One of K Encoding Scheme

Definition

It is a technique use to model labels for multi-class problems. Each label ($t_i$), is represented as a vector with $K$ dimensions where $K$ is the number of possible classes.

All the values in the vector consists of zeros except the element for the correct class, which is defined as $1$.

For an input $x_i$ belonging to class $C_k$, the label vector $t_i$ is defined as:

$$t_i=\left(t_1,\dots ,t_k,\dots ,t_K\right)=(0,\dots ,1,\dots ,0)$$

where the $k-$th element is $1$.

This $1-$of$-K$ label vector can also be interpreted as a probability vector. An example of this is the DeepFace system, which uses a “one-of-4030” encoding for its 4,030 face classes.

Example

Classification of images into one of three categories: Cat, Dog, or **Bird ** i.e (K=3) classes. According to the 1-of-K encoding scheme, the label for each image will be a 3-dimensional vector.

Label Modeled for an image from each class:

• If an input image $x$ is a Cat (Class 1), its label vector $t$ would be: $t=(1,0,0)$
• If an input image $x$ is a Dog (Class 2), its label vector $t$ would be: $t=(0,1,0)$
• If an input image $x$ is a Bird (Class 3), its label vector $t$ would be: $t=(0,0,1)$

Each vector has a '$1$' in the position corresponding to its class and '$0$'s in all other positions.