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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set SVM parameter range values for tuning [duplicate]

I am newbie to using svm for classification. I want to tune svm parameters by .TrainAutofunction in EmguCV. But I don't know what are the range(min-max value) of below parameters that I should give to ...
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A step of a proof regarding the Nadaraya-Watson estimator

Let the data be $(y_i , X_i) $ where $y_i$ is real valued and $X_i$ is a q-vector. The regression function for $y_i$ on $X_i$ is $g(x) = E(y_i | X_i = x)$, we can write this as: $$y_i = g(X_i) + ...
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What are “parts” in Haussler's definition of R-convolution kernels?

I have been reading about R-convolution kernels: http://citeseerx.ist.psu.edu/viewdoc/download?rep=rep1&type=pdf&doi=10.1.1.110.638. These important types of kernels are generalization of ...
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27 views

Valid result when adding two kernels with negative coefficient?

If $k_1$ and $k_2$ be a kernel in $ \mathbb{R}^n \times \mathbb{R}^n $. we know $k(x,z)=ak_1(x,z) + bk_2(x,z)$ (kernel addition) is still a valid kernel if $\: a,b \geq 0\,$ ($a,b$ is real numbers, ...
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48 views

Locally weighted regression VS kernel linear regression?

I am trying to make it clear the relationship of the listed three methods. According to my understanding kernel regression means : the weight vector W lies in the space spanned by training data. $$ ...
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1answer
49 views

Kernel methods in machine learning?

I am beginning to tackle geostatistics problems where I tried to apply kriging(gaussian processes) to interpolate demographical water drop. According to my understanding, kernel methods are something ...
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36 views

Getting the probability density kernel estimator with R

I am working on a density estimation project and I need to get an estimation of the density as well as an equation for the density estimator (and not the estimate). I am working with kernel ...
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12 views

What is the effective kernel for smoothing methods?

I'm learning different smoothing methods and the term "effective kernel" came up and I don't really understand it. By definition, for a smoothing method, the vector of estimates ...
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22 views

Is it meaningful to compute a radial kernel density estimate from 2D data?

I am working with 2D spatial data, $(X_i, Y_i),\; i=1, \cdots, N$. My current research requires estimating the density of the distances between those data points in each of the two dimensions. So ...
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19 views

What is the time complexity of binary classification of SVM?

One of the earliest solution to the SVM problem is SMO applied to dual form.What is the time complexity of SMO algorithm? What is the best known time complexity to solve SVM algorithm (non linear)?
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7 views

Differences and similarity between fuzzy sets and kernel functions

The concept of fuzzy membership function and kernels seems to be similar. Fuzzy however has a more elaborate theory of logic. It seems that kernels and fuzzy membership are used in different ...
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Good implementation of SVM with operator valued kernel

I've already come across the question Vector Valued SVM but the replies doesn't point to SVM with any Operator Valued Kernel. I understand that struct svm can solve the same by solving inference ...
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Recommended/estimated number of radial basis functions in RBFN

thank you for taking the time to read my question. I am attempting to make a Radial Basis Function Network to see if a relationship exists between input/output data that I have been collecting. I ...
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1answer
68 views

How do you transform a decision boundary in the angle kernel to the original space?

Say I have training data $S_n$ and each point is of the form $x = \langle x_1 , x_2 \rangle$ in the original space (i.e. $x^{(i)} \in \mathbb{R}^2$). I was considering the following kernel: $$ ...
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1answer
24 views

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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1answer
35 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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31 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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17 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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37 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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1answer
32 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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35 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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40 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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44 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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80 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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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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79 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
35 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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88 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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1answer
46 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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111 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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1answer
68 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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17 views

Kernel matrix is a covariance function

How to prove that the kernel matrix is actually a covariance matrix?
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1answer
16 views

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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22 views

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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15 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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1answer
74 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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78 views

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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34 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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24 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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1answer
107 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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28 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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70 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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65 views

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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33 views

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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1answer
36 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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1answer
75 views

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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27 views

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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34 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, ...