Editing Distance matrix (section)

=== Data Mining ===
A common function in data mining is applying [[cluster analysis]] on a given set of data to group data based on how similar or more similar they are when compared to other groups. Distance matrices became heavily dependent and utilized in [[cluster analysis]] since similarity can be measured with a distance metric. Thus, distance matrix became the representation of the similarity measure between all the different pairs of data in the set.

==== Hierarchical clustering ====
A distance matrix is necessary for traditional [[hierarchical clustering]] algorithms which are often heuristic methods employed in biological sciences such as phylogeny reconstruction. When implementing any of the hierarchical clustering algorithms in data mining, the distance matrix will contain all pair-wise distances between every point and then will begin to create clusters between two different points or clusters based entirely on distances from the distance matrix.

If N be the number of points, the complexity of hierarchical clustering is:

* Time complexity is <math>O(N^3)</math> due to the repetitive calculations done after every cluster to update the distance matrix
* Space complexity is <math>O(N^2)</math>