Manhattan Distance

• Taxicab distance or City Block distance, calculates the distance between real-valued vectors
• $D(x,y)={\Sigma }_{i=1}^k|x_i-y_i|$
• There is no diagonal movement involved in calculating the distance.
• Manhattan distance seems to work okay for high dim data, it is a measure that is somewhat less intuitive than Euclidean Distance, especially when using in high-dimensional data
• more likely to give a higher distance value than Euclidean Distance since it does not the shortest path possible.
• When your dataset has discrete and/or binary attributes, Manhattan seems to work quite well since it takes into account the paths that realistically could be taken within values of those attributes.