39k views

### What makes the Gaussian kernel so magical for PCA, and also in general?

I was reading about kernel PCA (1, 2, 3) with Gaussian and polynomial kernels. How does the Gaussian kernel separate seemingly any sort of nonlinear data exceptionally well? Please give an intuitive ...
16k views

### Feature map for the Gaussian kernel

In SVM, the Gaussian kernel is defined as: $$K(x,y)=\exp\left({-\frac{\|x-y\|_2^2}{2\sigma^2}}\right)=\phi(x)^T\phi(y)$$ where $x, y\in \mathbb{R^n}$. I do not know the explicit equation of $\phi$. I ...
5k views

### How to calculate decision boundary from support vectors?

I want to obtain decision boundary of SVM using OpenCV 2.4.11, but it seems that it's not returning it explicitly, but only support vectors. How we can calculate decision boundary from support ...
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### Getting distance of points from decision boundary with linear SVM?

I posted this originally in Stack Overflow but realize it might be more of a statistics question. I am using SKLearn to run SVC on my data. ...
963 views

### Are “kernel methods” and “reproducing kernel Hilbert spaces” related?

Are "kernel methods" and "reproducing kernel Hilbert spaces" related? Specifically, is the "kernel" used in the term "kernel methods" the same (type of) "kernel" as that used in the term "reproducing ...
560 views

### SVM basic theory?

I have some questions about SVM: In SVM there is a nonlinear and linear SVM. What is the difference between them? To do classification in SVM, we will find the linearly separable boundary (hyperplane)...
501 views

### Dimensionality of the Gaussian Kernel

I have read that the dimensionality of the feature map of the Gaussian Kernel is infinite. However I saw another post (Kernel SVM) stating that the feature map for a Kernel SVM maps to a ...
135 views

### Kernels in SVM primal form

For a soft margin SVM in primal form, we have a cost function that is: J(\mathbf{w}, b) = C {\displaystyle \sum\limits_{i=1}^{m} max\left(0, 1 - y^{(i)} (\mathbf{w}^t \cdot \mathbf{x}^{(i)} + b)\...
215 views

### SVM kernel mapping, finding boundaries in projected space

I have a question about the support vector machine (SVM) kernel trick. How do you find the boundaries of the training data set in kernel projected space? Is that the same boundaries as you can obtain ...