Separating colored point sets is an interesting problem in computational geometry with application in machine learning and pattern recognition. In this problem, we are given a geometric shape C and two point sets P and Q of total size n as red and blue points, respectiv More
Separating colored point sets is an interesting problem in computational geometry with application in machine learning and pattern recognition. In this problem, we are given a geometric shape C and two point sets P and Q of total size n as red and blue points, respectively. Now, we must separate red and blue points by this shape such that all the blue points lie inside it and all the red points lie outside it. In the previous work, we have some algorithms for rectangle and wedge separability but we do not have any algorithm for separating by a triangle and separating by a triangle with a fixed angle such as right triangle. In this paper, we present an efficient algorithm for right triangle seprability. In this algorithm, we use sweep line technique and introduce some events and process them. So, we can report all separating right triangles in O(nlog n) time.
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Clustering is one of the important techniques for knowledge discovery in spatial databases. density-based clustering algorithms are one of the main clustering methods in data mining. DBSCAN which is the base of density-based clustering algorithms, besides its benefits s More
Clustering is one of the important techniques for knowledge discovery in spatial databases. density-based clustering algorithms are one of the main clustering methods in data mining. DBSCAN which is the base of density-based clustering algorithms, besides its benefits suffers from some issues such as difficulty in determining appropriate values for input parameters and inability to detect clusters with different densities.
In this paper, we introduce a new clustering algorithm which unlike DBSCAN algorithm, can detect clusters with different densities. This algorithm also detects nested clusters and clusters sticking together. The idea of the proposed algorithm is as follows. First, we detect the different densities of the dataset by using a technique and Eps parameter is computed for each density. Then DBSCAN algorithm is adapted with the computed parameters to apply on the dataset. The experimental results which are obtained by running the suggested algorithm on standard and synthetic datasets by using well-known clustering assessment criteria are compared to the results of DBSCAN algorithm and some of its variants including VDBSCAN, VMDBSCAN, LDBSCAN, DVBSCAN and MDDBSCAN. All these algorithms have been introduced to solve the problem of multi-density data sets. The results show that the suggested algorithm has higher accuracy and lower error rate in comparison to the other algorithms.
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The point-set covering is one of the important problems in computational geometry, which has many applications. In this problem, the given points should be covered by at least one geometric shape. A variant of the problem is the point-set separation, in which there are More
The point-set covering is one of the important problems in computational geometry, which has many applications. In this problem, the given points should be covered by at least one geometric shape. A variant of the problem is the point-set separation, in which there are at least two different kinds of points which are colored by different colors. The geometric shapes, which are called separators, should only cover the points of the same color. In this paper, separation of blue and red points by a double-wedge of a given angle θ is considered. The proposed algorithm reports all separator θ angle double-wedges in optimal time O(nlogn).
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