@misc{17719,
  author = {Christos Chatzis and Carla Schenker and Max Pfeffer and Pedro Lind and Evrim Ataman},
  title = {A Time-aware tensor decomposition for concept evolution},
  abstract = {Time-evolving data are frequently represented as higher-order tensors with one of the modes being the time mode. For instance, neuroimaging signals might be arranged as a tensor of subjects-by-voxels-by-time, while social network data could be structured as a users-by-words-by-time tensor.

Tensor factorizations have emerged as effective unsupervised methods for analyzing such higher-order datasets and extracting the underlying patterns. However, they frequently overlook the temporal dimension. For instance, a reordering of the time points is allowed, which, although technically permissible, could result in a dataset that describes a fundamentally different evolution of events. Yet, these methods lack the capability to recognize or reflect these significant alterations in the data{\textquoteright}s temporal structure.

In recent studies, temporal regularizers are incorporated into the time mode to tackle this issue. Nevertheless, existing approaches still do not allow underlying patterns to change in time (e.g., spatial changes in the brain, contextual changes in topics). In this talk, we introduce the temporal PARAFAC2 (tPARAFAC2) model, a PARAFAC2-based tensor factorization with temporal regularization to compute a time-aware factorization of the input with the goal of extracting gradually evolving patterns, which is essential for understanding the data{\textquoteright}s continuous development through the underlying temporal dynamics. We use an Alternating Optimization (AO) - Alternating Direction Method of Multipliers (ADMM) based algorithm to fit the model and study different algorithmic approaches to handle missing data when fitting the model.

Using numerical experiments on simulated and real data, we demonstrate the effectiveness of tPARAFAC2 model in terms of recovering the underlying (evolving) patterns accurately in various challenging cases, in particular, in the presence of missing entries.},
  year = {2024},
  journal = {94th Annual meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2024)},
}