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The non-Archimedean normed space theory is an important research object in mathematical physics whose triangle inequality holds in a stronger form. In this note, we propose a generalized chordal distance and a non-Archimedean chordal distance for intuitionistic fuzzy sets. An illustrative example is given to calculate the constructed distances with the different parameters. And some experiments show that the new distances based on chordal distance and non-Archimedean distance are more efficient than the Euclidean-like distances in pattern recognition. [ABSTRACT FROM AUTHOR]

With the increasing use of mobile GPS (global positioning system) devices, a large volume of trajectory data on users can be produced. In most existing work, trajectories are usually divided into a set of stops and moves. In trajectories, stops represent the most important and meaningful part of the trajectory; there are many data mining methods to extract these locations. DBSCAN (density-based spatial clustering of applications with noise) is a classical density-based algorithm used to find the high-density areas in space, and different derivative methods of this algorithm have been proposed to find the stops in trajectories. However, most of these methods required a manually-set threshold, such as the speed threshold, for each feature variable. In our research, we first defined our new concept of move ability. Second, by introducing the theory of data fields and by taking our new concept of move ability into consideration, we constructed a new, comprehensive, hybrid feature-based, density measurement method which considers temporal and spatial properties. Finally, an improved DBSCAN algorithm was proposed using our new density measurement method. In the Experimental Section, the effectiveness and efficiency of our method is validated against real datasets. When comparing our algorithm with the classical density-based clustering algorithms, our experimental results show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The interferometric coherence map derived from the cross-correlation of two complex registered synthetic aperture radar (SAR) images is the reflection of imaged targets. In many applications, it can act as an independent information source, or give additional information complementary to the intensity image. Specially, the statistical properties of the coherence are of great importance in land cover classification, segmentation and change detection. However, compared to the amount of work on the statistical characters of SAR intensity, there are quite fewer researches on interferometric SAR (InSAR) coherence statistics. And to our knowledge, all of the existing work that focuses on InSAR coherence statistics, models the coherence with Gaussian distribution with no discrimination on data resolutions or scene types. But the properties of coherence may be different for different data resolutions and scene types. In this paper, we investigate on the coherence statistics for high resolution data over urban areas, by making a comparison of the accuracy of several typical statistical models. Four typical land classes including buildings, trees, shadow and roads are selected as the representatives of urban areas. Firstly, several regions are selected from the coherence map manually and labelled with their corresponding classes respectively. Then we try to model the statistics of the pixel coherence for each type of region, with different models including Gaussian, Rayleigh, Weibull, Beta and Nakagami. Finally, we evaluate the model accuracy for each type of region. The experiments on TanDEM-X data show that the Beta model has a better performance than other distributions. [ABSTRACT FROM AUTHOR]