In many parts of the world there are complex, violent interactions among groups with widely varying agendas. Situational awareness is difficult because there is rarely a clear distinction between good and bad actors, and there are constantly shifting alliances and oppositions between groups. This makes it difficult for analysts to understand the ecosystem of a country and region; still more to conceive of helpful interventions. We show how to use a newly developed spectral graph embedding technique that allows social networks with edge weights that are positive (alliance) and negative (opposition) to be modelled. We show the practical application by applying the technique to countries in North-West Africa, where civil wars are commonplace and complex islamist insurgencies have been active in the past few decades. A sense of the differences among these countries becomes visible, as well as a picture of the interactions among the key groups within each country.

Semi-supervised learning makes the realistic assumptions that labelled data is typically rare, and that unlabelled data that are similar are likely to belong to the same class. Unlabelled data are assigned the labels associated with their “most similar” labelled neighbors. For graph-based semi-supervised learning, “most similar” is defined by weighted multipath path length in a graph. When classes are of different sizes, or the number of labelled nodes per class is not the same across classes, the performance of existing graph-based algorithms degrades sharply. We develop a new algorithm that creates representative nodes for each class, connects them to the labelled nodes of that class, adds negative edges between them, embeds the resulting graph using a signed graph Laplacian technique, and then predicts the unlabelled nodes using distance-based techniques in the geometry of the embedding. Its performance matches current algorithms for balanced datasets, but is much better for datasets where the classes, or the number of labelled records, differ in size.

Defect prediction on projects with limited historical data has attracted great interest from both researchers and practitioners. Cross-project defect prediction has been the main area of progress by reusing classifiers from other projects. However, existing approaches require some degree of homogeneity (e.g., a similar distribution of metric values) between the training projects and the target project. Satisfying the homogeneity requirement often requires significant effort (currently a very active area of research).

Most relationships in a social network have an element of asymmetry: the strength of A's relationship to B need not be the same as B's to A; and relationships that are based on power or influence have a natural flow associated with them. It is therefore natural to model many kinds of social networks by directed graphs, with a node corresponding to each participant, and a weighted directed edge to each relationship. Spectral embeddings for directed graphs are known, but they have significant weaknesses. We design a new directed-graph embedding, show that its mathematical properties are appropriate, and demonstrate its application to some synthetic and real-world networks. As well as avoiding the weaknesses of known techniques, the new embedding also represents a property we call flow betweenness of each node, allowing for directed edge prediction.

Social networks consist of a set of participants and the pairwise relationships between them. There are several different types of networks, such as directed networks, networks with typed edges, dynamic networks and signed networks, as well as any composition of different types of networks. We develop a novel way to analyze such networks by considering the qualitatively different social roles that each individual can play in a network. For example, in a directed network, the participants have two social roles -- an incoming edge role and an outgoing edge role which are associated with the popularity and activity of each individual.

The relationships within criminal groups are of qualitatively different kinds, and are typically not symmetric because of issues of power and influence. Social network analysis techniques have not been able to model this richness of relationships well. We develop a new technique for spectral embedding of directed graphs, and combine it with a recently developed technique for spectral embedding of graphs with typed edges. We use the combination to model two 'Ndrangheta organized crime groups, and show that structure that is otherwise not visible can be extracted.

Social networks are often modelled by graphs, with nodes representing individuals, and positively weighted edges representing the strength of the relationships between them. Working directly with such graphs is difficult, and it has become common to use spectral techniques that embed graphs in a geometry, and then work with the geometry instead. In a good embedding, edges that are heavily (positively) weighted, and so represent strong interactions, cause the vertices they connect to be embedded close to one another. However, in some social networks there are also antagonistic relationships that are naturally represented by negatively weighted edges. The resulting graphs are called signed graphs. Clearly an embedding of such a signed graph should place nodes connected by positively weighted edges close together, but nodes connected by negatively weighted edges far apart. Existing spectral techniques to embed signed graphs have serious drawbacks. We derive two normalized spectral analysis methods for signed graphs and show, using real-world data, that they produce robust embeddings.

The interactions in real-world social networks change over time. Dynamic social network analysis aims to understand the structures in networks as they evolve, building on static analysis techniques but including variation. Working directly with the graphs that represent social networks is difficult, and it has become common to use spectral techniques that embed graphs in a geometry and then work with the geometry instead. We extend such spectral techniques to dynamically changing data by binding network snapshots at different times into a single directed graph structure in a way that keeps structures aligned. This global network can then be embedded. Pairwise similarity, as well as community and cluster structures can be tracked over time, and the idea of the trajectory of a node across time becomes meaningful. We illustrate the approach using a real-world dataset, the Caviar drug-trafficking network.

Most real-world social network analysis treats edges (relationships) as having different intensities (weights), but the same qualitative properties. We address the problem of modelling edges of qualitatively different types that nevertheless interact with one another. For example, influence flows along friend and colleagues edges differently, but treating the two sets of different kinds of edges as independent graphs surely misses interesting and useful structure. We model the sub graph corresponding to each edge type as a layer, and show how to weight the edges connecting the layers to produce a consistent spectral embedding, including for directed graphs. This embedding can be used to compute social network properties of the combined graph, to predict edges, and to predict edge types. We illustrate with Padgett's dataset of Florentine families in the 15th Century.