SoftMax and Multi-class classification

Review the argmax function

argmax: returns the index corresponding to the largest value in a sequence of numbers

Largest value in Z = 100

Corresponding index = 0

Therefore the argmax function will return zero

Multi-class

Logistic regression can be used for two classes, but how about if we wanted to solve the following three class problem

Instead of using one plane to classify the data, we will use one plane for each class

1. three equations representing three classes

2. Use the graph to represent equations

- nodes are representing the different components of X

- add nodes for each output Z

The edges represent the different learnable parameters with subscript indicating the

dimensions

This is the plane where Z equals zero

the line is where the decision plane intersects with the plane Z equals zero

Overlay the sample images, line split the class

If the input is in the blue region, the value of zero corresponding to the equation zero is the largest

=> Therefore, blue region has a higher value than the other regions

It works same in the other regions (red and yellow)

*Use the planes to classify this unknown point*

Calculate the output of the plane => apply the argmax function

result = class one (blue)

SoftMax

Since the actual distances, that is dot products for each input vector with the parameters connected to the probability

Similar to logistic regression

=> the process of classification is similar but we use the output of the probability

Other method

Sometimes SoftMax is not the best option for multi-class classification

1. One - vs - rest

2. One - vs - One

These methods are used for support vector machine

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