This week I implemented the structural integrity score on clusters generated by a Gaussian Mixture Model, and was able to ascribe a higher score to tight clusters than to wide clusters, and a higher score to means that are farther apart. While this provides an independent loss value for the structural integrity of the transformed data, I was stuck trying to combine it with the LMNN loss to form a differentiable loss function. Instead of using library functions for metric learning, I will try to write an algorithm that incorporates both the distance loss and the structure integrity and is differentiable by the transformation matrix.

Regarding the idea of applying contrastive loss to computer vision data, I reviewed the papers on Word2Vec and will familiarize myself with the ImageNet dataset and find a way to apply the contrastive loss model.