# SVDD vs once Class SVM

Can some one please explain me what is the difference between one class SVM and SVDD(support vector data description)

• Is there experience around in which cases one of these models is superior?
– MaxS
Dec 20, 2018 at 6:16

Support vector data description (SVDD) finds the smallest hypersphere that contains all samples, except for some outliers. One-class SVM (OC-SVM) separates the inliers from the outliers by finding a hyperplane of maximal distance from the origin.

If the kernel function has the property that $$k(\mathbf{x}, \mathbf{x}) = 1 \quad \forall \mathbf{x} \in \mathbb{R}^d$$, SVDD and OC-SVM learn identical decision functions. Many common kernels have this property, such as RBF, Laplacian and $$\chi^2$$.

SVDD and OC-SVM are also equivalent in the case that all samples lie on a hypersphere centered at the origin, and are are linearly separable from it.

See Lampert, C. H. (2009). Kernel methods in computer vision (Chapter 5) for more detailed descriptions of these models.

• if we had to solve the svdd as an optimization problem how can we generate the constraints Nov 8, 2017 at 8:32
• How do these two algos compare with XGBoost and other methods for classification problems? Let's say for something that is not medical classification, but something more simple like predictions in marketing? Mar 10 at 12:30

The one-class support vector machines (OCSVM) is a one-class classification technique similar to the SVDD. Instead of obtaining a bounding hypersphere around the training data, the OCSVM algorithm finds the maximal margin hyperplane that best separates the training data from the origin (Schölkopf et al. 1999). Similar to SVDD, the OCSVM algorithm uses kernel functions to map training data into a higher-dimensional feature space.

Reference