On Large-Scale Dynamic Topic Modeling with Nonnegative CP Tensor Decomposition

There is currently an unprecedented demand for large-scale temporal data analysis due to the explosive growth of data. Dynamic topic modeling has been widely used in social and data sciences with the goal of learning latent topics that emerge, evolve, and fade over time. Previous work on dynamic topic modeling primarily employ the method of nonnegative matrix factorization (NMF), where slices of the data tensor are each factorized into the product of lower-dimensional nonnegative matrices. With this approach, however, information contained in the temporal dimension of the data is often neglected or underutilized. To overcome this issue, we propose instead adopting the method of nonnegative CANDECOMP/PARAPAC (CP) tensor decomposition (NNCPD), where the data tensor is directly decomposed into a minimal sum of outer products of nonnegative vectors, thereby preserving the temporal information. The viability of NNCPD is demonstrated through application to both synthetic and real data, where significantly improved results are obtained compared to those of typical NMF-based methods. The advantages of NNCPD over such approaches are studied and discussed. To the best of our knowledge, this is the first time that NNCPD has been utilized for the purpose of dynamic topic modeling, and our findings will be transformative for both applications and further developments.Comment: 23 pages, 29 figures, submitted to Women in Data Science and Mathematics (WiSDM) Workshop Proceedings, "Advances in Data Science", AWM-Springer serie

Compact representation of temporal processes in echosounder time series via matrix decomposition

The recent explosion in the availability of echosounder data from diverse ocean platforms has created unprecedented opportunities to observe the marine ecosystems at broad scales. However, the critical lack of methods capable of automatically discovering and summarizing prominent spatio-temporal echogram structures has limited the effective and wider use of these rich datasets. To address this challenge, we develop a data-driven methodology based on matrix decomposition that builds compact representation of long-term echosounder time series using intrinsic features in the data. In a two-stage approach, we first remove noisy outliers from the data by Principal Component Pursuit, then employ a temporally smooth Nonnegative Matrix Factorization to automatically discover a small number of distinct daily echogram patterns, whose time-varying linear combination (activation) reconstructs the dominant echogram structures. This low-rank representation provides biological information that is more tractable and interpretable than the original data, and is suitable for visualization and systematic analysis with other ocean variables. Unlike existing methods that rely on fixed, handcrafted rules, our unsupervised machine learning approach is well-suited for extracting information from data collected from unfamiliar or rapidly changing ecosystems. This work forms the basis for constructing robust time series analytics for large-scale, acoustics-based biological observation in the ocean