Abstract
Tensor decompositions are multi-way analysis tools which have been successfully applied in a wide range of different fields. However, there are still challenges that remain few explored, namely the following: when applying tensor decomposition techniques, what should we expect from the result? How can we evaluate its quality? It is expected that, when the number of components is suitable, then few redundancy is observed in the decomposition result. Based on this assumption, we propose a new method, NORMO, which aims at estimating the number of components in CANDECOMP/PARAFAC (CP) decomposition so that no redundancy is observed in the result. To the best of our knowledge, this work encompasses the first attempt to tackle such problem. According to our experiments, the number of non-redundant components estimated by NORMO is among the most accurate estimates of the true CP number of components in both synthetic and real-world tensor datasets (thus validating the rationale guiding our method). Moreover, NORMO is more efficient than most of its competitors. Additionally, our method can be used to discover multi-levels of granularity in the patterns discovered.

Abstract
Social networks are becoming larger and more complex as new ways of collecting social interaction data arise (namely from online social networks, mobile devices sensors, ...). These networks are often large-scale and of high dimensionality. Therefore, dealing with such networks became a challenging task. An intuitive way to deal with this complexity is to resort to tensors. In this context, the application of tensor decomposition has proven its usefulness in modelling and mining these networks: it has not only been applied for exploratory analysis (thus allowing the discovery of interaction patterns), but also for more demanding and elaborated tasks such as community detection and link prediction. In this work, we provide an overview of the methods based on tensor decomposition for the purpose of analysing time-evolving social networks from various perspectives: from community detection, link prediction and anomaly/event detection to network summarization and visualization. In more detail, we discuss the ideas exploited to carry out each social network analysis task as well as its limitations in order to give a complete coverage of the topic.