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

Using Markov Models to Mine Temporal and Spatial Data

Référence du projet ANR BIODIVAGRIM : ANR 07 BDIV 02Markov models represent a powerful way to approach the problem of mining time and spatial signals whose variability is not yet fully understood. 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: carottAge (Gnu GPL)Les modèles de Markov sont des modèles puissants pour analyser des signaux temporels et spatiaux dont la variabilité n'est pas entièrement comprise. Dans ce chapitre, nous présentons notre méthodologie pour fouiller différentes sortes de signaux ayant des propriétés différentes: signaux continus ou discrets, simples ou composites. Cette méthodologie s'appuie sur des modèles de Markov cachés du second-ordre tels qu'implantés dans la boîte à outils CarottAge (licence Gnu-GPL)

Bayesian approach to Spatio-temporally Consistent Simulation of Daily Monsoon Rainfall over India

Simulation of rainfall over a region for long time-sequences can be very useful for planning and policy-making, especially in India where the economy is heavily reliant on monsoon rainfall. However, such simulations should be able to preserve the known spatial and temporal characteristics of rainfall over India. General Circulation Models (GCMs) are unable to do so, and various rainfall generators designed by hydrologists using stochastic processes like Gaussian Processes are also difficult to apply over the vast and highly diverse landscape of India. In this paper, we explore a series of Bayesian models based on conditional distributions of latent variables that describe weather conditions at specific locations and over the whole country. During parameter estimation from observed data, we use spatio-temporal smoothing using Markov Random Field so that the parameters learnt are spatially and temporally coherent. Also, we use a nonparametric spatial clustering based on Chinese Restaurant Process to identify homogeneous regions, which are utilized by some of the proposed models to improve spatial correlations of the simulated rainfall. The models are able to simulate daily rainfall across India for years, and can also utilize contextual information for conditional simulation. We use two datasets of different spatial resolutions over India, and focus on the period 2000-2015. We propose a large number of metrics to study the spatio-temporal properties of the simulations by the models, and compare them with the observed data to evaluate the strengths and weaknesses of the models

3D medical volume segmentation using hybrid multiresolution statistical approaches

This article is available through the Brunel Open Access Publishing Fund. Copyright © 2010 S AlZu’bi and A Amira.3D volume segmentation is the process of partitioning voxels into 3D regions (subvolumes) that represent meaningful physical entities which are more meaningful and easier to analyze and usable in future applications. Multiresolution Analysis (MRA) enables the preservation of an image according to certain levels of resolution or blurring. Because of multiresolution quality, wavelets have been deployed in image compression, denoising, and classification. This paper focuses on the implementation of efficient medical volume segmentation techniques. Multiresolution analysis including 3D wavelet and ridgelet has been used for feature extraction which can be modeled using Hidden Markov Models (HMMs) to segment the volume slices. A comparison study has been carried out to evaluate 2D and 3D techniques which reveals that 3D methodologies can accurately detect the Region Of Interest (ROI). Automatic segmentation has been achieved using HMMs where the ROI is detected accurately but suffers a long computation time for its calculations