Bandwidth selection in support vector data description for classification or outlier detection

A computing device comprising:

• a processor;
• and
• a non-transitory computer-readable medium operably coupled to the processor, the computer-readable medium having computer-readable instructions stored thereon that, when executed by the processor, cause the computing device to
• compute a mean pairwise distance value between a plurality of observation vectors, wherein each observation vector of the plurality of observation vectors includes a variable value for each variable of a plurality of variables;
• compute a tolerance value based on a number of the plurality of observation vectors;
• compute a scaling factor value based on the number of the plurality of observation vectors and the computed tolerance value;
• compute a Gaussian bandwidth parameter by multiplying using the computed mean pairwise distance value and the computed scaling factor value;
• train a support vector data description (SVDD) model using the plurality of observation vectors by computing an optimal value of an objective function that includes a Gaussian kernel function that uses the computed Gaussian bandwidth parameter value, wherein the objective function associated with the optimal value defines a set of support vectors selected from the plurality of observation vectors to define a boundary around the plurality of observation vectors;
• and
• output the computed Gaussian bandwidth parameter value and the defined a set of support vectors for determining if a new observation vector is an outlier or for classifying the new observation vector.

A method of determining a bandwidth parameter value for a support vector data description for outlier identification, the method comprising:

• computing, by a computing device, a mean pairwise distance value between a plurality of observation vectors, wherein each observation vector of the plurality of observation vectors includes a variable value for each variable of a plurality of variables;
• computing, by the computing device, a tolerance value based on a number of the plurality of observation vectors;
• computing, by the computing device, a scaling factor value based on the number of the plurality of observation vectors and the computed tolerance value;
• computing, by the computing device, a Gaussian bandwidth parameter value by multiplying the computed mean pairwise distance value and the computed scaling factor value;
• training, by the computing device, a support vector data description (SVDD) model using the plurality of observation vectors by computing an optimal value of an objective function that includes a Gaussian kernel function that uses the computed Gaussian bandwidth parameter value, wherein the objective function associated with the optimal value defines a set of support vectors selected from the plurality of observation vectors to define a boundary around the plurality of observation vectors;
• and
• outputting, by the computing device, the computed Gaussian bandwidth parameter value and the defined a set of support vectors for determining if a new observation vector is an outlier or for classifying the new observation vector.