Temporal analysis of social networks using three-way DEDICOM.

Abstract

DEDICOM is an algebraic model for analyzing intrinsically asymmetric relationships, such as the balance of trade among nations or the flow of information among organizations or individuals. It provides information on latent components in the data that can be regarded as "properties" or "aspects" of the objects, and it finds a few patterns that can be combined to describe many relationships among these components. When we apply this technique to adjacency matrices arising from directed graphs, we obtain a smaller graph that gives an idealized description of its patterns. Three-way DEDICOM is a higher-order extension of the model that has certain uniqueness properties. It allows for a third mode of the data, such as time, and permits the analysis of semantic graphs. We present an improved algorithm for computing three-way DEDICOM on sparse data and demonstrate it by applying it to the adjacency tensor of a semantic graph with time-labeled edges. Our application uses the Enron email corpus, from which we construct a semantic graph corresponding to email exchanges among Enron personnel over a series of 44 months. Meaningful patterns are recovered in which the representation of asymmetries adds insight into the social networks at Enron.

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

“…12. This result is also consistent with that illustrated in [8]. More detailed analysis of matrices R and D can be found in [11,20].…”

“…The original experiment first introduced in [8,11] used the Enron email database [57]. We here replicate this experiment to illustrate the benefits of our HALS algorithm for DEDICOM.…”

“…Tensor decompositions capture multilinear structures in higher-order data-sets, where the data have more than two modes [5][6][7][8][9]. Tensor decompositions and multi-way analysis allow naturally to extract hidden (latent) components and investigate complex relationships among them, for example, in exploration of social networks [4,10,11].…”

“…Lundy et al [19] presented an application of three-way DEDICOM to skew-symmetric data for paired preference ratings of treatments for chronic back pain (with additional constraints to obtain meaningful results). Bader et al analyzed email communications of Enron company using the three-way DEDICOM model [8,20].…”

Tensor decompositions for feature extraction and classification of high dimensional datasets

“…• If the factors A (n) are orthogonal and the feature matrices F (k) are dense, approximation (13) corresponds to a model called DEDICOM (Decomposition into Directional COMponents) [17].…”