The difference of kernels in SVM? Can someone please tell me the difference between the kernels in SVM:  


*

*Linear  

*Polynomial  

*Gaussian (RBF)

*Sigmoid   


Because as we know that kernel is used to mapped our input space into high dimensionality feature space.
And in that feature space, we find the linearly separable boundary..
When are they are used (under what condition) and why?
 A: The linear kernel is what you would expect, a linear model. I believe that the polynomial kernel is similar, but the boundary is of some defined but arbitrary order
(e.g. order 3:  $ a= b_1 + b_2 \cdot X + b_3 \cdot X^2 + b_4 \cdot X^3$).
RBF uses normal curves around the data points, and sums these so that the decision boundary can be defined by a type of topology condition such as curves where the sum is above a value of 0.5. (see this picture )

I am not certain what the sigmoid kernel is, unless it is similar to the logistic regression model where a logistic function is used to define curves according to where the logistic value is greater than some value (modeling probability), such as 0.5 like the normal case.
A: Relying on basic knowledge of reader about kernels.
Linear Kernel: $K(X, Y) = X^T  Y$
Polynomial kernel: $K(X, Y) = (γ\cdot X^T  Y + r)^d , γ > 0$
Radial basis function (RBF) Kernel: $K(X, Y) = \exp(\|X-Y\|^2/2σ^2)$ which in simple form can be written as $\exp(-γ \cdot \|X - Y\|^2), γ > 0$
Sigmoid Kernel: $K(X, Y) = \tanh(γ\cdot X^TY + r) $ which is similar to the sigmoid function in logistic regression.
Here $r$, $d$, and $γ$ are kernel parameters.
A: This question can be answered from theoretical and practical point of view. From theoretical according to No-Free Lunch theorem states that there are no guarantees for one kernel to work better than the other. That is a-priori you never know nor you can find out which kernel will work better.
From practical point of view consult the following page:
How to select kernel for SVM?
A: While reflecting on what a kernel is "good for" or when it should be used, there are no hard and fast rules. 
If you're classifier/regressor is performing well with a given kernel, it is appropriate, if not, consider changing to another. 
Insight into how your kernel may perform, specifically if it is a classification model, might be gained by reviewing some visualisation examples, e.g. https://gist.github.com/WittmannF/60680723ed8dd0cb993051a7448f7805
