Intro to Metric Learning

Relative Relationship Form (a weaker supervision) → ordinal regression

→ Metric Learning: task of learning a distance (or similarity) function over objects

• input: 2 or more exampels
• output: a (non-negative) score → distance may have different meaning depending on data (i.e. meaning of relationship in the training data)

Overview

• Learning to Rank
• Widely used metric learning methods: (1) Triplet Loss (2) Contrastive Learning
• with applications in CV: face clustering, video recommendation, image/video representation learning

Learning to Rank

• train data of 'lists of items' with some partial order specified between items in each list
• evaluation metric: Normalized Discounted Cumulative Gain (NDCG)
  • graded relevance DCG: higher position in output list gets more importance
  • NDCG = DCG / maximum possible DCG $\in [0,1]$

Triplet Loss

make dist(anchor, positive) < dist(anchor, negative)

$L = \displaystyle \sum_i^N \Big[ \| f(x_i^a) - f(x_i^p)\|_2^2 - \|f(x_i^a) - f(x_i^n) \|2^2 + \alpha \Big]+$

Collection of negative data

• random negatives → easy triplets: often too easy to distinguish
• Online negative mining: look for hard negatives from current batch, instead of using one initially assigned
  • compute kNN from each anchor to every other instance in batch → find closest instance that is not a positive pair to that anchor