Binary Shapelet Transform for Multiclass Time Series Classification

Shapelets have recently been proposed as a new primitive for time series classification. Shapelets are subseries of series that best split the data into its classes. In the original research, shapelets were found recursively within a decision tree through enumeration of the search space. Subsequent research indicated that using shapelets as the basis for transforming datasets leads to more accurate classifiers. Both these approaches evaluate how well a shapelet splits all the classes. However, often a shapelet is most useful in distinguishing between members of the class of the series it was drawn from against all others. To assess this conjecture, we evaluate a one vs all encoding scheme. This technique simplifies the quality assessment calculations, speeds up the execution through facilitating more frequent early abandon and increases accuracy for multi-class problems. We also propose an alternative shapelet evaluation scheme which we demonstrate significantly speeds up the full search

Hybrid Variational Autoencoder for Time Series Forecasting

Variational autoencoders (VAE) are powerful generative models that learn the latent representations of input data as random variables. Recent studies show that VAE can flexibly learn the complex temporal dynamics of time series and achieve more promising forecasting results than deterministic models. However, a major limitation of existing works is that they fail to jointly learn the local patterns (e.g., seasonality and trend) and temporal dynamics of time series for forecasting. Accordingly, we propose a novel hybrid variational autoencoder (HyVAE) to integrate the learning of local patterns and temporal dynamics by variational inference for time series forecasting. Experimental results on four real-world datasets show that the proposed HyVAE achieves better forecasting results than various counterpart methods, as well as two HyVAE variants that only learn the local patterns or temporal dynamics of time series, respectively

Sequential Patterns Post-processing for Structural Relation Patterns Mining

Sequential patterns mining is an important data-mining technique used to identify frequently observed sequential occurrence of items across ordered transactions over time. It has been extensively studied in the literature, and there exists a diversity of algorithms. However, more complex structural patterns are often hidden behind sequences. This article begins with the introduction of a model for the representation of sequential patterns—Sequential Patterns Graph—which motivates the search for new structural relation patterns. An integrative framework for the discovery of these patterns–Postsequential Patterns Mining–is then described which underpins the postprocessing of sequential patterns. A corresponding data-mining method based on sequential patterns postprocessing is proposed and shown to be effective in the search for concurrent patterns. From experiments conducted on three component algorithms, it is demonstrated that sequential patterns-based concurrent patterns mining provides an efficient method for structural knowledge discover

Euler Characteristic Curves and Profiles: a stable shape invariant for big data problems

Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to distribute, it is hard to generalize to multifiltrations and is computationally prohibitive for big data-sets. In this paper we study the concept of Euler Characteristics Curves, for one parameter filtrations and Euler Characteristic Profiles, for multi-parameter filtrations. While being a weaker invariant in one dimension, we show that Euler Characteristic based approaches do not possess some handicaps of persistent homology; we show efficient algorithms to compute them in a distributed way, their generalization to multifiltrations and practical applicability for big data problems. In addition we show that the Euler Curves and Profiles enjoys certain type of stability which makes them robust tool in data analysis. Lastly, to show their practical applicability, multiple use-cases are considered.Comment: 32 pages, 19 figures. Added remark on multicritical filtrations in section 4, typos correcte