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Nataraja, a cluster of a thousand suns.
Clusters
Clustering is a simple idea containing notions of coalescence
and merging. Clustering is an concept whose significance as a
physcial process I've come to appreciate more of as time in years
pass by. Through experience and studying the writings of physicists,
particularly Satosi Watanabe and David Bohm, I've grown aware of the
dynamic movement in physical objects as a kind of essential
expression of the physical laws.
I think that Satosi Watanabe's illustrations [1] of clustering leading
to the formula for entropy is beautiful in simplicity. It captures
the essence of David Bohm's idea of movement in physical processes;
something which I think is deeply fundamental about the universe.
The clustering process can also be seen as a splitting of a whole
into parts [2]. This pattern in Nature can be seen in binary
tilings.
Piet Mondrian; image: www.artknowledgenews.com
The binary symmetry can be seen in the binary Yin-Yang pattern of King
Wen-Wang's 64 hexagrams [3].
64 Hexagrams; image: www.kheper.net
A technique in computer programming called hashing is an efficient
way of indexing data using a type of pseudo-random number generator
algorithm. The computation of this index uses the data itself,
and an algorithm that tries to point this index evenly among the data.
With respect to tile coding [4] hashing introduces a direct computational
way to get from a branch down to a leaf quickly.
A cluster, with respect to neurons and software, is composed of a list
of the automaton's attributes in the form of computer data structures.
These representations of synthetic neurons can be transformed or
rewritten into primitive input sequences of long strings containing
words and phrases.
Phi above describes the neural wave in a cluster layer.
Neuronal Cluster
We can make a conceptual jump to the Prism software now by having
the Phi function be the "hashbuckets". The hashbuckets in Prism
is used solely for speeding up the computational process and reducing
complexity. It has no analog to any real neural process discovered
so far. This scheme makes it possible to use a randomizing algorithm
like a directional pointer into a neural circuit location.
I now think of the Prism software as a the neural network which consists
of template matching lookup tables aided by fast hashing algorithms to
the Fourier lexicons in these tables. I've evolved the model for neurons
to be analogous to one which looks formally like a wave model because
of the way the real brain waves propagate through specific neural
channels or pathways. On the other hand, I want to model the semantic
network which can recognize language.
We want to do as much preprocessing or "training" of the input data
as possible. In terms of wave analysis we try to get a best
estimate or description of the input signal as possible by creating
a description of it in terms of a simple function. This simple function
is a Gabor wave packet. In the grammatical representation using strings,
the pattern cluster becomes the characteristic coefficient. The Prism
program uses these "pattern descriptor coefficients" to
classify an input signal. A group of these coefficients make up
the pattern descriptor dictionary.
References
1.
Satosi Watanabe, Pattern Recognition: Human and Mechanical,
Dynamic Coalescence Model - Clustering As Merger, p 160-166.
2.
ibid., Clustering as Cleavage, p 166-178 (this is a continuation
on the theme of entropy minimization)
3. The following is a quote from:
http://en.wikipedia.org/wiki/I_Ching#Binary_sequence
In his article Explication de l'Arithmetique Binaire (1703) Gottfried
Leibniz writes that he has found in the hexagrams a base for claiming
the universality of the binary numeral system. He takes the layout of
the combinatorial exercise found in the hexagrams to represent binary
sequences, ...
4.
Richard S. Sutton and Andrew G. Barto web page on:
Reinforcement Learning: An Introduction, section 8.3.2
Tile Coding
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