# 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 $U$.