S型函数
![](http://images.weserv.nl/?url=//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Sigmoid_function_01.png/220px-Sigmoid_function_01.png)
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S型函数(英語:sigmoid function,或稱乙狀函數)是一種函数,因其函數圖像形状像字母S得名。其形狀曲線至少有2個焦點,也叫“二焦點曲線函數”。S型函数是有界、可微的实函数,在实数范围内均有取值,且导数恒为非负[1],有且只有一个拐点。S型函数和S型曲线指的是同一事物。
其级数展开为:
其他S型函數案例見下。在一些學科領域,特別是人工神经网络中,S型函數通常特指邏輯斯諦函數。
常見的S型函數
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- 一些代數函數, 例如
所有連續非負的凸形函數的積分都是S型函數,因此許多常見概率分布的累积分布函数會是S型函數。一個常見的例子是误差函数,它是正态分布的累积分布函数。
参考文献
- ^ 1.0 1.1 Han, Jun; Morag, Claudio. The influence of the sigmoid function parameters on the speed of backpropagation learning. Mira, José; Sandoval, Francisco (编). From Natural to Artificial Neural Computation. Lecture Notes in Computer Science 930. 1995: 195–201. ISBN 978-3-540-59497-0. doi:10.1007/3-540-59497-3_175.
- Mitchell, Tom M. Machine Learning. WCB–McGraw–Hill. 1997. ISBN 0-07-042807-7.. In particular see "Chapter 4: Artificial Neural Networks" (in particular pp. 96–97) where Mitchell uses the word "logistic function" and the "sigmoid function" synonymously – this function he also calls the "squashing function" – and the sigmoid (aka logistic) function is used to compress the outputs of the "neurons" in multi-layer neural nets.
- Humphrys, Mark. Continuous output, the sigmoid function. [2015-02-01]. (原始内容存档于2015-02-02). Properties of the sigmoid, including how it can shift along axes and how its domain may be transformed.
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