﻿OrderedConnectivityMatrix Class
Class OrderedConnectivityMatrix reorders the rows and columns of an connectivity matrix so that the most affiliated elements appear as clusters of higher values along the diagonal.

Namespace: CenterSpace.NMath.Stats

# Syntax

C#
```[SerializableAttribute]
public class OrderedConnectivityMatrix : ConnectivityMatrix```
Visual Basic
```<SerializableAttribute> _
Public Class OrderedConnectivityMatrix _
Inherits ConnectivityMatrix```
Visual C++
```[SerializableAttribute]
public ref class OrderedConnectivityMatrix : public ConnectivityMatrix```

# Remarks

The connectivity matrix a symmetric matrix, A, of non-negative values where aij is a measure of the connectivity of element i and j. The values aij may be 0 and 1 with 1 indicating that elemets i and j are adjacent and 0 indicating that they are not. They may also be floating point numbers. For example the values aij may be real numbers between 0 and 1 and indicate the probability, or belief that elements i and j are adjacent.
First a hierarchical cluster analysis is performed on the elements represented in the connectivity matrix. For the purpose of clustering the elements represented in the connectivity matrix are labeled 0, 1, 2,...,n-1, where n is the number of the elements. Given two integers, i and j, the provided distance function should return the distance between the ith and jth elements. If no distance function is provided the default distance function returns the value 1.0 - aij for the distance between the ith and jth elements, where aij is the i, jth element of the connectivity matrix A. After the hierarchical clustering process, the leaf nodes of the dendrogram produced from the results are traversed in order to produce a permutation vector. This permutation vector is used to reorder the rows and columns of the input connectivity matrix, causing the most affiliated elements to appear as clusters of higher values along the diagonal.
References: "Constructing and Reconstructing the Reorderable Matrix" Harri Siirtola1 and Erkki Mäkinen
"Concept Map: Clustering Visualizations of Categorical Domains" David Rouff and Mark McLean

# Inheritance Hierarchy

System..::..Object
CenterSpace.NMath.Matrix..::..DoubleSymmetricMatrix
CenterSpace.NMath.Stats..::..ConnectivityMatrix
CenterSpace.NMath.Stats..::..OrderedConnectivityMatrix