Idea of inner structure to explain
diversity
As forming process, from origin to superficial feature, that is
final
observed value, by some transformation stages , inner structure of the
observed is hidden.
i think that intellectual
pattern recognition is to clarify the inner
structure.
In early age, in order to explain diversity, that is, many
observed samples are born out of one original image, i thought the idea
of
multistage structure, which observed final object is made from original
one by some transformation stages. showing figure below.
For instance, when observed value is defined as frequency spectrum,
like image reflected on a curved distorted mirror, transformation which
converts frequency higher or lower must be necessary.
And in actual, solving multistage structure equation, due to its
many degrees of freedom, solution cannot be determined. Any convenient
answer value can be required by many degrees of freedom of multistage.
So, as it is, multistage structure equation isn't useful
for pattern
recognition.
(Addition) Characterized
Structure
Let's think about general purpose structure which is able to produce
everything. And change general purpose structure to one structure which
can produce restricted production by limited degrees of freedom.
Suppose that its name is characterized structure. Kinds of
character will be many.
Using the characterized structure, forced solve how input sample is
produced. It will be classified into two, that one is that represents
well by the characterized structure, another is that does not fit
to represent it by the characterized structure.
When solving structure equation, as many degrees of freedom, we cannot
get proper answer which is explanatory. Is this matter solved by
consisting of characterized structures ?
Matching and Learning
In fact, it is not achievable to perfectly compose the
sample of produce by structures. So, matching is judgment of whether,
as a part of it, the sample includes the structure, produce by
the structure, the feature. When the sample includes some kinds
of structure, some characterized structures, it will be based on
combination of them.
Learning is to estimate common core, structure , which is included as a
common along every sample.
Diversity reduction
In order to reduce diversity of observed shape, i think of
utilizing
harmonic elements of speech wave, of which basic cycle is
fundamental frequency of speech signal wave (pitch). As use harmonic
elements,
diversity caused by transformation which converts frequency higher or
lower can be avoided.
Similar to formula of Quantum mechanics, transformation operator F
which connects original image x, that corresponds to sound
source in this content, with observed value y, may make group. i
think its possibility.
Especially, regarding to human speech, quantity of kind of
the group may be limited number, due to physically allocation and their
movement of human mouth, tongue, and nose. i
guess so.
What discriminate-able is
In this world, there are two kinds. One is what can
be discriminated. Another is what cannot be discriminated because of
its chaotic state or undistinguished complex. So, i think that
the
necessary condition to be discriminate-able maybe exists. Like Complex
Function Theory including useful ways born out of only one simple
theorem, i dream of that some useful ways will be developed from the
necessary condition to be discriminate-able. Simultaneous
Existence is defined as concept of discriminate-able, that is,
relative ones are co-exist.
Mathematics application of these idea
The idea, simultaneous existence,
inner structure, and so
on should be corresponded to mathematics method for actual
solution of pattern recognition problem. Limited value function, for
example is n-value (n={2,3, ...}), is one mathematics method of
simultaneous existence. Inner structure is represented as structure
equation. Also, every production trace, it may be huge, is other
mathematics method of inner structure. To estimate and determinate
everything of inner structure at once won't go well, due to its
many degrees of freedom. One better method is that determinate
outline and then divide into parts and consider detail, and do that
procedure repeatedly until reasonable state, like cell division
process in biology.
If it is applied to speech recognition,
from simple discrimination which any sound is or not, to more
mixed discrimination, until the discrimination level of human ability,
that may is similar to human evolution process.
Find
out key of phoneme in diversity per time dimension
Speech signal changes per time. It's hard to determine perfectly time
division of the phoneme on speech signal wave.
So, suppose that there are two kinds of portion, one is key portion
which means phoneme, and another is transitional portion which is
secondary effect and is less important.
And then, i think that,
A: Course from one key to next key isn't single way, but many
courses is possible,
because transitional portion can change roughly. So, database made from
them will not converge.
B: Analyze inner structure of key portion and its around, whether it
hide hint to recognize.
Comparison of speech signal change per time dimension with mountain
climbing.
From way in to top of mountain, from top of mountain to the top of next
mountain,
from the top of next mountain to way out, there are many possible
courses which you
can choose. This is compared to diversity per time
dimension.
However, top of mountain and its around which is compared to key of
phoneme is only
one for each mountain.
And also, mountain geographical features like soft slope or cliff, that
is structure, may
give hint to recognize.
No.13(E), 13 April 2008
A
proverb: "Science is like that, even though you open one door ahead,
one
more door will appear."
