For many applications in data mining and knowledge discovery in
databases, clustering methods are used for data reduction.
If the amount of data increases like in image information
mining, where one has to process GBytes of data, for instance, many of the existing clustering algorithms cannot be applied because of a high computational complexity. To overcome this disadvantage, we developed an efficient clustering algorithm called dyadic k-means. The algorithm is a modified and enhanced version of the traditional k-means. Whereas k-means has a computational complexity of O(nk) with n samples and k clusters, dyadic k-means has one of O(n \log k).
Our algorithm is particularly efficient for the grouping of
very large data sets with a high number of clusters. In this article we will present statistically-based methods for the objective evaluation of clusters obtained by dyadic k-means. The main focus is on how well the clusters describe the data point distribution
in a multi-dimensional feature space and how much information can be obtained from the clusters. Both the filling of the feature space with samples and the characterization of this configuration with dyadic k-means produced clusters will be considered. We will use the well-established scatter matrices to measure the compactness and separability of clustered groups in the feature space. The probability of error, which is another indicator for the characterization of samples in the featuer space by clusters, will be calculated for each point, too. This probability delivers the relationship of each point to its cluster and can therefore be considered as a measurement of cluster reliability. We will test the evaluation methods both on a synthetic and a real world data set.
The recognition and classification of urban structures from SAR observations is a particularly complex task. In this article we present a new concept aiming at the accurate and detailed classification of the city scenes observed with metric resolution SAR sensors. SAR images of build-up areas at resolution of 2-3 meters are characterized by strong patterns induced by the geometry of buildings and the phenomenology of scattering of the radar signals. Thus, resulting in high complexity images. The accuracy of image interpretation relies on the descriptive power of the low level image information extraction. The article presents a method based on the Bayesian concepts. A hierachical 3 layers model is used for the SAR observations. The first layer describes the speckle effect as a Gamma distribution, the second, the cross-section, is modeled as Gibbs Random Field (GRF), the third layer the parameters of the Gibbs random field is considered a Jeffrey's prior. The GRF describes the cross-section structures induced by the geometry of the buildings. The model is non-stationary, its parameters adapt locally to the image structures.
The recognition and classification of urban structures from SAR observations is a particularly complex task. In this article we present a new concept aiming at the accurate and detailed classification of the city scenes observed with metric resolution SAR sensors. SAR images of build-up areas at resolution of 2-3 meters are characterized by strong patterns induced by the geometry of buildings and the phenomenology of scattering of the radar signals. Thus, resulting in high complexity images. The accuracy of image interpretation relies on the descriptive power of the low level image information extraction. The article presents a method based on the Bayesian concepts. A hierachical 3 layers model is used for the SAR observations. The first layer describes the speckle effect as a Gamma distribution, the second, the cross-section, is modeled as Gibbs Random Field (GRF), the third layer the parameters of the Gibbs random field is considered a Jeffrey's prior. The GRF describes the cross-section structures induced by the geometry of the buildings. The model is non-stationary, its parameters adapt locally to the image structures.
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