I am trying to plot the hyperplane for the model I trained with LinearSVC and sklearn. Note that I am working with natural languages; before fitting the model I extracted features with CountVectori. The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Flexible planning and scheduling software for Windows and Mac. Ideal when sticky notes aren't enough, but traditional project management software is too complex. A hyperplane is, in general, a plane-like geometric shape that exists in four or more “spacial” dimensions, thus the “hyper” part. It’s not so different from a 2d plane, or a plane that you can imagine floating at some rotation in 3d space.
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In the last post we saw about the kernels and visualized the working of an SVM kernel function. To catch up with the happenings visit : https://codingmachinelearning.wordpress.com/2016/08/02/svm-visualizing-the-kernel-function/
Now we know how the plot looks in 3 dimension. Now we will try to plot the hyperplane for separating this data set
I have manually drawn the hyperplane in the above diagram. We will try to validate our intuition in this case to make sure what I claim actually happens.
Our kernel function is K(x,y)=(x, y, x2+y2 ). Now we need to plot this hyperplane that separate the points.
If we see the values in the plot generated we can see that the value for the hyper plane will be
- X-axis : -1.5 to 1.5 (length of the plane)
- Y-axis : -1.5 to 1.5 (breadth of the plane)
- Z-axis : .5 (height at which the plane separates red and blue)
Plot a meshgrid with these values and we can see that it matches our claim.
The code to generate the plots have been provided in my github account. Here we have manually plotted the decision boundary. Now we will try to get the same result using the scikit learn svm classifier and validate our results to see if it matches our intuition.
This is the output of using a linear kernel gives accuracy of 58%. We can see its performance is very bad trying to separate non-linear data set.
The performance of SVM on this data set using a ‘rbf’ kernel is given below. It has 100 percent classification accuracy which is stunning.
This basically is the projection of the hyper-plane on to the lower dimension. But also remember that this does use the gaussian function as its kernel function not what we defined in the beginning. 32 bit mac. Please follow the below link to read up more on gaussian kernels.
This wraps up our little discussion on SVM and how it works. In the next post we will look into another classifier – the logistic regression and hope to understand it better.
Code for the Plots available on my github account: https://github.com/vsuriya93/coding-machine-learning/blob/master/SVM/code.py
Useful Links:
- Gaussian Kernel : https://www.quora.com/What-is-the-intuition-behind-Gaussian-kernel-in-SVM
- SVM scikit learn: http://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC