Some details about ENVI's Support Vector Machine (SVM) classifier

This Help Article discusses some of the details in ENVI's Support Vector Machine (SVM) classifier and its parameters.
 
During the SVM processing, ENVI first stretches the data. Is this to normalize the data before processing?

There is a data normalization prior to SVM classification. SVM requires the normalization of numeric inputs. Normalization places the attribute numeric values on the same scale and prevents attributes with a large original scale from biasing or dominating the solution.

For data normalization, usually there are two options: Gaussian normalization (linear scaling by unit variance and offset by mean value) and linear normalization (linear scaling by unit range and offset by minimum value). ENVI implements linear normalization as preprocessing in SVM.

What is the purpose of gamma? What is the significance of setting gamma to the inverse of the number of bands?

In the help for SVM in ENVI it describes four types of kernels: linear, polynomial, RBF and sigmoid. Gamma is the parameter in the kernel function for all kernel types except linear. A kernel is a function that transforms the input data to a high-dimensional space so that the data is separable and the problem can be solved in the new space. Different gamma values control different transformations.

The default value of gamma is the inverse of the number of bands. It is a reasonable but not a perfect default value. Gamma and penalty are critical parameters that affect the accuracy of the SVM classification. It is not known beforehead which gamma and penalty values are the best for one problem. To identify good gamma-penalty values, usually a "grid-search" on gamma and penalty using cross-validation can be applied. Using a coarse grid followed by a refined search can reduce search time.

How can we compute the cross-validation?

Cross-validation is a standard classification evaluation technique. Usually a k-fold cross-validation is used, and k is usually from 4 to10. In 10-fold cross-validation, the original sample is partitioned into 10 subsamples where 9 subsamples are used as training data, and the remaining 1 subsample is used as validation data. By selecting a different subsample as validation data each time, you have 10 different ways to select training and validation data. Classify the image with the 10 different selections, then average the accuracy to get an overall accuracy estimate. By using the cross-validation technique, you get a better estimation of classification accuracy.

What is the the Pyramid Reclassification Threshold and the best way to determine its value?

When you set a pyramid level > 0, SVM first classifies on the lower resolution image. If the classified pixel has a probability less than the Pyramid Reclassification Threshold, the classification result of this pixel is considered unreliable and the pixel will be reclassified at a higher resolution. This is a way to potentially reduce the computation time since SVM is a time-consuming algorithm. If speed is unimportant, then it is suggested that the pyramid level be set to 0 so that it uses the full resolution image. If you set the pyramid level > 0, then 0.9 would be a reasonable value for the Pyramid Reclassification Threshold.

Review on 12/31/2013 MM