I met with Professor Verma this week to review my two attempts in formulating a structural integrity score. My first formulation is called the Cosine Score and is based on the sum of pairwise normalized dot products of the centered data points. While the math is intuitive, this method only works for two target clusters, and breaks down for three or more target clusters.

My second formulation is called the Distance Concentration Score, which is derived from a distance matrix of pairwise distances among all data points. The method is based on the hypothesis that for clusters that are divided and separately evenly, there is an optimal average distance between data points of different clusters. It then computes a score based on how close the average pairwise distance is to the optimate average distance using a Gaussian formula.

Professor Verma provided helpful feedback on my initial attempts, and encouraged me to try to incorporate these formulations into the overall metric learning objective function, which I intend to implement with MMC.