SVM: Support Vector Machines

Training Initialization Dialog

Parameter Information


Classification Input

The SVM training process requires the supplied expression data and an additional initial presumptive classification which indicates which elements are initially presumed to have a relationship. Two options are provided for selecting members of the initial classification.

Use SVM Classification Editor

This option causes an editor application to be launched in order to allow a flexible tool for finding and marking elements to be positive members of the initial classification. This classification can be save as an SVC file for later recovery of these initial settings.

Use Classification File

This allow the loading of an initial classification from an existing SVC file.

Kernel Matrix Construction

One can select to construct a polynomial or a radial kernal matrix.

Polynomial Kernel Function Parameters

The polynomial option is the default and three parameters are used to define the kernel construction.

Constant

An additive constant. (c)

Coefficient

A multiplicative constant. (w)

Power

A power factor. (p)

Polynomial Kernel Function

K(i,j) = [w*(Dist(i,j)+c)]p

Radial Basis Function Parameters

The Radial Basis checkbox is used to select to use this type of Kernal generating function.

Width Factor

Radial width factor (w, see in below formula).

Radial Basis Kernel Function

K(x,y) = e( - (||x - y||^2)/(2w^2))

Training Parameters

Diagonal Factor

Constant added to the main diagonal of the kernel matrix. Adding this factor to the main diagonal of the kernel is required to force the matrix to be 'positive definite'. The definition of a positive definite matrix is best reviewed in books devoted to linear algebra but this state is achieved by selecting a constant of sufficient magnitude.

This positive definite state of the kernel matrix is required for the SVM algorithm to yeild meaningful results. Testing values starting at 1.0 and increasing may be required to find an appropriate value. If the value is too low all elements will be partitioned in the negative class. For a range of values for this factor a stable set of elements may be classified as positive. At very high values there is a tendancy to force all positive expamples to be in the positive class regardless of their similarity of expression.

Threshold

This value is used as a stopping criteria for the weight optimization phase of training. Optimizing the weights produced during training is an iterative process which converges on an optimal set of weights to separate the positive and negative examples. This threshold dictates how stable the weights must be before the optimization process is terminated. Selection of a threshold that is very low could cause the optimization process to take an extremely long time and yet yeild similar results to those where a higher threshold value was used which terminated the process earlier.

Constraints

This check box selects to apply limits to weights produced during training.

Positive Constraint

The upper limit to produced weights.

Negative Constraint

The lower limit to produced weights.