The difference between logistic regression and softmax regression

Question

I know that logistic regression is intended for binary classification and softmax regression for a multiclass problem. Will there be any differences if I prepare several models of logistic regression with the same data and normalize their results in order to get a classifier with several classes instead of using one softmax model. I guess the result is the same. May I say: "the entire classifier of multiclasses is a cascading result of binary classifiers." (except neural network)

Answer 1

There are slight differences in several logistic regression models and softmax output.

Essentially, you can match an input of size d with one output k times or match an input of size d with k outputs once. However, several logistic regression models are confusing and work worse in practice. This is due to the fact that most libraries (TensorFlow, Caffe, Theano) are implemented in low-level compiled languages ​​and are highly optimized. Since the management of several logistic regression models is likely to be at a higher level, it should be avoided.

Answer 2

, .

1. Softmax Regression - , k- k (0, 1).
2. , (0 1). Softmax Regression .
3. :
   • LR:
   • Softmax:

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

Answer 3

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. 10 [0-9], , 10 , , , .

, softmax . , . , , - , .

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

: , softmax 2 . , - . , 2- softmax, ( 2- ).

. , softmax , .

, .

Answer 4

softmax, (z1, z2) z = z1-z2

softmax(z1, z2) = exp(z1)/(exp(z1) + exp(z2)) = exp(z1 - z2)/(exp(z1-z2) + exp(0)) = exp(z)/(exp(z) + 1)