Using Markov Models to Mine Temporal and Spatial Data
Jean‐François Mari, Florence Le, El Ghali, Marc Benot, Catherine Eng, Annabelle Thibessard, Pierre Leblo · InTech eBooks · 2011
The mining of temporal and / or spatial signals by graphical models can have several purposes: Segmentation : in this task, the GM clusters the signal into stationary (or homogeneous) and transient segments or areas (Jain et al., 1999).The term stationnary means that the signal values are considered as independent outcomes of probability density functions (pdf).These areas are then post-processed to extract some valuable knowledge from the data.Pattern matching : in this task, the GM measures the a posteriori probability P(model = someLabel/observedData).When there are as many GM as labels, the best probability allows the classification of an unknown pattern by the label associated with the highest probability.Background modelling : in order to make proper use of quantitative data, the GM is used as a background model to simulate an averaged process behavior that corrects for chance variation in the frequency counts (Huang et al., 2004).The domain expert compares the simulated and real data frequencies in order to distinguish if he / she is facing to overor under-represented data that must be investigated more carefully.In this chapter, we will present a general methodology to mine different kinds of temporal and spatial signals having contrasting properties: continuous or discrete with few or many modalities.This methodology is based on a high order Markov modelling as implemented in a free software: CARROTAGE (see section 3).Section 2 gives the theoretical basis of the modelling.Section 3 describes a general flowchart for mining temporal and spatial signals using CARROTAGE.The next section is devoted to the description of three data mining applications following the same flowchart.Finally, we draw some conclusions in section 5.