SSL Review -2

Overview of Zero-Shot learning

  • the seen classes

    • the classes covered by labeled training instances in the feauture space
  • the unseen classes

    • unlabeled testing instances in the feature space which belong to another set of classes
  • the feature space

    • a real number space
    • each instance is represented as a vector within it
    • each instance is usually assumed to belong to one class
  • definition

    • the Set of Seen Classes:
      $$S=\\{c_{i}^{s}\|i=1,……,N_{s}\\}$$
      
      • a seen classes:$c_{i}^{j}$
    • the Set of Unseen Classes:
      $$U=\\{c_{i}^{u}\\|i=1,N_{u}\\}$$
      
    • an unseen class:$C_{i}^{u}$
    • Denote that :${S}\bigcap{U}=\varnothing$
    • The Feature Space:$X$, which is $D-dimensional$: $R^{D}$
    • The set of labeled training instances belonging to seen classes:

      $$D^{tr}=\{(x_{i}^{tr},y_{i}^{tr})\in X\times S\}$$

    • for each labeled instance $(x_i^{tr},y_i^{tr})$,

      • $x_i^{tr}$ :the instance in the feature space ,
      • $y_i^{tr}$: the corresponding class label .
    • The set of testing instances:
      $$X^{te}=\{x_i^{te}\in X\}{i=1}^{N{te}}$$
      where each $x_i^{te}$ is a testing instance in the feature space.
    • The corresponding class labels for $X^{te}$:
      $$Y^{te}=\{y_i^{te}\in U\}{i=1}^{N{te}}$$
      which are able to be predicted.

      Definition 1.1 (Zero-Shot Learning)

  • Given labeled training instances $D^{tr}$ belonging to the seen classes $S$,zero-shot learning aims to learn a classifier $f^u(\cdot):X\rightarrow U$ that can classify testing instances $X^{te}$(i.e. to predict $Y^{te}$) belonging to the unseen classes $U$.