## On the properties of Hyperbolic Tangent Kernel

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How do Hyperbolic Tangent Kernels work? That is what is the intuition behind them? Can you provide proofs and examples for illustration?

Hyperbolic Tangent Kernels are defined as: $$K(x, x^\prime) = tanh\bigg(\alpha (x\cdot x^\prime) + c\bigg)$$

For example, for Gaussian RBF kernel, the intuition is that the support vectors affect the decision surface based on the locality of influence. What is the analog for Hyperbolic Tangent (Sigmoid Kernels)?

Some references on the Hyperbolic Tangent Kernels are:

Question was closed 2016-03-10T11:04:20.293

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This was cross-posted to http://stats.stackexchange.com/questions/199620/on-the-properties-of-hyperbolic-tangent-kernel . Either site may be fine for this question. Since the other post got an answer that @Ragnar liked more, I propose this be closed as a duplicate. (Generally, we don't cross post.)

– Sean Owen – 2016-03-09T20:59:38.510

I'm voting to close this question because it's a cross post and seems the OP found it better suited to stats SE – Sean Owen – 2016-03-10T11:04:20.293

Sigmoid kernels owe their popularity to neural networks, which traditionally used the sigmoid activation function. Sigmoid kernels de-emphasize extreme correlation. In a way they behave a bit like correlation coefficients, which also has a limited range, emphasizing similarity in orientation. $c$ shifts the operating point on the sigmoid, affecting the relative emphasis of the angle between the inputs. Perhaps this visualization (for $c=0$) might help mentally visualize this: