Contents
How does the SVM kernel increase the dimensionality?
The kernel itself increase the dimensionality, in order to classify the input. As output you have only one (using generic SVM), either is from the desired class or not. So the kernel DOES increase the dimensionality, but what you get as result of the SVM is just one value.
How does SVM take care of dimensionality reduction?
The accuracy of classification of SVM classified image was 64.70% (k=0.4361) whereas, the accuracy of the SVMDRC classified image was 82.35% (k=0.7197). The results thus indicate that SVM takes care of dimensionality to a limited degree. The complete framework is a single-step process written in an open-source language R.
How to check the performance of a SVM model?
The function prints the following model evaluation metrics: SVM model performance metrics. Image by author. We can see that the model performance on test data is similar to that on training data, which gives reassurance that the model can generalize well using the default hyperparameters.
When to use machine learning for dimensionality reduction?
Classification techniques based on machine learning algorithms such as Support Vector Machine is preferably applied for performing classification of high dimensionality data. However, in practice, prior to applying SVM classifier, performing dimensionality reduction on hyperspectral data is a conventional step.
Is the VC dimension of the SVM model proof?
In fact, as far as I know, there is no known proof of the VC dimension of the SVM model (we know, that it is a gap tolerant classifier, which should have lower VC dimension, but it is far from being a dimension proof). The VC dimension doesn’t map to the amount of SVs of a given solution.
The VC dimension doesn’t map to the amount of SVs of a given solution. The VC dimension is the maximum number of dataset samples that can be shattered perfectly by the model for any combination of the labels associate with those points. On the other hand, support vectors are the points that define the hyperplane.
Is there a dependency between support vectors and VC dimension?
Unfortunately there is no easy “one-to-one” dependency between the number of support vectors and the VC dimension of the data. In fact, as far as I know, there is no known proof of the VC dimension of the SVM model (we know, that it is a gap tolerant classifier, which should have lower VC dimension, but it is far from being a dimension proof).