Linear Threshold Function

A Linear Threshold Function is a threshold function that uses a sign function.

• Context:
  • It can be defined as [math]\displaystyle{ f_w(x) : f_w(x) = \operatorname{sign}(x \cdot w) }[/math].
• Example(s):
  • Heaviside Step Activation Function.
  • [math]\displaystyle{ f(x) = \begin{cases} 0, & \mbox{for } x \lt 0 \\ 1, & \mbox{for } x \geq 0 \end{cases} }[/math].
  • …
• Counter-Example(s)
  • Sigmoid Function.
• See: Linear Function, Linear Classifier.

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References

2013

• http://en.wikipedia.org/wiki/Artificial_neuron
  • … Depending on the specific model used, it can receive different names, such as semi-linear unit, Nv neuron, binary neuron, linear threshold function or McCulloch–Pitts (MCP) neuron. …

2009

• (Rabani & Shpilka, 2009) ⇒ Yuval Rabani, and Amir Shpilka. (2009). “Explicit Construction of a Small Epsilon-net for Linear Threshold Functions.” In: Proceedings of the 41st annual ACM symposium on Theory of computing. doi:10.1145/1536414.1536502
  • QUOTE: We give explicit constructions of epsilon nets for linear threshold functions on the binary cube and on the unit sphere.

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