# 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)

- the Set of Seen Classes:
- 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 $U$.