Combiner mappings
(This topic is mainly important for PRTools programmers designing mappings)
Mappings of the combiner type operate on other mappings and not directly on data. They are used to modify the properties of a given mapping. An example is classc which converts a classifier that outputs class densities to one that results in posterior probabilities. In addition there are the fixed combiners designed of combining set of classifiers that are grouped in a stacked (i.e. in the same vector space) or parallel (in different vector spaces) way.
There are not many checks programmed for combiners. It is easy to apply a wrong mapping to a combiner. Usually only after applying data to mappings errors will be generated. This may confuse users as these errors are not always directly meaningful.
The main rules for combining a combiner mapping V with arbitrary fixed and trained mappings W, untrained mappings U and trained mappings T are
W2 = W1*V |
The mapping W1 is modified by V . Also if V is not a combiner then this holds. In that case, however, the two mappings W1 and V are just stored as a sequential combiner in W2 and executed in the given order without modifications. |
A2 = A1*(W*V) |
Mappings should first by applied to combiners before data is processed. |
T2 = A*(U*V) = A*U*V = T1*V |
Untrained mappings are usually insensitive for combiners. Usually, order of processing makes in this case no difference. |
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.