M-tree

M-trees are tree data structures that are similar to R-trees and B-trees. It is constructed using a metric and relies on the triangle inequality for efficient range and k-nearest neighbor (k-NN) queries.While M-trees can perform well in many conditions, the tree can also have large overlap and there is no clear strategy on how to best avoid overlap. In addition, it can only be used for distance functions that satisfy the triangle inequality, while many advanced dissimilarity functions used in information retrieval do not satisfy this. M-trees are tree data structures that are similar to R-trees and B-trees. It is constructed using a metric and relies on the triangle inequality for efficient range and k-nearest neighbor (k-NN) queries.While M-trees can perform well in many conditions, the tree can also have large overlap and there is no clear strategy on how to best avoid overlap. In addition, it can only be used for distance functions that satisfy the triangle inequality, while many advanced dissimilarity functions used in information retrieval do not satisfy this. As in any Tree-based data structure, the M-Tree is composed of Nodes and Leaves. In each node there is a data object that identifies it uniquely and a pointer to a sub-tree where its children reside. Every leaf has several data objects. For each node there is a radius r {displaystyle r} that defines a Ball in the desired metric space. Thus, every node n {displaystyle n} and leaf l {displaystyle l} residing in a particular node N {displaystyle N} is at most distance r {displaystyle r} from N {displaystyle N} , and every node n {displaystyle n} and leaf l {displaystyle l} with node parent N {displaystyle N} keep the distance from it.