One-Class Support Vector Machines

So I want to make sure I have this right. First, I'm an undergrad computer engineering major with much more hardware/EE experience than software. This summer I have found myself using a clustering algorithm that uses one-class SVM's. Is an SVM just a mathematical model used to classify/separate input data? Do SVM's work well on data sets with one attribute/variable? I'm guessing no to the latter, possibly because classification with a single attribute is practically stereotyping. My guess is SVM's perform better on datasets that have multiple attributes/variable开发者_如何学Cs to contribute to classification. Thanks in advance!

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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 can separate them. Though, so-called kernel trick may be used to produce much more attributes by combining existing. With more attributes you can get higher-dimensional space, where all instances can be separated (video). Unfortunately, one attribute cannot be combined with itself, so for one-dimensional space kernel trick is not applicable.

So, the answer to your question is: SVM may be used on sets with only one attribute if and only if instances of 2 classes are linearly separable by themselves.