Dynamical data modeling methodology for multidimensional scaling.

1. Genotype Information,Genotype Information,
Stochastic Resonance Synergetics,Stochastic Resonance Synergetics,
and Dynamical Data Modelingand Dynamical Data Modeling
Milan JovovicMilan Jovovic

2. Modeling approach based on free energyfree energy and
distortion energydistortion energy
Near linear model - aims for the simplest
explanations
Estimation of clustering dynamical parameters
by statistical inference
Multi-spectral decomposition, in hierarchy of
scales
Application: scale analysis of complex systemsApplication: scale analysis of complex systems
Multi-scale decomposition via
dynamical cascades

3. Introduction (1 of 2)
Clustering parameters:
• Selected window of computation: Wr
• Computed cluster vector within Wr
Statistical inference defines PDF, with the associated
distortion energies, F and V.
Energy functions are generally multi-dimensional and
non-convex/concave
Non-linear map defines dynamical scale-space
clustering.
Clustering is a model-free approach to signal decomp.Clustering is a model-free approach to signal decomp.
c


4. Introduction (2 of 2)
Data binding – no ordering relation assumed (model-free), although a
priori neighboring information used - speeds up numerical computation.
Brain waves: 2 nucleons decomp.

5. Model of signal distortion:
- definitions
Distortion measure:
1. d = z2
= (Cx-X)2
+ (Cy-Y)2
e.g. in still images
2. d = z2
= e.g. in motion images
2
][ vIIt

⋅∇+
Partition functions: ,
2
∑
−
=
rW
z
rZ
β
Distortion energies -
free energy, and variance:
( )∑=
rW
PvxdV

,
PDF: ,
2
Z
r
P
zβ−
=
( ) ,log
1
, r ZvF
β
β −=


6. Scale-space computing
Series of convex/concave min/max of free energy F
 brings in eq. up-scale melting & down-scale cooling:
( ) ( ) ,
1
0
∫=
β
ββ
β
β dVF ( )
( )∫
=
−
β
ββ
β 0
dV
rZ
( )
)1(
.
,2
β
δβ
∂
∂
±=
−=
∂
∂
−= ∑
F
PIc
c
F
c
rW


Evolution scheme – path integrals:
Way to move through the scale-space ?

7. Motion through the scale-space:
wave information propagation
Mass-energy-information conservation principle
Coupling +/- mass-energy possible
12
ββ >
( )β,vF

Vv grad=

(1)
(2)
)2(
v
V
v 

∂
∂
±=δ
)3(
β
δβ
∂
∂
±=
F
∫ ∫ =
∂
∂
+
∂
∂
=
S S
d
v
V
vd
F
dU 0β
β


V
F 2
2
2
∇=
∂
∂
β

8. Most singular manifolds (MSM), and a data nucleons
 MSM (2 colors), and a nucleon (4 colors)

9. MSM(white) coupled to the rain patterns.
Still images decomposition

10. Scalable coding
Coupled data structure of the hierarchy of
binary decompsitions.
Efficient coding, control, data transfer.
Parallelization: computing and control by
parallel computing architectures.
(v4, W4)(v3, W3)
(v2, W2)(v1, W1)(v0, W0)
βc
3
(v3
, W3
)
βc
2
(v2
, W2
)
βc
0
(v0
, W0
)
βc
1
(v1
, W1
)

11. Focus on computability and complexity –
relationship to statistical physics
o Computing paradigm assumes:
o Motion via scale-space wave information propagation, and
o Uncertainty relation wrt the information content of a cluster
o What makes it polynomial in complexity (ref. 2)?
o Unique statistical description, although chaotic motion possible
o No strange attractors due to the conservative motion
 Within this description: multi-scale decomposition of the information
content into clusters
 Coupling of the energy exchange – synergetics
 Coupled manifolds spanning the content of the information clusters

12. Summary presentation of current work
Scalable data decomposition:
• genotype information, encription and coding,
• progressive transmission
• segmented control
Multidimension scaling:
• Dynamical cascades via space-time synergism.
Images: multi-spectral decomposition and clusters
couplings, spectral signature recognition
Movements:
• trajectory analysis
• learning
Bio/chemical informatics:
• data-mining and knowledge discovery
Synchronous computing scheme: upscale melting &
downscale cooling
Parallel computing implementation

13. Perspective and future directions
Scale-space approach to computing, analysis,
and signal control.
Bioinformatics, computational physics.
Model of signal distortion analogous to that of the
networked physical systems.
Dynamical data modeling: multidimensional
scaling via spatio-temporal synergism.
Segmented control of multispectral components.
Parallel computer implementation.

14. BIBLIOGRAPHY
Jovovic, M., [2013], Genotype Information and the Space-Time Generatio
Jovovic, M., [2012], Stochastic Resonance Synergetics (SRS)
Hypothesis: A Road to Attention, Memory, and Behavioral Data-
driven Study
Jovovic, M., [2011], Brain wave synergies, analysis and coding
Jovovic, M., G. Fox, [2007], Multi-dimensional data scaling – dynamical
cascade approach, Technical Report - Indiana University, USA.
Jovovic, M., H. Yahia, I. Herlin [2003], Hierarchical scale
decomposition of images – singular features analysis, Technical report,
INRIA, AIR Lab, France.
Jovovic, M., S. Jonic, D. Popovic [1999], Automatic synthesis of
synergies for control of reaching – hierarchical clustering. Medical
Engineering and Physics.