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The lower weighted median is 2 with partition sums of 0.49 and 0.5, and the upper weighted median is 3 with partition sums of 0.5 and 0.25. In the case of working with integers or non-interval measures, the lower weighted median would be accepted since it is the lower weight of the pair and therefore keeps the partitions most equal. However, it ...
An important ingredient in the calculus on finite weighted graphs is the mimicking of standard differential operators from the continuum setting in the discrete setting of finite weighted graphs. This allows one to translate well-studied tools from mathematics, such as partial differential equations and variational methods, and make them usable ...
The median of three vertices in a tree, showing the subtree formed by the union of shortest paths between the vertices. Every tree is a median graph. To see this, observe that in a tree, the union of the three shortest paths between pairs of the three vertices a, b, and c is either itself a path, or a subtree formed by three paths meeting at a single central node with degree three.
the point minimizing the sum of distances to a set of sample points. This is the same as the median when applied to one-dimensional data, but it is not the same as taking the median of each dimension independently. It is not invariant to different rescaling of the different dimensions. Quadratic mean (often known as the root mean square)
In a multiplicatively weighted Voronoi diagram, the distance between a point and a site is divided by the (positive) weight of the site. [1] In the plane under the ordinary Euclidean distance , the multiplicatively weighted Voronoi diagram is also called circular Dirichlet tessellation [ 2 ] [ 3 ] and its edges are circular arcs and straight ...
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average.
For the 1-dimensional case, the geometric median coincides with the median.This is because the univariate median also minimizes the sum of distances from the points. (More precisely, if the points are p 1, ..., p n, in that order, the geometric median is the middle point (+) / if n is odd, but is not uniquely determined if n is even, when it can be any point in the line segment between the two ...
A median graph is an undirected graph in which for every three vertices , , and there is a unique vertex ,, that belongs to shortest paths between any two of , , and . If this is the case, then the operation x , y , z {\displaystyle \langle x,y,z\rangle } defines a median algebra having the vertices of the graph as its elements.
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