我理解这个维基页面所说的内容(http://en.wikipedia.org/wiki/Multinomial_logistic_regression)，但我不知道如何得到随机梯度下降的更新规则。很抱歉在这里问这个问题（这实际上只是关于机器学习理论而不是实际实现）。能有人提供一个带解释的解决方案吗？提前感谢！

回答：

我碰巧写了实现softmax的代码，我主要参考了这个页面 http://ufldl.stanford.edu/wiki/index.php/Softmax_Regression

这是我在Matlab中写的代码，希望对你有帮助

function y = sigmoid_multi(weight,x,class_index)%%  weight feature_dim * class_num%%  x      feature_dim * 1%%  class_index  scalar    sum = eps;    class_num = size(weight,2);    for i = 1:class_num        sum = sum + exp(weight(:,i)'*x);    end    y = exp(weight(:,class_index)'*x)/sum;endfunction g = gradient(train_patterns,train_labels,weight)    m = size(train_patterns,2);    class_num = size(weight,2);    g = zeros(size(weight));    for j = 1:class_num        for i = 1:m            if(train_labels(i) == j)                g(:,j) = g(:,j) + (1 - log( sigmoid_multi(weight,train_patterns(:,i),j) + eps))*train_patterns(:,i);            end        end    end    g = -(g/m);endfunction J = object_function(train_patterns,train_labels,weight)    m = size(train_patterns,2);    J = 0;    for i = 1:m        J = J + log( sigmoid_multi(weight,train_patterns(:,i),train_labels(i)) + eps);    end    J = -(J/m);endfunction weight = multi_logistic_train(train_patterns,train_labels,alpha)%%  weight feature_dim * class_num%%  train_patterns  featur_dim * sample_num%%  train_labels  1 * sample_num%%  alpha   scalar     class_num = length(unique(train_labels));     m = size(train_patterns,2); %% sample_number;     n = size(train_patterns,1); % feature_dim;     weight = rand(n,class_num);     for i = 1:40        J = object_function(train_patterns,train_labels,weight);        fprintf('objec function value : %f\n',J);        weight = weight - alpha*gradient(train_patterns,train_labels,weight);     end    end