Difference between logistic regression and softmax regression

Question

I know that logistic regression is for binary classification and softmax regression for multi-class problem. Would it be any differences if I train several logistic regression models with the same data and normalize their results to get a multi-class classifier instead of using one softmax model. I assume the result is of the same. Can I say : "all the multi-class classifier is the cascading result of binary classifiers". (except neuron network)

Answer 1

Echoing on what others have already conveyed.

1. Softmax Regression is a generalization of Logistic Regression that summarizes a 'k' dimensional vector of arbitrary values to a 'k' dimensional vector of values bounded in the range (0, 1).
2. In Logistic Regression we assume that the labels are binary (0 or 1). However, Softmax Regression allows one to handle classes.
3. Hypothesis function:
   • LR:
   • Softmax Regression:

Reference: http://ufldl.stanford.edu/tutorial/supervised/SoftmaxRegression/