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Operations on Classifiers

Classifiers are a special type of mappings. All operations defined for mappings apply to classifiers as well. What is specific for trained classifiers is that their output space, the space they map to, has axes that correspond to the classes the classifier has been trained for. So the basic mapping definition:

 input space --> mapping --> output space

looks for a classifier:another:

 input space --> classifier --> classifier space

Applied to a collection of objects represented in these spaces by datasets A and D, coded by D = A*W:

 input dataset A --> classifier W --> classification matrix D

The dataset D has as many columns (dimensions) as there are classes defined for W. The class names stored in the classifier W (that are derived from the dataset used for training W and that can be found by classname(W) ) are used for setting the feature labels of D. They can be retrieved by getfeatlab(D).

The standard classifiers used in PRTools are of two types: density based and distance based classifiers. The density based classifiers (e.g. qdc and parzenc) output in D the densities of the objects of A weighted by the class prior as set by the dataset used for training W. The distance based classifiers result in class confidences: numbers between 0 and 1 derived from a sigmoid mapping (sigm) of a linearly scaled distances to the classifier. These distances are between -inf and +inf. The scaling is optimized for the training set by cnormc using an ML approach that interprets the confidences as class posteriors. The scaled distances can be retrieved by D*invsigm.

The outputs of density based classifiers can be converted to class posteriors (which can also be understood as class confidences) by D = D*classc. This has no influence on the outcomes of distnace based classifiers. The following constructs are equivalent (suppose U is an untrained classifier and T a dataset used for training:

W = T*U; D = A*W; D = D*classc;
W = T*U; D = A*W*classc;
W = T*U*classc; D = A*W;
W = T*(U*classc); D = A*W;

Like mappings, classifiers can be combined in several ways:

They are discussed separately.


operations: basic, datasets, datafiles, mappings, classifiers, stacked, parallel, sequential, dyadic
commands: datasets, representation, classifiers, evaluation, clustering and regression, examples, support