Temporal and Spatial Data Mining with Second-Order Hidden Models
  In the frame of designing a knowledge discovery system, we have developed
stochastic models based on high-order hidden Markov models. These models are
capable to map sequences of data into a Markov chain in which the transitions
between the states depend on the \texttt{n} previous states according to the
order of the model. We study the process of achieving information extraction
fromspatial and temporal data by means of an unsupervised classification. We
use therefore a French national database related to the land use of a region,
named Teruti, which describes the land use both in the spatial and temporal
domain. Land-use categories (wheat, corn, forest, ...) are logged every year on
each site regularly spaced in the region. They constitute a temporal sequence
of images in which we look for spatial and temporal dependencies. The temporal
segmentation of the data is done by means of a second-order Hidden Markov Model
(\hmmd) that appears to have very good capabilities to locate stationary
segments, as shown in our previous work in speech recognition. Thespatial
classification is performed by defining a fractal scanning ofthe images with
the help of a Hilbert-Peano curve that introduces atotal order on the sites,
preserving the relation ofneighborhood between the sites. We show that the
\hmmd performs aclassification that is meaningful for the agronomists.Spatial
and temporal classification may be achieved simultaneously by means of a 2
levels \hmmd that measures the \aposteriori probability to map a temporal
sequence of images onto a set of hidden classes.
