation part, igniter, propulsion unit, and power. Nanoscale EMs (nEMs)particularly offer the promise of much higher energy densities, faster rate of energy release, greater stability, and more security sensitivity to unwanted initiation). nEMs could therefore give response to microenergetics challenges. This paper provides a comprehensive review of current research activities in nEMs for microenergetics application. While thermodynamic calculations of flame temperature and reaction enthalpies are tools to choose desirable EMs, they are not sufficient for the choice of good material for microscale application where thermal losses are very penalizing. A strategy to select nEM is therefore proposed based on an analysis of the material diffusivity and heat of reaction. Finally, after a description of the different nEMs synthesis approaches, some guidelines for future investigations are provided

Synthesis process of nanowired Al/CuO thermite.

Al/CuO nanothermites were fabricated by thermal oxidation of copper layer at 4501C for 5 hand by aluminum thermal evaporation: thermal evaporation allows producing thin layer less than 2 mminsize. The copper has been deposited by electroplating or thermal evaporation depending on the required thickness. The obtained diameter of Al/CuO nanowiresis 150–250nm. Al/CuO nanowires composite were characterized by scanning electronmicroscopy (SEM), X-raydiffraction (XRD), differential scanning calorimetry (DSC) and differential thermal analysis (DTA). Two distinct exothermicreactions occurred at 515 and 6671C and total energy release of this thermite is 10kJ/cm

Synthesis of large-area and aligned copper oxide nanowires from copper thin film on silicon substrate

Large-area and aligned copper oxide nanowires have been synthesized by thermal annealing of copper thin films deposited onto silicon substrate. The effects of the film deposition method, annealing temperature, film thickness, annealing gas, and patterning by photolithography are systematically investigated. Long and aligned nanowires can only be formed within a narrow temperature range from 400 to 500°C. Electroplated copper film is favourable for the nanowire growth, compared to that deposited by thermal evaporation. Annealing copper thin film in static air produces large-area, uniform, but not well vertically aligned nanowires along the thin film surface. Annealing copper thin film under a N2/O2 gas flow generates vertically aligned, but not very uniform nanowires on large areas. Patterning copper thin film by photolithography helps to synthesize large-area, uniform, and vertically aligned nanowires along the film surface. The copper thin film is converted into bicrystal CuO nanowires, Cu2O film, and also perhaps some CuO film after the thermal treatment in static air. Only CuO in the form of bicrystal nanowires and thin film is observed after the copper thin film is annealed under a N2/O2 gas flow