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Questions tagged [kernel-functions]

Questions about the similarity functions used in machine learning to compare inputs in implicit higher-dimensional feature spaces.

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Checking if a kernel is valid

The kernel is $K(x,z) = \sum_{i=1}^D (x_i+z_i)$ My approach was trying to express $K = \phi(x)^T\phi(z) = (x_1 x_2 ... x_D \quad 1 1 ...1)(1 1 ...1\quad z_1 z_2 ... z_D )^T$ where $\phi$ is 2Dx1 ...
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kernel function from polynomial basis functions

In chapter 3 & 6 of Bishop's Pattern Recognition and Machine Learning, he showed that the equivalent kernel based on eqn (3.62) and the standard kernel based on the feature space mapping eqn (6.10)...
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Basics of virtual runtime - CFS Algorithm

It's known that virtual runtime is updated based on nice values of different processes and the rbtree stores different nodes based on the value of virtual runtime. If a process is doing IO, it's taken ...
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RBF Kernel unit matrix with ones on the main diagonal

I study multivariate time series. I'm interested in the outlier detection (noise reduction) in each of the series. I found the following article (pdf file) and I want to try to use this practice. but ...
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How do we mathematically figure out if a SVM kernel function overfits?

Looking at the kernel function (Gaussian, polynomial. chi-squared, etc) how do we figure out that changing which value will cause overfitting? In my perspective, if we increase (for example) the ...
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Vertex deletion to perfect matching

You are given a Graph G and an integer k. The question is: Does G contain a vertex set X of size at most k such that deleting X results in a graph of degree at most 1? Design an FPT (or a ...
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Some questions on kernels and Reinforcement Learning

I've a test in a few days and I've a few issues with some of the subjects. Let's start with kernels, basically I understood that a kernel needs to be positive semi-definite and symmetric in order to ...
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Calculating Contiguous String Kernel efficiently

I am given two strings, $\overline{a},\overline{b}$ in a finite alphabet, $\Sigma$, and a positive integer $k$. I want to compute the $k$-th order contiguous string kernel, which is defined to be ...
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some kernel and greater margin, how this occures?

I read following notes, and couldn't get it. any idea or hint would highly appreciated. a SVM classifier using a second order polynomial kernel. The first polynomial kernel maps each input data x to ...
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399 views

Kernel Perceptron vs Polynomial Perceptron

I was looking at Support Vector machines (SVM) kernels. Looking at Polynomial Kernel and Kernel Perceptron I was curious how they differ? Work Done Polynomial Kernel: $d_{k+1}(x)=d_{k}(\bar{x})+\...
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Merging two disconnected graphs

Firstly, I'd like to apologize for any misused terms or ways I could have made the description much more succinct. It's been a while since I took machine learning during my bachelor's. I have two ...
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Support Vector Machines as Neural Nets?

This is more of a conceptual question. I have learned about Neural Nets, and I have some clue as to how Support Vector Machines work. I read somewhere however that given the appropriate kernel (is ...
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Why are kernel methods with RBFs effective for handwritten digits (letters) classification?

The question emerged while reading Ch. 3 of Rasmussen & Williams http://www.gaussianprocess.org/gpml/. In the end of this chapter, the authors gave results for the problem of handwritten digits ...