Applying energy transformation analysis to determine the weights of sequences

Analyzed the methods to determine the weights for two relational measures: (1) an approximation grade, and (2) a similarity grade. An approximation measurement is introduced to differentiate how close they are between two sequences. On the other hand, a similarity measurement is derived to discriminate how similar they are between two sequences. Using the maximum entropy method, the weights for approximation grades were determined by solving the optimization problem via the Lagrange multipliers method, and these results could be explained in a reasonable manner according to the Laplacian principle of indifference. However, a linear data transformation from the original comparable sequences to the variation sequences must be done to apply these variation sequences to evaluate the similarity grade. To analyze this transformation a simple dynamic system was developed; furthermore, the energy function called the Lyapunov function, was utilized for constructing the ratio of power dissipation during this transformation so that the weights for similarity grades were determined. Finally, the verification of the weights determined for two relational measures was ensured through means of examining two examples