Taxicab Norm

Taxicab norm is a distance metric in which the distance between two points is the sum of the absolute differences of their coordinates. In other words, it is the distance between two points in a Cartesian plane if a person can only travel along the grid lines. Taxicab norm is also known as Manhattan distance, city block distance, or L1 norm. It is commonly used in machine learning algorithms, especially in clustering and classification problems. For example, in image processing, taxicab norm can be used to measure the similarity between two images by comparing the differences in their pixel values. In addition, taxicab norm is used in optimization problems, such as linear programming, where the objective function is a linear combination of absolute values of variables.
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