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Context-Dependent Thinning 7

3.1. Determinism

Repeated application of the CDT procedures to the same input should produce the same output.

3.2. Variable number of inputs

The procedure should process one, two, or several codevectors. One important case of input is a vector
in which several component codevectors are superimposed.

3.3. Sampling of inputs

Each component codevector of the input should be represented in the output codevector by a fraction of
its 1s (or their reversible permutation).

3.4. Proportional sampling

The number of 1s representing input component codevectors in the output codevector should be
proportional to their density. If the number of 1s in
a and b is the same, then the number of 1s from a
and b in thinned ab should also be (approximately) the same.

3.5. Uniform low density

The CDT procedures should maintain (approximately) uniform low density of output codevectors (small
number
M' of 1s) under varied number of input codevectors and their correlation degree.

3.6. Density control

The CDT procedures should be able to control the number M' of 1s in output codevectors within some
range around
M (the number of 1s in the component codevectors). For one important special case, M'=M.

3.7. Unstructured similarity

An output codevector of the CDT procedures should be similar to each component codevector at the
input (or to its reversible permutation). Fulfillment of this requirement follows from fulfillment of the
sampling of inputs requirement (3.3). The thinned codevector for
ab is similar to a and b. If the densities
of component codevectors are the same, the magnitude of similarity is the same (as follows from the
requirement of proportional sampling, 3.4).

3.8. Similarity of subsets

The reduced representations of a given component codevector should be similar to each other to a degree
that varies directly with the similarity of the set of other codevectors with which it is composed. The
representation of
a in the thinned abc should be more similar to its representation in the thinned abd
than in thinned aef.

3.9. Structured similarity

If two sets (collections) of component items are similar, their thinned codevectors should be similar as
well. It follows from the similarity of subsets requirement (3.8). If
a and a' are similar, b and b' are
similar, then thinned
ab should be similar to thinned a'b'. Or, thinned abc should be similar to thinned
abd.

3.10. Binding

Representation of a given item in an output thinned codevector should be different for different sets
(collections) of component items. Representation of
a in thinned abc should be different from the
representation of
a in thinned abd. Thus the representation of a in the thinned composite codevector
contains information on the other components of a composite item.

4. Versions of the Context-Dependent Thinning procedures



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