| Characteristic for most real-world data mining tasks are the availability of a large number of unlabeled examples and the large rates of noise obliterating the similarity patterns. We study datasets with such characteristics collected across a wealth of domains - web search queries, celestial systems, anthropological artifacts, surveillance footages, etc. Diverse as they are, data from these domains turn out to have intuitive time series representation. As a major theme herein we advocate the belief that the time series representation is versatile enough to allow for accurate learning in the presence of noise, and when there are few or no labeled examples available. This is further achieved without compromising on the efficiency and the scalability of the problems at hand.;For certain applications the noisy patterns themselves can be of particular interest - anomalous trajectories, surprising web queries, erroneously recorded light-curves - identifying them, and drawing the domain expert's attention to them, often leads to unexpected discoveries. The early chapters of the thesis introduce the time series discords as a notion of "interesting" outliers in the high dimensional representation space. We develop an effective and highly efficient discord detection algorithm, which used in a parallel fashion can handle hundreds of millions of examples in only a few hours. We then turn our attention to the question of how to decouple the noise from the structured signal within the data. The problem can be especially hard when the time series are embedded within complex, non-convex topological spaces. Local manifold reconstruction techniques, such as Isomap and Locally Linear Embedding, easily fail in the realistic settings of noise. An extension of the Isomap algorithm is thus derived, that remedies the effect of noise and learns more accurately the data embedding subspaces. As a more principled approach, we further develop a dual treatment of the time series manifold reconstruction problem. It computes a global density estimate of the data, which is then regularized locally through the help of multiple factor analyzer models. This results into smoothly reconstructed time series manifolds, unbiased by the effect of the noisy examples. Cast within a semi-supervised framework, our method achieves similar accuracy and several orders of magnitude speed-up over the state of the art transductive learning approaches. |
