The data in many disciplines such as social networks, Web analysis, etc. is link-based, and the link structure can be exploited for many different data mining tasks. In this article, we consider the problem of temporal link prediction: Given link data for times 1 through T , can we predict the links at time T + 1? If our data has underlying periodic structure, can we predict out even further in time, i.e., links at time T + 2, T + 3, etc.? In this article, we consider bipartite graphs that evolve over time and consider matrix- and tensor-based methods for predicting future links. We present a weight-based method for collapsing multiyear data into a single matrix. We show how the well-known Katz method for link prediction can be extended to bipartite graphs and, moreover, approximated in a scalable way using a truncated singular value decomposition. Using a CANDECOMP/PARAFAC tensor decomposition of the data, we illustrate the usefulness of exploiting the natural three-dimensional structure of temporal link data. Through several numerical experiments, we demonstrate that both matrix- and tensor-based techniques are effective for temporal link prediction despite the inherent difficulty of the problem. Additionally, we show that tensor-based techniques are particularly effective for temporal data with varying periodic patterns.

Two-way arrays or matrices are often not enough to represent all the information in the data and standard two-way analysis techniques commonly applied on matrices may fail to find the underlying structures in multi-modal datasets. Multiway data analysis has recently become popular as an exploratory analysis tool in discovering the structures in higher-order datasets, where data have more than two modes. We provide a review of significant contributions in the literature on multiway models, algorithms as well as their applications in diverse disciplines including chemometrics, neuroscience, social network analysis, text mining and computer vision.

Motivation: The success or failure of an epilepsy surgery depends greatly on the localization of epileptic focus (origin of a seizure). We address the problem of identification of a seizure origin through an analysis of ictal electroencephalogram (EEG), which is proven to be an effective standard in epileptic focus localization. Summary: With a goal of developing an automated and robust way of visual analysis of large amounts of EEG data, we propose a novel approach based on multiway models to study epilepsy seizure structure. Our contributions are 3-fold. First, we construct an Epilepsy Tensor with three modes, i.e. time samples, scales and electrodes, through wavelet analysis of multi-channel ictal EEG. Second, we demonstrate that multiway analysis techniques, in particular parallel factor analysis (PARAFAC), provide promising results in modeling the complex structure of an epilepsy seizure, localizing a seizure origin and extracting artifacts. Third, we introduce an approach for removing artifacts using multilinear subspace analysis and discuss its merits and drawbacks. Results: Ictal EEG analysis of 10 seizures from 7 patients are included in this study. Our results for 8 seizures match with clinical observations in terms of seizure origin and extracted artifacts. On the other hand, for 2 of the seizures, seizure localization is not achieved using an initial trial of PARAFAC modeling. In these cases, first, we apply an artifact removal method and subsequently apply the PARAFAC model on the epilepsy tensor from which potential artifacts have been removed. This method successfully identifies the seizure origin in both cases. Contact:acare@cs.rpi.edu