Overview of Zero-Shot learning

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title: SSL Review -2
date: 2019-03-10 10:10:25
tags: SSL
mathjax: true

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 $U$.

• General idea:
  - transfer the knowledge contained in the training instances $D^{tr}$ to the task of testing instance classfication.
  - The label spaces covered by the training and the testing instances are disjoint.
  - Zero-Shot learning is a subfield of transfer learning.

• Transfer learning
  - knowledge contained in the source domain and source task is transferred to the target domain for learning the model in the target task.
  - Transfer learning can be classified into :
  1、homogeneous transfer learning
  >>the feature spaces and the label spaces are the same.
  2、heterogeneous transfer learning
  >>the feature spaces and/or the label spaces are different.
  - Zero-shot learning:
  >> the source feature space is the feature space of training instances.
  >> the target feature space is the feature space of testing instances.
  >> they are the same , both are $X$.
  >>the source label space is the seen class set $S$
  >> the target label space is the unseen class set $U$
  >>Belong to heterogeneous transfer learning with different label spaces(briefly: HTL-DLS)

• Many existing methods for HTL-DLS are proposed for problems under the setting in which there are some labeled instances for the target label space classes .

• However in Zero-Shot learning,no labeled instances belonging to the target space classes(the unseen classes ) are available .

• Auxiliary information for the no labeled instances problem in zero-shot learning problem.

  • Should contain information about all of the unseen classes.
  • This is to guarantee that each of the unseen classes is provided with corresponding auxiliary information.
  • Should be related to the instances in the feature space.
  • This is to guarantee that the auxiliary information is usable.

• Existing works.

  • The approach to involve auxiliary information is inspired by the way human beings recognize the world.

  • Humans can perform zero-shot learning with the help of some semantic background knowledge.

    -for example: with the knowldge that" a zebra looks like a horse, and with stripes."
    we can recognize a zebra even without having seen one before, as long as we know what a horse looks like and what the pattern “stripe” looks like.

  • The Auxiliary information involved by existing zero-shot learning methods is usually some Semantic information.

  • It forms a space that contains both the seen and the unseen classes(Refer to Semantic Space)

  • Semantic Space:

    • similar to the feature space, is usually a real number space
    • each class has a corresponding vector representation , (refered to as the Class prototype or prototype for short of this class)
    • We denote $\Gamma$ as the Semantic Space :
      • $\mathcal{\Gamma}$ is M-dimensional,usually $\mathbb{R}^{M}$ .
      • $t_i^s\in\Gamma$ as the class prototypes for seen class $c_i^s$.
      • $t_i^u\in\Gamma$ as the class prptotype for unseen class $c_i^u$
      • Denote $T^s=\{t_i^s\}_{i=1}^{N_s}$ as the set of protptypes for seen classes
      • Denote $T^u=\{t_i^u\}_{i=1}^{N_u}$ as the set of prototypes for unseen class
      • Denote $\Pi(\cdot):S \cup U\rightarrow \Gamma$ as a class prototyping function that takes a class label as input, and outputs the corresponding class prototype.
    • In zero-shot learning , $D^{tr}$、 $T^s$、 $T^u$ involved in obtaining the zero-shot classifier $f^u(\cdot)$.