One Pager Cheat Sheet

• The Manhattan Distance, also known as city block distance or taxicab geometry, calculates the distance between two coordinates in a grid-like path, similar to pathways on a city map, rather than a direct line.
• The Manhattan Distance, measured along grid-like city blocks, is calculated using the formula ( d = |x_1 - x_2| + |y_1 - y_2| ) and is implemented in machine learning (especially in clustering algorithms, such as the K-Nearest Neighbors) and other applications where a distance metric between two datasets or vectors is needed, with libraries in languages like Python (particularly the cityblock function from the scipy.spatial.distance library) simplifying the process.
• The Manhattan Distance, also known as city block distance, measures the total distance traveled along a grid by calculating the combined horizontal and vertical distance covered, mimicking navigation in a city built on a grid system.
• The Manhattan distance between two vectors C (3,2,5) and D (4,1,7) is calculated by summing the absolute differences of their coordinates, resulting in a Manhattan Distance of 4.
• The Manhattan Distance, also known as "L1 distance" or "Taxicab" or "City block" distance, originated from the grid-like street layout of Manhattan, is a geometric concept that calculates the total horizontal and vertical distances between two points, and has diverse applications in fields including computer vision, games, robotics, and economics.
• The Manhattan Distance, which is the sum of the absolute differences between two vectors, is crucial in Machine Learning and preferred over the Euclidean distance metric as the dimensions of the data increase.