Structural Generative Descriptions for Temporal Data

Abstract

In data mining problems the representation or description of data plays a fundamental role, since it defines the set of essential properties for the extraction and characterisation of patterns. However, for the case of temporal data, such as time series and data streams, one outstanding issue when developing mining algorithms is finding an appropriate data description or representation. In this thesis two novel domain-independent representation frameworks for temporal data suitable for off-line and online mining tasks are formulated. First, a domain-independent temporal data representation framework based on a novel data description strategy which combines structural and statistical pattern recognition approaches is developed. The key idea here is to move the structural pattern recognition problem to the probability domain. This framework is composed of three general tasks: a) decomposing input temporal patterns into subpatterns in time or any other transformed domain (for instance, wavelet domain); b) mapping these subpatterns into the probability domain to find attributes of elemental probability subpatterns called primitives; and c) mining input temporal patterns according to the attributes of their corresponding probability domain subpatterns. This framework is referred to as Structural Generative Descriptions (SGDs). Two off-line and two online algorithmic instantiations of the proposed SGDs framework are then formulated: i) For the off-line case, the first instantiation is based on the use of Discrete Wavelet Transform (DWT) and Wavelet Density Estimators (WDE), while the second algorithm includes DWT and Finite Gaussian Mixtures. ii) For the online case, the first instantiation relies on an online implementation of DWT and a recursive version of WDE (RWDE), whereas the second algorithm is based on a multi-resolution exponentially weighted moving average filter and RWDE. The empirical evaluation of proposed SGDs-based algorithms is performed in the context of time series classification, for off-line algorithms, and in the context of change detection and clustering, for online algorithms. For this purpose, synthetic and publicly available real-world data are used. Additionally, a novel framework for multidimensional data stream evolution diagnosis incorporating RWDE into the context of Velocity Density Estimation (VDE) is formulated. Changes in streaming data and changes in their correlation structure are characterised by means of local and global evolution coefficients as well as by means of recursive correlation coefficients. The proposed VDE framework is evaluated using temperature data from the UK and air pollution data from Hong Kong.Open Acces