Generator mappings

A generator mapping generates from an input dataset an output dataset in the same vector space. The output dataset can be smaller or larger, may contain just original objects (possibly duplicates) or new ones. The output objects can be based on sampling, interpolation or extrapolation of the input objects. Examples are gendat, gendatp and gendatk.

The following rules apply if a dataset A is processed by a sequential combining of a generator G with a fixed mapping F, an untrained mapping U or a trained mapping T. W is an arbitrary mapping.

A*(G*W) = A*G*W This is the same as G*W is not combined
F2 = G*F Fixed mapping, although it generates as well
U2 = G*U Untrained mapping, which will use the generated dataset for training
T2 = G*T Trained mapping, although it generates new incoming test objects first
A2 = A*G*F Generates a new dataset A*G and maps it by F
T = A*G*U Generates a new dataset A*G and uses it to train U
A2 = A*G*T Generates a new dataset A*G and maps it by T
U3 = A*G*U1*U2 = T1*U2 A*G is used to train U1. There the data stream stops. See below for a proper training of U1*U2
U3 = A*(G*U1)*U2 = T1*U2 This is the same as the brackets are neglected
T = A*G*(U1*U2) = T1*T2 T1 = A*G*U1 and T2 = A*G*T1*U2. So A*G is used for training U1 as well as U2, following the rules of combining untrained mappings.
T = A*((G*U1)*U2) = T1*T2 T1 = A*G*U1 and T2 = A*T1*U2. So U2 is trained by the original objects!

An example is:

E = prcrossval(A,(gendat([],0.1)*proxm([],'m',2))*qdc,2,10)

The dataset A is used in a crossvalidation experiment for a dissimilarity based classifier qdc. The representation set uses a random 10% of the training set. All training objects, including the representation set, are used for training qdc.

elements: datasets datafiles cells and doubles mappings classifiers mapping types.
operations: datasets datafiles cells and doubles mappings classifiers stacked parallel sequential dyadic.
user commands: datasets representation classifiers evaluation clustering examples support routines.
introductory examples: Introduction Scatterplots Datasets Datafiles Mappings Classifiers Evaluation Learning curves Feature curves Dimension reduction Combining classifiers Dissimilarities.
advanced examples.