Fixed mappings
A fixed mapping transforms one vector space into another in a data independent way. Its operation just depends on some user defined parameter settings. An example is the sigmoid scaling: F = sigm([],s) in which s defines the smoothness of the function. It is called by B = A*F in which A is an input dataset and B is the transformed result.
The following rules apply if a dataset A is processed by a sequential combination of a fixed mapping F with another fixed mapping,an untrained mapping U or a trained mapping T. W is an arbitrary mapping.
A2 = A*(F1*F2) = A*F1*F2 |
This is the same as F1*F2 is not combined |
F2 = G*F |
Fixed mapping, it generates as well |
G2 = F*G |
Generator, the data is transformed by a fixed mapping. |
T = A*(F*U) = F*(A*F*U) |
The untrained mapping U is trained by A*F. The resulting trained mapping is preceded by F to transform new data to the space in which U has been trained. |
An example is:
U = pcam([],10)*ldc;
T = A*(im_resize([],32,32)*U)
The untrained mapping defines a mapping on the first 10 principal components and performs in this space a linear classifier assuming normal class densities. Training preceded by resizing all images to 32*32 pixels in order to make the images comparable is . A can be a dataset as well as a datafile.
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.
