SVM with polynomial kernel visualization

What people said

Recommends Amro · 2010-10 · Stack Overflow · on “Help me understand linear separability in a binary SVM”

Check out this [this video] that illustrates an example of linearly inseparable points that become separable by a plane when mapped to a higher dimension.

Recommends ffriend · 2011-07 · Stack Overflow · on “One-Class Support Vector Machines”

SVM tries to build hyperplane separating 2 classes (AFAIK, in one-class SVM there's one class for "normal" and one class for "abnormal" instances). With only one attribute you have one-dimensional space, i.e. line . Thus, hyperplane here is a dot on the line. If instances of 2 classes (dots on this line) may be separated by this hyperplane dot (i.e. they are linearly separable), then yes, SVM may be used. Otherwise not. Note, that With several attributes SVM still may be used to classify even linearly unseparable instances. On the next image there are 2 classes in two-dimensional space (2 attributes - X and Y), one marked with blue dots, and the other with green. You cannot draw line that ca

Recommends soufanom · 2013-01 · Cross Validated Stack Exchange · on “Test for linear separability”

Well, support vector machines (SVM) are probably, what you are looking for. For example, SVM with a linear RBF kernel, maps feature to a higher dimenional space and tries to separet the classes by a linear hyperplane. This is a nice short SVM video [this video] illustrating the idea. You may wrap SVM with a search method for feature selection (wrapper model) and try to see if any of your features can linearly sparate the classes you have. There are many interesting tools for using SVM including LIBSVM [LINK] , MSVMPack [LINK] and Scikit-learn SVM [LINK] .

Recommends gung - Reinstate Monica · 2013-06 · Cross Validated Stack Exchange · on “What is a "kernel" in plain English?”

The following video was proposed by an anonymous potential editor as "a great visualisation of what Thylacoleo explained:" [this video]

Recommends Pedrom · 2013-10 · Stack Overflow · on “How do I extend a support vector machine algorithm to a high dimensional data set?”

If you can imagine how the line of the 2D case would become a d-dimensional hyperplane for higher dimensions, then you are pretty much done. The actual classification occurs when you test a point over the hyperplane, which will give you a positive number if the point belongs to class 1 or negative if it belongs to class 2. Notice that in the formula there is no restriction for the dimension of each point: [Image courtesy of wikipedia] And in case you are curious about what happens with the non-linear case when you use the kernel trick, I would like to share with you a video that illustrates very well the idea. [this video]

Recommends ogrisel · 2013-12 · Stack Overflow · on “What is the difference between a decision boundary and a hyperplane?”

The decision boundary for a linear support vector machine is an (affine) hyperplane [LINK] . For non-linear kernel support vector machines, the decision boundary of the support vector machine is not an hyperplane in the original feature space but a non-linear hypersurface (a surface of dimension n_features - 1 ) whose shape depends on the type of kernel. However, the kernel function can be interpreted as inducing a non-linear mapping from the original feature space to some kernel space. In the kernel space then the decision function of the SVM is an hyperplane. Here is a video [this video] that gives an intuitive descriptions of the relation between the two for the polynomial kernel.

Recommends Pedrom · 2014-02 · Stack Overflow · on “Binary classification using radial basis kernel SVM with a single feature”

This video shows what happen in a kernel mapping, it is not using the RBF Kernel, but the idea is the same: [this video] As for the 1D case, there is not much difference, it would be something like this:

Recommends ccsv · 2014-04 · Cross Validated Stack Exchange · on “svm classification visualization”

Here is a video I found that would be closest to what you are looking for: [this video] It shows SVM being applied to 3D. It is very difficult to graphically visualize dimensions higher than 3 and would usually cause more confusion. With higher dimensions all I would use is vectors to and show significant points but this only would make sense if someone understands how it works in lower dimensions

Recommends mon · 2017-01 · Cross Validated Stack Exchange · on “How to select landmarks of Kernel to run SVM”

Objective Clarify how to choose the kernel reference points (landmarks) to identify the non-linear boundary. [LINK] Background Going through SVM at Coursera ML - Support Vector Machine [LINK] and trying to understand how to choose the landmarks to measure the distances to feed into the Gaussian Kernel. It says "put the landmarks in the exact same locations as all the training examples ". [LINK] [LINK] Question Not clear why "the exact same locations of all the training data". Why using all the data? Number of features M and the number of data N is different and I suppose M << N. Then should we choose M number of data to use landmarks? Why not considering if a data to use as a landmark is cla

Recommends Djib2011 · 2018-04 · Cross Validated Stack Exchange · on “Why the name "kernel" in stats and ML?”

A kernel is used a multitude of times in Machine Learning and statistics. A few examples are: In Support Vector Machines a kernel [LINK] is a function that maps the data to a higher-dimensional space where the problem becomes linearly solvable (watch this [this video] ). Kernel Density Estimation [LINK] Kernel Density Estimation is a non-parametric way to estimate the probability density function of a random variable. In this context a kernel [LINK] is simply a weighting function used in kernel density estimation. The last link also has a few more uses of the word kernel in statistics. In Convolutional Neural Networks , a kernel is a small matrix that is used to perform the convolution between th