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.

learn more… | top users | synonyms

0
votes
0answers
37 views

Kernel Smoothing in R [closed]

I am trying to apply a Kernel Smooth to data in a vector format, I run the following lines of code: ...
0
votes
0answers
21 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 ...
0
votes
1answer
28 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 ...
0
votes
0answers
29 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 ...
4
votes
1answer
24 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 ...
0
votes
0answers
19 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 ...
0
votes
1answer
63 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 ...
1
vote
1answer
27 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: ...
0
votes
0answers
26 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 ...
0
votes
1answer
31 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 ...
1
vote
0answers
12 views

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 ...
0
votes
0answers
38 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, ...
1
vote
1answer
29 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?
0
votes
2answers
38 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 ...
1
vote
1answer
37 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 ...
1
vote
0answers
52 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 ...
1
vote
1answer
56 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 ...
0
votes
0answers
13 views

Kernel matrix is a covariance function

How to prove that the kernel matrix is actually a covariance matrix?
0
votes
1answer
13 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 ...
0
votes
0answers
20 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, ...
0
votes
0answers
11 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 ...
3
votes
1answer
66 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 ...
2
votes
2answers
58 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 - ...
0
votes
0answers
17 views

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 $\vec{x}^*$ ...
0
votes
0answers
31 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 ...
0
votes
0answers
16 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 ...
1
vote
1answer
59 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: ...
0
votes
0answers
26 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 ...
0
votes
0answers
33 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 ...
0
votes
0answers
40 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? ...
0
votes
0answers
23 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 ...
2
votes
1answer
27 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 ...
0
votes
1answer
50 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} ...
0
votes
0answers
26 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 ...
0
votes
0answers
8 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, ...
1
vote
1answer
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, ...
1
vote
1answer
110 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 ...
0
votes
0answers
26 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 ...
0
votes
0answers
28 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 ...
1
vote
1answer
188 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 ...
4
votes
2answers
109 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 ...
0
votes
1answer
139 views

kernels and similarity (in R)

I am trying fit different kernels to calculate similarity matrix in R. Here is example data - X matrix : ...
0
votes
0answers
21 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 $x$ ...
0
votes
1answer
63 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 ...
1
vote
1answer
56 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 ...
2
votes
1answer
121 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 ...
1
vote
1answer
76 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 ...
0
votes
0answers
8 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 ...
0
votes
0answers
92 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 ...
1
vote
1answer
155 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) $$ ...