1. Silicon Cortex ONR Sponsored
Current Student Members:
Li, Yuan
Ozturk, Mustafa Can
Xu, Dongming
Visiting Professor and Post-Doc
Dr. Michael Stiber
Dr. Mark Skowronski

2. Introduction
Inspired by Freeman’s computational model of olfactory cortex
A biological model on chip
Information processing using nonconvergent dynamics
Freeman’s Reduced KII Network

3. Group Members Applications of Freeman Model and Simulation Software
Mark
Applications of Freeman Model and Echo State Network
Can
Spiking Freeman Model
Yuan
Dynamical Analysis and Analog VLSI
Dongming

4. Freeman Model K0 cell, H(s) 2nd order low pass filter Q(x)
Hierarchical nonlinear dynamic model of cortical signal processing from rabbit olfactory neo-cortex.
K0 cell, H(s) 2nd order low pass filter
Q(x)
Reduced KII (RKII) cell (stable oscillator)

5. RKII Network Capable of several dynamic behaviors:
High-dimensional, scalable network of stable oscillators.
Fully connected M-cell and G-cell weight matrices (zero diagonal).
Capable of several dynamic behaviors:
Stable attractors (limit cycle, fixed point)
Chaos
Spatio-temporal patterns
Synchronization
Generalization
Associative Memory

6. Applications of Freeman Model and Echo State Network Mustafa Can Ozturk
Using KII as a Dynamical Associative Memory
Simplified model of reduced KII set.
Echo State Network (ESN):
Average State Entropy (ASE) criterion to evaluate the information contained in the output states
Linear system approximation of ESN
Optimal pole locations in ESN
SIN(x) to SIN7(x)
wBbB
dByB
dBxB W
WBinB
L(x)
WBout
Block Diagram of ESN

7. Applications of Freeman Model and Echo State Network Mustafa Can Ozturk
Poles Positions
Systems with uniformly distributed
poles generally have better performance
Different distributions of output states
have different ability for functional approximation

8. Spiking Freeman Model Yuan Li
Replace K0 output block with integrate & fire neuron.
Encode values with firing rates.
Avoid distributing sensitive analog values.
Smaller circuits
Use digital busses and multiplexers.
Summation of pulses trivial in current mode
Status: measurement
IF Neuron

9. Spiking Freeman Model Yuan Li
RKII as input-controlled oscillator

10. Dynamical Analysis and Analog VLSI Dongming Xu
Dynamical behavior of a single reduced KII set
Synchronization analysis of coupled reduced KII sets and logical computation using synchronization
Information processing achieved by cooperation of different functional layers
Analog chips
Small chip area and low power (25 uW/cell)

11. Dynamical Analysis and Analog VLSI Dongming Xu
16 K0 cells to build 8 RKII oscillators
Digital circuit to provide external control of coupling weights
Status: measurement

12. Applications and Simulation Tool Dr. Mark Skowronski
Simulations
Implementation of KIII in Matlab (gui, mex),
Demonstration of various chaotic attractors through random weights,
Discovery of multiple basins of attraction, selected by random initial conditions,
Developed attractor identification scheme
Applications
Speech processing
I saw things you don’t see.

13. Applications and Simulation Tool Dr. Mark Skowronski

14. Applications and Simulation Tool Dr. Mark Skowronski
Two regimes of operation as an associative memory of binary patterns:
Energy Readout
for Static Patterns
Synchronization Through Stimulation (STS) for Time Varying Patterns
Network weights for each regime set by outer product rule variation and by hand.

15. Applications and Simulation Tool Dr. Mark Skowronski
\IY\ from “she”
\AA\ from “dark”
\AE\ from “ask”
18 HFCC-E coeffs. converted to binary
Energy-based RKII associative memory
Variable overlap between learned centroids
Overlap controlled by binary feature conversion
More overlap more spurious outputs

16. Conclusions Biologically inspired model,
Great potential for computations,
Natural solution of hardware implementation using analog VLSI

17. MOTOROLA Project 2004 Current members Prof. John G. Harris
Dr. Mark D. Skowronski
Meena Ramani, Ph.D. student
Harsha Sathyendra, Ph.D. student
Ismail Uysal, Ph.D. student
&
Prof. Alice Holmes, Audiology
Sharon Powell, Au.D. student

18. MOTOROLA Project 2004 Funding from MOTOROLA since 2000
Previous CNEL members
Tom Reinke, M.S. `01
Marc Boillot, Ph.D. `02
Bill O’Rourke, M.S. `02
Kaustubh Kale, M.S. `03
Lingyun Gu, `04
Publications in SPEECH PROCESSING
Speech Enhancement
Energy redistribution, voiced/unvoiced
ASA San Diego `04
JASA, 2004 (revision)
Energy redistribution, spectral transitions
ASA Cancun `02
Loudness Enhancement
Bandwidth expansion
ISCAS Vancouver `04

19. MOTOROLA Project 2004 Bandwidth Extension Current 2004 projects:
Telephone BW is Hz
Goal: Extend BW to 0-4 kHz and 0-8 kHz on the phone.
Methods: predictive models for vocal tract and excitation information.

20. MOTOROLA Project 2004 Assistive Listening Devices
Current 2004 projects:
Assistive Listening Devices
20 million Americans are hard of hearing.
Goal: Develop cell phones as ALDs.
Methods: speech enhancement algorithms, audiologic listening tests

21. Brain Dynamics Research
Anant Hegde
Hui Liu
Advisor: Jose Principe

22. Goals Develop seizure detection algorithms Artifact rejection
Analyze spatio-temporal dependencies in ECOG

23. EEG dynamics descriptors
Several non-linear dynamical features used as EEG descriptors
Short-Term-Lyapunov (STLmax) exponent characterizes the maximum rate of divergence (chaos) in signal’s trajectory; applied on short segments of data
Reasonably good w.r.t epileptic seizure detection
Computationally expensive
Sensitive to parameter settings and Artifacts

24. Recurrence Time Statistic (RTS)
Alternative dynamical descriptor
Non-parametric
Computationally simpler
Less sensitive to parameter settings

25. ROC curves for Seizure Detection

26. Noisy EEG & Corresponding ICA Decomposed Components
Z1(n)
y1(n)
Z2(n)
y2(n)
Z3(n)
y3(n)
Z4(n)
y4(n)
Z5(n)
y5(n)
Z6(n)
y6(n)
Noise Component

27. Pre and Post artifact removal

28. Performance Comparison

29. Spatio-temporal dependencies
Dependency analyses using SOM-based Similarity Index (SI) measure
Achieves significant computational improvement on the original SI measure
Characterizes asymmetric dependency between two time-structures

30. Results on P092
Spring 2004

31. Spatio-temporal clustering
Developed clustering techniques to characterize spatio-temporal channel interactions
Same can be applied to “cluster” the channels as well

32. Papers
Hui Liu, J. B. Gao, Kenneth E. Hild II, José C. Príncipe, J. Chris Sackellares, “Epileptic Seizure Detection from ECoG Using Recurrence time Statistics,” IEEE EMBS conference, September 2004.
Hui Liu, Kenneth E. Hild II, J. B. Gao, Deniz Erdogmus, José C. Príncipe, J. Chris Sackellares, “Evaluation of a BSS Algorithm for Artifacts Rejection in Epileptic Seizure Detection,” IEEE EMBS conference, September 2004.
Anant Hegde, Deniz Erdogmus, José C. Príncipe, “Synchronization analysis of Epileptic ECOG data using SOM-based Similarity Index (SI) Measure,”, IEEE EMBS conference, September 2004.

33. Future directions
Develop techniques to automatically identify artifact components from estimated sources
Apply spectral clustering technique to spatio-temporal clustering problems
Investigate other techniques to quantify functional relationships in multivariate time-structures

34. Bio-Nano Project (Brain slice)
Dr. Jose C. Principe
Brian Davis
Good morning everyone. Thanks for coming. What I am going to present today is about local modeling paradigm based on SOM for nonlinear nonautonomous system.

35. Information-theoretic learning (ITL) research overview
Jian-Wu Xu, Rati Agrawal, Kyu-Hwa Jeong, Seungju Han,
Puskal Pokharel, Sudhir Rao

36. Outlines Application of ITL to varies of problems
State estimation, time series analysis, spectral clustering, etc.
Develop other training algorithms to improve the performance
training during test phase
Examine ITL from other perspectives
Kernel method, information geometry

37. Jian-wu Xu Apply ITL to state estimation
How to extend Kalman filter to nonlinear, nongaussian case by using ITL.
Relationship between ITL and kernel methods
a new perspective of ITL, kernel size selection

38. --Improved performance in nonlinear channels
Rati Agrawal
ITL methods to matched filter
Use Cauchy-Schwartz Quadratic Mutual Information to extend matched filter in nonlinear case for signal detection.
Achievement
--Improved performance in linear channel corrupted by impulsive noise (e.g.: Cauchy distributed noise)
--Improved performance in nonlinear channels

39. examine ITL from information geometrical perspective
Seungju Han
Information geometry
examine ITL from information geometrical perspective
Distance measure
approximate Kullback-Leibler(KL) divergence by Cauchy Schwartz(CS) distance or Euclidean(ED) distance measure

40. Kyu-Hwa Jeong
Training in test phase
Update the adaptive system during the test (application) phase based on ITL
Minimize the distance between pdf of the desired signal for training and pdf of the test output

41. Puskal Pokharel
Explore novel methods of time correlation with higher moments using kernel methods
Use ITL measures like entropy, mutual information, etc for time series analysis

42. ---determine number of clusters K from the data directly
Sudhir Rao
ITL methods for Spectral Clustering
-- use Cauchy Schwartz(CS) distance or Euclidean(ED) distance measure for spectral clustering
---determine number of clusters K from the data directly
--- connection between spectral clustering and kernel methods(KPCA)

43. Modeling and Controller Design for LoFLYTE Unmanned Aerial Vehicle (UAV)
Dr. Jose C. Principe
Jeongho Cho
Jing Lan
Good morning everyone. Thanks for coming. What I am going to present today is about local modeling paradigm based on SOM for nonlinear nonautonomous system.

44. ? Objectives System identification GMM & SOM based multiple modeling
No apriori knowledge about the plant
Input-output measurements
GMM & SOM based multiple modeling
Controller design
Multiple model based controller (IC, PID, SMC)
Let me describe the system considered for this study.
It is the LoFLYTE® testbed aircraft designed by Accurate Automation Corporation.
LoFLYTE® stands for Low Observable Flight Test Experiment which is jet powered subscale model flown by remote control.
it flies slower than the speed of sound, but it has the same "waverider" shape designed for Mach five flight.
The waverider shape improves fuel consumption by decreasing air resistance at speeds greater than mach one. The full scale aircraft will take off horizontally in the near future. Then it will use airbreathing engines to accelerate to a cruising speed of Mach 5 at a very high altitude.
It will end its flight by landing on a conventional runway.

45. LoFLYTE testbed aircraft
Low Observable Flight Test Experiment flown by remote control
Fly slower than the speed of sound, but "waverider" shape designed for Mach five flight
Improves fuel consumption by decreasing air resistance
Cruising speed of Mach 5 at a very high altitude
Landing on a conventional runway.
Let me describe the system considered for this study.
It is the LoFLYTE® testbed aircraft designed by Accurate Automation Corporation.
LoFLYTE® stands for Low Observable Flight Test Experiment which is jet powered subscale model flown by remote control.
it flies slower than the speed of sound, but it has the same "waverider" shape designed for Mach five flight.
The waverider shape improves fuel consumption by decreasing air resistance at speeds greater than mach one. The full scale aircraft will take off horizontally in the near future. Then it will use airbreathing engines to accelerate to a cruising speed of Mach 5 at a very high altitude.
It will end its flight by landing on a conventional runway.

46. Modeling techniques State space Global – Local –
Compact representation
Construct once and fit all over
state space (MLP, Polynomial, etc)
Local –
Nearest-neighbor methods 
a simple model
Adhere to the local shape
of an arbitrary surface
Local linear models have performed
very well in time series prediction
SOM-based Modeling
& Gaussian Mixture Modeling
Generally modeling techniques can be divided into global and local modeling.
Global models attempt to yield a compact representation of an underlying dynamical system.
In addition, global models are constructed once and fit all over state space, while local models are trained to represent local regions
For example, feedforward neural networks such as MLP has been successfully applied to input-output modeling of nonlinear processes.
Local models are usually based on nearest-neighbor methods so that a simple model is constructed using only the neighboring points.
Thus, they have the ability to adhere to the local shape of an arbitrary surface, which is difficult especially in cases when the dynamical system characteristics vary considerably throughout the state space.
As Farmer and Sidorowich have already shown, local linear models, despite their simplicity, provide an effective and accurate approximation for autonomous system.
Simply speaking, global modeling use all the data distributed in this voronoi tessellation and local modeling uses only one voronoi region.

47. GMM-based multiple models
Consist a set of expert systems, each follow standard Gaussian distribution, and an integrating network.
Describe a complex system using combination of a set of simple system, Gaussian distribution.
What is SOM? SOM is a clustering algorithm based on unsupervised competitive learning which means SOM is trained without a teacher.
This is SOM and each cell is called PE.
It was first proposed by Teuvo Kohonen in 1981 as a visualization tool.
SOM is a topology that converts particular feature of input patterns into the spatial location of a PE.
Also, it preserves the topology of the data, it is robust to missing values, and it is easy to visualize the map. Consequently, SOM is a nonlinear projection of the input space on a 1 or 2-d discrete lattice.
These properties make SOM a prominent tool in data mining.
The application of SOM includes a number of areas such as image processing and speech recognition, process control, economical analysis, and diagnosis in industry and medicine.

48. SOM-based multiple models
Self-Organizing Map (SOM)
Unsupervised competitive learning
Divide the operating regime into local regions
Build local mappings in positions given by prototype vector
Winning PE
What is SOM? SOM is a clustering algorithm based on unsupervised competitive learning which means SOM is trained without a teacher.
This is SOM and each cell is called PE.
It was first proposed by Teuvo Kohonen in 1981 as a visualization tool.
SOM is a topology that converts particular feature of input patterns into the spatial location of a PE.
Also, it preserves the topology of the data, it is robust to missing values, and it is easy to visualize the map. Consequently, SOM is a nonlinear projection of the input space on a 1 or 2-d discrete lattice.
These properties make SOM a prominent tool in data mining.
The application of SOM includes a number of areas such as image processing and speech recognition, process control, economical analysis, and diagnosis in industry and medicine.
Input Layer
Competition Layer
(SOM)
Local modeling Layer

49. Controller design based on a SOM
Inverse controller – can be easily utilized since each model is linear (it seeks to model the inverse of the plant)
SOM - determines the current operating region and triggers the corresponding controller
Embedding
Each model can be approximated by Taylor series expansion using inputs and outputs corresponding each PEs
Therefore the modeling problem becomes one of choosing the a and b to describe the dynamics.
Model 1
Controller 1 : :
Model N
Controller N
Embedding

50. Control performance of lateral motion
Tracking an arbitrary trajectory (SNR = 20dB)
(a) by MSMC (b) by MIC (c) by TDNNC
The first nonautonomous system we consider is initially proposed by Narendra.
The signal was generated by random uniformly distributed control input. For local linear modeling, the embedding dimension is chosen based on Lipschitz index, however, it is not easy to find the point starting the steady state from this figure.
Thus the embedding dimension for control input and output are chosen arbitrarily so that the model has the form.
The result was not satisfactory and the larger size of the SOM did not make the performance better because, as seen in this equation, it is very difficult to model the cube term of control input and the power term of the state with linear models.
Thus we tried to approximate the system with 2nd order hammerstein model.

51. Further Study SOM-based multiple models GMM-based multiple models
Better switching mechanism
BIBO stability obtained by SMC
Stability issue under the noise and modeling error
GMM-based multiple models
Optimization of training criteria besides MSE
Investigation of other embedding data
Design Robust controller
In this work, we have tried to construct a neural architecture capable of capturing locally the underlying dynamics of a nonautonomous system with the help of SOM.
SOM has a superior clustering capability and determines the region where the state dynamics is.
Thus it is used to select a model.
Because of simplicity and effectiveness local modeling has been used to represent local dynamics and local polynomial modeling was presented for better estimation.
As a result, we have presented efficient modeling algorithms called LMSOM and LMMCP for nonautonomous system.
Both proposed methods take the concept of self-organization in input-output joint space extended with multiple models.
The proposed strategy verified that the SOM successfully quantizes the i/o joint space and the local models produce promising results.
In addition this method is implementable on low cost electronics.