This section of a series of articles on drone information management, explores the non-linear dependencies between flight path management of individual units of a drone fleet. Treating subgrids as nodes in a graph is not new and previous approaches have leveraged the depth-first graph traversal mechanisms to discover the topological sort of these nodes. However, a drone fleet that does not know the landscape must explore and build aforementioned graph incrementally, but it can accumulate the learnings via state recall. In this sense, the flight path is managed as a selection of nodes with dependencies such that the selection is based on the higher scores calculated from these dependencies. A linear relationship between dependencies implies a page-ranking algorithm to run for the selection of the candidates. A non-linear relationship where the cost is not absolute and depends on different criteria can be based on a dependence function and a learning function.

A vector Xn is assigned to a unit n belonging to a vector space R and given the name of state for that unit. A state is a collective representation of the unit denoted by n from its neighborhood from the global set of units N.    

   Xn =  summation Hw(In, Xu, Iu), n belongs to N 

Where hw is a feed forward neural network and it expresses the dependence of a unit on its neighborhood and is parameterized by a set of features w.   

The state xn is the solution of the following system of equations:   

1. A dependence function and    

2. A learning function   

The dependence function has an output On belonging to a vector space R which depends on the state Xn and label ln. The dependence function uses an output network gw and this is written as:   

   

   On = Gw(Xn, In), n belongs to N

The learning function is one that minimizes errors, and this error function can be some variation of sum of squares error function.   

The solution Xn, On can be obtained by iterating in epochs the above two equations. Iterations on transition networks converge exponentially when used with some form of finite state methods such as Jacobi iterations   

The Jacobi iteration gives eigen values and eigen vectors.