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CCECE 2003 Signal Classification through Multifractal Analysis and Complex Domain Neural Networks V. Cheung, K. Cannons, W. Kinsner, and J. Pear* Department of Electrical & Computer Engineering Signal and Data Compression Laboratory

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May 5, 2003

Signal Classification through Multifractal Analysis and Complex Domain Neural Networks

V. Cheung, K. Cannons, W. Kinsner, and J. Pear*

Department of Electrical & Computer Engineering Signal and Data Compression Laboratory *Department of Psychology University of Manitoba, Winnipeg, Manitoba, Canada

CCECE 2003

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Outline

Introduction
Background

► Variance fractal dimension trajectory ► Kohonen self-organizing feature map ► Probabilistic neural network ► Complex domain neural network

Experimental Results and Discussion
Conclusion

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Introduction

Classification of signals that are:

► Stochastic ► Self-affine ► Non-stationary ► Multivariate ► From non-linear systems

Eg. multi-channel speech signals, multi-lead ECGs
r EEGs

Introduction Background Results Conclusion

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Fish Dishabituation Signals

X Z Y Fish Tank Mirror

Introduction Background Results Conclusion

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System Design

Introduction Background Results Conclusion

Feature Extraction VFDT SOFM Signals Signal Classification Classification PNN CNN

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Variance Fractal Dimension Trajectory

Temporal multifractal characterization

► Calculate the variance fractal dimension of a small

segment of the signal in a sliding-window fashion over the entire signal [Kins94]

► Reveals the underlying complexity of the signal ► Provides a normalizing effect

Advantages of the variance fractal dimension

► Easy to compute

■ Measure the variance of amplitude increments at different scales

► Can be computed in real-time

Introduction Background Results Conclusion

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VFDT Plot

VFDT Introduction Background Results Conclusion

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Self-Organizing Feature Maps (SOFM)

Topology-preserving neural networks using

competitive unsupervised learning [Koho84]

Two uses in this paper

► Clustering

■ Aid in constructing the training and testing sets

► Feature Extraction

■ Dimensionality reduction

Introduction Background Results Conclusion

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Probabilistic Neural Networks

Neural network implementation of the Bayes
ptimal decision rule [Spec88]

► eg. Spam filters

Advantages

► Asympotically Bayes optimal

■ Good classifiers

► Trains orders of magnitude faster than other NNs

Disadvantages

► Slower execution than other NNs ► Require large amounts of memory

Introduction Background Results Conclusion

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Complex Domain Neural Networks (CNN)

Advantages

► Works with inputs in their natural complex valued form ► Faster training ► Better generalization

Disadvantages

► More complexity

■ Convoluted partial derivatives involving complex analysis

Ref: [Mast94]

Introduction Background Results Conclusion

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CNN Architecture

Input Layer Hidden Layer Output Layer 1 2 3

Introduction Background Results Conclusion

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Experiment #1

95% Confidence Interval: [62.77%, 70.69%] 50.00% 93 70 23 4 59.04% 65 111 12 3 92.47% 4 4 135 3 2 100.00% 24 1 Expected 4 3 2 1 Correct

Class. Rate

Experimental Average Correct Classification Rate: 66.73% VFDT

Classification

PNN

X-Axis Signals

Introduction Background Results Conclusion

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Experimental Results Summary

87 91 80 87 96 CNN X & Z 4 3 2 1 Average Rate (%) Classification Rate (%) Classifier Signal 91 95 84 95 100 PNN X & Z 58 91 47 29 63 PNN Z 67 50 59 92 100 PNN X VFDT

X-Axis Signals

VFDT

Z-Axis Signals

CNN PNN

Introduction Background Results Conclusion

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SOFM Feature Extraction

SOFM VFDT

X-Axis Signals

VFDT

Z-Axis Signals

CNN PNN 66 67 PNN X 61 58 PNN Z 88 91 PNN X & Z 85 87 CNN X & Z + SOFM VFDT Average Rate (%) Classifier Signal

Introduction Background Results Conclusion

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Conclusions

A system capable of classifying self-affine,

stochastic, non-stationary, multivariate signals

riginating from non-linear processes was

developed

Feature extraction involving variance fractal

dimensions and self-organizing feature maps shown to be effective

Probabilistic neural networks and complex domain

neural networks shown to be capable of performing the desired classification

Introduction Background Results Conclusion

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Acknowledgements

Natural Sciences and Engineering Research

Council (NSERC) of Canada

University of Manitoba

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References

[ChCa03] V. Cheung and K. Cannons, Signal Classification through Multifractal Analysis and Neural Networks. BSc Thesis. Dept. of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, 106 pp., 2003. [Kins94]

W. Kinsner, “Batch and real-time computation of a fractal dimension

based on variance of a time series,” Technical Report, DEL94-6; UofM; June 15, 1994, (v+17) 22 pp. [Koho84] T. Kohonen, Self-Organization and Associative Memory. Berlin: Springer-Verlag, 1984. [Mast94] T. Masters, Signal and Image Processing with Neural Networks: A C++ Sourcebook. New York, NY: John Wiley & Sons, Inc., 1994. [Spec88] D.F. Specht, “Probabilistic neural networks for classification, mapping, or associative memory”, IEEE International Conference on Neural Networks, vol. 1, pp. 525-532, July 1988.