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A Study of Distance Metrics in Document Classification
Published in Sk Md Obaidullah, KC Santosh, Teresa Gonçalves, Nibaran Das, Kaushik Roy, Document Processing Using Machine Learning, 2019
Ankita Dhar, Niladri Sekhar Dash, Kaushik Roy
The Chebyshev distance can be defined on the feature vectors to measure the greatest of the differences between two vector spaces along the standard coordinates. It is measured using the equation below. Disi,j=maxlil−jl
Variable-dimensional Flower Pollination obstacle avoidance algorithm on autonomous walking of NAO robot in dynamic environment
Published in Advanced Robotics, 2019
Shuhuan Wen, Nannan Zhou, Di Zhang, Yanfang Zhao, Qiguang Zhu
The Chebyshev distance defines the absolute value of the maximum value of each coordinate numerical difference between the two points. Assuming and on the two-dimensional space, and then the Chebyshev distance between A and B is Euclidean distance is a common distance, which represents the true distance or natural length between two points. It is expressed on the two-dimensional space as follows. Because the robot will pass through the column between the initial location and the target location in the grid map from the starting location to the target location of the robot, a key grid is selected from each passed column to represent the whole path. During the moving process of the robot, the target location would not change while the robot location change constantly. So the path is expressed by using reverse order way. That is, the expressed method of each key grid experienced from the target location to the robot location is the row coordinate in this column of the grid. In Figure 1, the path can be expressed as. The dimension is equivalent to the number of columns between the robot location and the target location. It is expressed as follows. The path between every key points is not always connected directly because the robot moves toward the adjacent freedom grid each time. To some extent, the distance between the two key points complies with the feature of Chebyshev distance. However, Chebyshev distance represents the moving steps of the robot. Actually, the moving natural length of each robot may be different and has the characteristics of Euclidean distance. Because the adjacent key points comply with , robot position and target location ,, the fitness function is defined as follows. The fitness function combines the characteristics of Chebyshev distance and Euclidean distance, and tends to make the robot choose the obstacle avoidance path with the minimum steps and the shortest route. Thus the problem of finding the optimal obstacle avoidance path becomes an optimization problem, that is, finds a feasible path to obtain the minimum value. In the paper, a new algorithm is proposed based on Flower Pollination algorithm to achieve the optimal path planning.