Kernel refers to weighting functions used in non-parametric estimation techniques (such as kernel density estimation or kernel smoothing). DO NOT USE this tag for [kernel-trick] which is reserved for kernel methods in machine learning.

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Covariance function to draw an inverse function

In a Gaussian Process (GP), we know that choice of the covariance function determines the shape of function that can be drawn from the GP. eg. Constant : $\sigma _{o}^{2}$ Draws constant function ...
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How to prove that Radial Basis Function can be derived by mapping function?

How to prove the radial basis function $k(u,v) = \int_{\mathbb{R}^d} \phi_t(u)\phi_t(v)dt $ can be integrated out by mapping function? $$\phi_{t}(u) = \frac{1}{(2\pi\Sigma)^{d/2}} ...
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22 views

Correct arguments for svm() function in R

I'm looking to implement a linear and non-linear SVM in R but having some confusion over which argument to use in svm(). For the linear SVM I want to add in the penalty $\gamma$ for soft margin. This ...
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17 views

Relationship between kernel function for distance (locally weighted regression) and kernel function for SVMs?

I am reading Tom Mitchell's Machine Learning. In section 8.2.3, he defines: Kernel function is the function of distance that is used to determine the weight of each training example. In other words, ...
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7 views

Optimized Bandwidth Kernel Density Estimation

I have been trying to use kernel method to estimate pdf of a variable, so i divided the data i have (45000) into training and validation. Training data was used to come up with the pdf and the rest of ...
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Local linear regression in R — locfit() vs locpoly() [migrated]

I am trying to understand the different behaviors of these two smoothing functions when given apparently equivalent inputs. My understanding was that locpoly just ...
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26 views

Comparison of Non-Stationary Time Series Trends

I am trying to compare two readings of the same occurrences from two different sources, forming two time series. I would like to assign a metric to their similarity/dissimilarity, but the method I am ...
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30 views

Regression with a kernel

I have a fixed kernel and a set of points. I do SVC with the flavor of SVM classification i'm working on (assume it's just a regular SVM) and i obtain a classifier represented by an explicit vector of ...
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32 views

density function of the mixture of two NHPP

I'd like to know how can I calculate the density function of the mixture of two non-homogeneous Poisson process? I should mention that I have the kernel densities of those NHPP s. I can also describe ...
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27 views

Does a polynomial kernel with degree less than 1 satsify mercers condition

Consider the polynomial kernel: $$K(\boldsymbol{x}, \boldsymbol{x}') = (\boldsymbol{x}^{T} \boldsymbol{x}'+c)^{d}$$ This kernel satisfies the mercers theorem/condition. Since I never saw any ...
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22 views

What is a kernel parameter in Extreme Learning Machines?

I am using the MATLAB function elm_kernel but I don't know what the Kernel_Para variable do. Where can I learn about this? Also Regularization_coefficient. It looks similar to ...
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107 views

Which hyperplane separates these two classes?

I have a dataset of 3 dimensional points in two classes, I want to separate between the two. As the plot suggests, these two are completely separable but I don't know the formula to form the ...
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31 views

Does the method of computing feature weights for linear kernel SVM also works for radial Kernel SVM?

I searched for how to find feature weights and found this stackoverflow answer. It gives the following equation to get the weights: ...
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38 views

Combining multiple feature subsets through ensemble classification methods?

I have a set of $N$ samples to be classifies in a binary classification problem. I have extracted features from these samples from 4 different perspectives (views) of every samples. Hence I have 4 ...
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35 views

What are the various basic kernels available?

I am currently following the book Gaussian Processes for Machine Learning by C.E. Rasmussen and C.K.I. Williams and I have come across various kernels in their Chapter 4 I have also gone through the ...
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How to Mine Tree Structures?

To learn similarities/differences between different instances (that are in the form of tree), what are the suitable methods/approaches? I know kernel methods and particularly tree kernels, but would ...
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60 views

Bimodal or Unimodal check using plot of Gaussian Kernel Density in R

I have a question on checking for bimodal distributions. When I try to use the Kernel based approach in R, ...
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1answer
32 views

Inner Product Kernel $k(x,y) = (1+\epsilon)^{\langle x, y \rangle}$

Where in the literature is the inner product kernel $k(x,y) = (1+\epsilon)^{\langle x, y \rangle}$ mentioned? Does it have a name?
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48 views

Kernel SVM on sparse data

I have a sparse dataset where a lot of the columns (features) contain mostly zero values. Class labels are multiple discrete categories (10 classes to be precise). I'm wondering if this should trouble ...
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38 views

Intuition behind RKHS

Why has RKHS become such an important concept in machine learning in recent times. Is it because it allows us to represent a function of combination of linear functions? What areas of mathematic does ...
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75 views

Distance measure for categorical attributes for k-Nearest Neighbor

For my class project, I am working on the Kaggle competition - Don't get kicked The project is to classify test data as good/bad buy for cars. There are 34 features and the data is highly skewed. I ...
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62 views

What kernel function can be used to project data into a feature space that is a “circle”?

I am working with cyclical data (Days 1-7, hours 1-24). I want to project it into a feature space that can understand that 1 and 7 are close days and 1 and 24 are closer than 22 and 24, etc, and then ...
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13 views

Kernel matrix is a covariance function

How to prove that the kernel matrix is actually a covariance matrix?
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Has deconvolution been applied to nodes in a sensor network?

Convolution, and blind deconvolution, is generally applicable where there is some "truth" function describing a physical process, and then some kind of distortion. I have a bunch of sensors in a ...
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Selecting kernel or binary similarity measures

Currently, I am facing a choice of encoding some information either in a binary vector or a normalized (Gaussian) floating point vector of the same length. For instance it could be in the format [ 1, ...
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12 views

Kernel Methods for Binary Vectors

I am currently involved in a project which requires a minor point in choosing a proper similarity metric for a set of binary vectors, i.e. all components are either 1 or 0 . Currently, the go-to ...
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68 views

“…if the data is linearly separable”

I keep hearing this phrase as a precursor to many algorithms, but I am not sure how exactly one goes about finding out if the data is indeed, linearly separable. Of course, if the data has ...
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Using a gaussian kernel in SVM. How exactly is this then written as a dot product?

I am attempting to use SVMs for my class project. For this project, I have selected the gaussian kernel as, well, the kernel. That is, $$ k(\mathbf{x}_1, \mathbf{x}_n) = e^{-\gamma ||\mathbf{x}_1 - ...
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Incorporating kernel into multiple regression

Let's say I have predictors $ \{x_1, x_2, ..., x_m, ... x_p\} $. I want to fit a multiple regression using $\{x_1,...,x_m\}$, but give more weight to points that are close to a particular $\vec{x}^*$ ...
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32 views

My support vectors don't look correct

I am trying to classify a toy dataset using SVM. I only have two features and 20 instances. The decision boundary seems correct, however, the support vectors dont look correct. This is the relevant ...
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20 views

r-pnn, normalization and different distance measures for each variable

Since pnn is a NN that uses a Radial kernel to classify data, I think the distance measure is key and, in consequence, the normalization of the data. Am I right? How does pnn package calculate the ...
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69 views

Kernel density estimation on bounded support

I was looking for some way to deal with boundary bias of kde in case of unit interval. One example is an usage of Chen estimators (or Beta estimators; an example might be seen here: ...
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27 views

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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41 views

SVM with pre-computed kernel and zero bias

I have an optimization function, where I need to give my own kernel matrix and bias value is zero. The kernel matrix is calculated using the data but there is no specific formula for it. If I have a ...
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LIBSVM for pre-computed kernel and zero bias (b values is zero)

I want to do binary classification and I'm using LIBSVM library for that. I have a precomputed Kernel and my bias value (b) is zero. Can I do this in LIBSVM or do I have to use some other library? ...
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Usage of libsvm with RBF kernel and no Offset

I'm using libsvm for the binary classification and using a precomputed Kernel. In my particular problem there is no bias term (it's zero). Is there anyway to adjust the bias term in libsvm (and not ...
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29 views

How to choose a kernel for KDE

There are a lot of kernels available for a univariate KDE. R uses normal by default, but the efficacy discussion seems to support the use of Epanechnikov. What should influence kernel choice for ...
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What is the toolkit that implements Cost sensitive Support Vector Machine?

I need implementation of cost sensitive support vector machine. The cost is different for each training example (unlike each class). So problem is to solve $max_\alpha$ $-1/2 \sum_{i,j} ...
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Use cases for P-Kernel for SVMs

I've been reading the book by Cristianini on Kernels (2004) where generative kernels (like p-kernel and fisher-kernel, not to be confused with polynomial kernel!) are described. I am interested in ...
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Can a kernel function for GP-regression use measurement information?

when building a kernel function for a Gaussian-Process-Regression I am asking myself whether the kernel function is allowed to contain information from the measurements. To ask a little more general, ...
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29 views

References to papers/books that uses a kernel to smooth a discrete distribution

Since a kernel, such as Gaussian, is often used to smooth out the distribution of discrete points in 1D, 2D or 3D, I believe there must be some study materials or research work that have used this, ...
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why simulated gamma distributed data have negative kernel values?

I know that Gamma distribution does not allow 0 or negative values. I was doing some simulation and when I write this code in R ...
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How are local and global plug-in bandwidths different in kernel smoothing regression?

I'm looking into an R package 'lokern.' It provides two bandwidths selectors, global and local plug-in bandwidth. I would like to understand the difference between two methods. My understanding is ...
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34 views

Covariance vs Bandwidth of Kernel Density Estimate

I've been working with the scipy gaussian kde implementation (here), but I don't quite understand the difference between the bandwidth factor and the covariance matrix. I'm using it for a single ...
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206 views

What are basic differences between Kernel Approaches to Unsupervised and Supervised Machine Learning

I got nice graphical representation of Machine learning for clustering / classification. Source: Kernel Approaches to Unsupervised and Supervised Machine Learning by Sun-Yuan Kung Here are my ...
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When do kernel based method perform better than the regular

I am used with linear models. I can see rising use of kernel based method particularly in machine learning. The following is an example Gaussian kernel using ...
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165 views

kernels and similarity (in R)

I am trying fit different kernels to calculate similarity matrix in R. Here is example data - X matrix : ...
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25 views

Parameter estimation of gaussian function kernel using cross-validation

I need to estimate (using cross-validation), the parameters $\sigma$ and $\lambda$ of the Gaussian kernel: $K_G(x,y) = \sigma^2 \exp{(-\frac{1}{2\lambda^2}\sum_{i,j}(x_{ij}-y_{ij})^2})$ where $x$ ...
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68 views

“Negative density” for non-negative variables [closed]

Having an integer positive variable (number of days) in an experiment, I got negative values for the kernel density plots using R. I have read other posts relating to this topic. They admitted that ...
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Applying an RBF kernel first and then train using a Linear Classifier

I will start off by saying that I don't have a concrete understanding of whats under the hood of a SVM classifier. I am interested in using an SVM with the RBF kernel to train a two class ...