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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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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7 views

Custom kernel in R [closed]

There are many kernels in common use, apparently. How can I implement a custom kernel in R? For example, is there a density-like command that takes a kernel ...
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7 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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13 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
17 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
16 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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8 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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6 views

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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1answer
25 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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61 views

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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18 views

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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17 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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1answer
130 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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2answers
71 views

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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1answer
59 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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14 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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1answer
32 views

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 ...
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1answer
72 views

How to get percentiles from empirical density in R?

The density() function in R allows me to enter observations and get an empirical density that I can plot x and y values. I like ...
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1answer
61 views

Where can I use kernels other than Gaussian (like Cauchy, laplacian) in kernel methods in machine learning? Or maybe in kernel density estimation?

In few papers I read that - kernel used doesn't really matter for kernel density estimation but bandwidth of the kernel is the most important factor. But I did not see any mathematical explanation to ...
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5 views

How accurate sum of kernel function needs to be, so that we can use it in Mean shift algorithm (may be for image segmentation)?

Mean shift is a procedure for locating the maxima of a density function given discrete data sampled from that function. It is useful for detecting the modes of this density. This is an iterative ...
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54 views

Spectral clustering using RBF Kernel function in R

I have extracted user-features and item features in my recommender system using a modified SVD approach built on ALSE (loosely based on Yehuda Koren's paper). I now want to cluster items not directly ...
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1answer
87 views

Extracting decision function variable from libsvm

I'm trying to use LIBSVM's single class SVMs for some classification and need to extract the following sum post classification (i.e. the variable that the decision function takes in) $$ ...
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47 views

STRING KERNELS FOR LIBSVM

I'm working on a protein classification problem and i'm using edit distance kernel defined in libSVM. Now, for instance, the implementation of spectrum kernel is very difficult, but i want try to test ...
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36 views

Evolution strategies in libsvm

I'm working on protein multi-classification problem. I'm using libsvm and the edit distance kernel. This kernel depends from a parameter (gamma). I'm able to get the best parameters (gamma and C) ...
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3answers
109 views

Do kernel methods “scale” with the amount of data?

I've been reading about kernel methods, where you map original $N$ data points to a feature spaces, compute the kernel or gram matrix and plug that matrix into a standard, linear algorithm. This all ...
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1answer
66 views

Improving SVM classification

I have a classification problem (bioinformatics domain) where I have around 333 features. Currently, I am first selecting features (using importance feature of random forest) and then pushing the same ...
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10 views

In RVM, is the kernel allowed to depend on the full dataset?

I want to use Relevance Vector Machines and need to define my custom made kernel. I was wondering if it is allowed for the kernel to depend on the full dataset. For exampe, I can calculate a certain ...
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15 views

construct/load dataset that performs better with diffusion kernel than other kernel

I'm looking for a dataset on which a diffusion kernel (also called heat kernel), used via SVM, would get better accuracy than other kernels for the classification task. I want to use such a dataset to ...
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44 views

Linear Kernel taking more time to train than RBF Kernel (SVR)

I'm doing a Support Vector Regression with about 70k samples with 500 features each. I'm using sklearn implementation of SVR and my input for the train set is a sparse matrix. But, for my surprise, ...
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1answer
97 views

Understand the reasons of using Kernel method in SVM

I understand that one can use kernel functions (i.e. radial kernel) to create non-linear decision boundary. However, there is something with my logic and I am sure there is something that I clearly ...
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1answer
34 views

Local log-likelihood for multiclass linear regression model

In page 206 of the book 'Elements of statistical learning', the author wrote: The local log-likelihood for this $J$ class model can be written $\sum_{i=1}^NK_\lambda (x_0, ...
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1answer
96 views

Kernel density estimator function explanation needed

I'm studying about kernel density estimation and from wikipedia I get this formula: $$\hat{f}_h(x, h) = \frac{1}{n}\sum^{n}_{i=1}K_h(x-x_i) = \frac{1}{nh}\sum_{i=1}^nK(\frac{x-x_i}{h}).$$ I think ...
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1answer
71 views

Clustering structured data: Assessing the similarity of documents that appear in tree structure

Usually when performing text document clustering, similarities across documents are assessed based on the lexical content of documents. But, in my problem, I wish to consider both the lexical content ...
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1answer
106 views

Accuracy changes with permutation of input data in Libsvm with precomputed kernel?

I'm doing quite simple SVM classification at the moment. I use a precomputed kernel in LibSVM with RBF and DTW. When I compute the similarity (kernel-) matrix, everything seems to work very fine ... ...
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1answer
65 views

Efficient evaluation of multidimensional kernel density estimate

I've seen a reasonable amount of literature about how to choose kernels and bandwidths when computing a kernel density estimate, but I am currently interested in how to improve the time it takes to ...
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108 views

What's wrong with my Kernel algorithm (Kernel SVD)?

I have a user-item matrix $A$ as data input, which is a sparse matrix containing a large number of missing values (as zeros). Each row is a user, and each column is an item. Generally, I am conducting ...
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27 views

Regression of family of marginal density functions

From a large sample of triples $(X, Y, U)$ I need to estimate a function $(x, y, u) \mapsto f(x, y, u)$, such that for each fixed $x, y$, the function $u \mapsto f(x, y, u)$ is a density function; ...
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Prove that this exponential kernel is positive definite

Let $x,y\in R^d$ and $d:R^d\times R^d \rightarrow R$ a metric on $R^d$ be given. The exponential kernel is defined by: $k(x,x')=e^{−αd(x,x')}$ where $α>0$. The kernel matrix is defined as the ...
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1answer
62 views

Cascade Combination of Kernel Functions

I have a question regarding machine learning and specifically kernel functions. Suppose we have a Kernel function, say $K(x)$, and also another distinct one, say $K'(x)$. I want to know is $K(K'(x))$ ...
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34 views

Difference between Primal, Dual and Kernel Ridge Regression

I would like to basically ask what the title says. What is the difference between Primal, Dual and Kernel Ridge Regression? People are using all three, and because of the different notation that ...
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1answer
63 views

Linear Kernel in Baysian Linear Regression

I came up with http://mlg.eng.cam.ac.uk/duvenaud/cookbook/index.html and it is actually very useful. At some point it says If you use just a linear kernel in a GP, you're simply doing Bayesian ...
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68 views

Derive squared exponential covariance function

In Gaussian Processes, SVMs, kernels are used (as to my understanding) as similarity measure. However, they have the constraint that any kernel has to be represented as a dot product. i.e. ...
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2answers
256 views

Prediction with scikit and an precomputed kernel (SVM)

I am kind of a newbie in the MachineLearning area and evaluating some tools etc. to get a feeling for it. For a project I am using a tool that creates a precomputed kernel (gram matrix) and also is ...
2
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1answer
72 views

Finding the cluster centers in kernel k-means clustering

I think this is the most easily understood topic in Kernel K Means Clustering. But assuming that I am not an expert in Machine Learning, can someone tell me how does someone calculate Kernel K means ...
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1answer
39 views

What's wrong with the intuition that kernel measures similarity between observations?

Near the middle of page 16 of Andrew Ng's notes on SVM, he explained an intuitive view of kernel as measuring similarity between observations, but then added the caveat that there are things wrong ...
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67 views

Need a working algorithm to find out optimal kernel bandwidth for density estimation

I am looking for a working algorithm for find out optimal kernel bandwidth for density estimation. I need to write my own program in pascal instead of using R or Matlab. So far all algorithms I ...
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35 views

Kernel PCA number of components

When using Kernel PCA for dimensionality reduction is there any simple criterion which can be used to determine the number of components to use? I am using Kernel PCA with linear kernel, which would ...
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1answer
108 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 ...
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42 views

How to find out optimal KDE bandwidth via Bootstrap Aggregation

I am a programmer and trying to do some data analysis. Since I am very interested in statistics, and I have learned a lot of programming languages, learning how to use professional packages such as ...
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1answer
74 views

Kernel smoothing for Edgeworth expansion

Suppose I have an estimator which includes an indicator function in the objective function, then the objective function is not smooth. But if I want to approximate the behavior of this estimator in ...