# Questions tagged [kernel-trick]

Kernel methods are used in machine learning to generalize linear techniques to nonlinear situations, especially SVMs, PCA, and GPs. Not to be confused with [kernel-smoothing], for kernel density estimation (KDE) and kernel regression.

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### How to intuitively explain what a kernel is?

Many machine learning classifiers (e.g. support vector machines) allow one to specify a kernel. What would be an intuitive way of explaining what a kernel is? One aspect I have been thinking of is ...
75k views

### How to select kernel for SVM?

When using SVM, we need to select a kernel. I wonder how to select a kernel. Any criteria on kernel selection?
21k views

### What is a “kernel” in plain English?

There are several distinct usages: kernel density estimation kernel trick kernel smoothing Please explain what the "kernel" in them means, in plain English, in your own words.
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 ...
68k views

### Linear kernel and non-linear kernel for support vector machine?

When using support vector machine, are there any guidelines on choosing linear kernel vs. nonlinear kernel, like RBF? I once heard that non-linear kernel tends not to perform well once the number of ...
10k views

### How can SVM 'find' an infinite feature space where linear separation is always possible?

What is the intuition behind the fact that an SVM with a Gaussian Kernel has inﬁnite dimensional feature space?
18k views

### How to prove that the radial basis function is a kernel?

How to prove that the radial basis function $k(x, y) = \exp(-\frac{||x-y||^2)}{2\sigma^2})$ is a kernel? As far as I understand, in order to prove this we have to prove either of the following: For ...
4k views

### Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform any other methods?

I have seen people have put a lot of efforts on SVM and Kernels, and they look pretty interesting as a starter in Machine Learning. But if we expect that almost-always we could find outperforming ...
44k views

### Which search range for determining SVM optimal C and gamma parameters?

I am using SVM for classification and I am trying to determine the optimal parameters for linear and RBF kernels. For the linear kernel I use cross-validated parameter selection to determine C and for ...
26k views

### Difference between a SVM and a perceptron

I am a bit confused with the difference between an SVM and a perceptron. Let me try to summarize my understanding here, and please feel free to correct where I am wrong and fill in what I have missed. ...
7k views