Improvement Least-Distance Measure Model with Coplanar DMU on Strong Hyperplanes

Deming least-squares fit to multiple hyperplanes

A method is derived to fit a set of multidimensional experimental data points having a priori uncertainties and possibly also covariances in all coordinates to a straight line, plane, or hyperplane of any dimensionality less than the number of coordinates. The least-squares formulation used is that of Deming, which treats all coordinates on an equal basis. Experimentalists needing to fit a line...

ON k-STRONG DISTANCE IN STRONG DIGRAPHS

For a nonempty set S of vertices in a strong digraph D, the strong distance d(S) is the minimum size of a strong subdigraph of D containing the vertices of S. If S contains k vertices, then d(S) is referred to as the k-strong distance of S. For an integer k > 2 and a vertex v of a strong digraph D, the k-strong eccentricity sek(v) of v is the maximum k-strong distance d(S) among all sets S of k...

2 Separating Hyperplanes 3 Banach–mazur Distance

We’ll use the above result to show why the polar of the polar of a convex body is the body itself. Recall that for a convex body K, we had defined its polar K∗ to be {p|k · p ≤ 1∀k ∈ K}. Theorem 2 Let K be a convex body. Then K∗∗ = K. Proof We know that K∗ = {p|k · p ≤ 1∀k ∈ K}. Similarly K∗∗ = {y|p · y ≤ 1∀p ∈ k∗}. Let y be any point in K. Then, by the definition of the polar, for all p ∈ K∗ w...

Multimodal registration of MR images with a novel least-squares distance measure

In this work we evaluate a novel method for multi-modal image registration of MR images. The key feature of our approach is a new distance measure that allows for comparing modalities that are related by an arbitrary gray-value mapping. The novel measure is formulated as least square problem for minimizing the sum of squared differences of two images with respect to changing gray-values of one ...

Revision of a fuzzy distance measure