How do we find patterns in author-keyword associations, evolving over time? Or in DataCubes, with product-branch-customer
sales information? Matrix decompositions, like principal component analysis (PCA) and variants, are invaluable
tools for mining, dimensionality reduction, feature selection, rule identification in numerous settings like streaming
data, text, graphs, social networks and many more.However, they have only two orders, like author and keyword,
in the above example. We propose to envision such higher order data as tensors, and tap the vast literature on the topic. However, these methods do not necessarily scale up, let alone operate on semi-infinite streams. Thus, we introduce the dynamic tensor analysis (DTA) method, and its variants. DTA provides a compact summary for high-order and high-dimensional
data, and it also reveals the hidden correlations. Algorithmically,we designed DTA very carefully so that it is (a)
scalable, (b) space efficient (it does not need to store the past) and (c) fully automatic with no need for user defined
parameters. Moreover, we propose STA, a streaming tensor analysis method, which provides a fast, streaming approximation
to DTA. We implemented all our methods, and applied them in two real settings, namely, anomaly detection and multi-way
latent semantic indexing. We used two real, large datasets, one on network flow data (100GB over 1 month) and one
from DBLP (200MB over 25 years). Our experiments show that our methods are fast, accurate and that they find interesting
patterns and outliers on the real datasets.