Evolutionary Feature Extraction for SAR Air to Ground ATR Statistical Approach

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Evolutionary Feature Extraction for SAR Air to
Ground Moving Target Recognition a Statistical
Approach
Evolving Hardware Dr. Janusz StarzykOhio
University
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Neural Network Data Classification

• Concept of Logic Brain
• Random learning data generation
• Multiple space classification of data
• Feature function extraction
• Dynamic selectivity strategy
• Training procedure for data identification
• FPGA implementation for fast training process

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Neural Network Data Classification

Abdulqadir Alaqeeli, and Jing Pang

• Concept of Logic Brain
• Threshold setup converts analog to digital
  world
• Logic Brain is possible based on artificial
  neural
• network
• Random learning data generation
• Gaussian distribution random multiple dimension
• data generation
• Half data sets prepared for learning procedure
• Another half used later for training procedure

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Neural Network Data Classification

• Multiple space classification of data
• Each space can be represented by a set of
  minimum base vectors
• Feature function extraction and dynamic selecting
  strategy
• Conditional entropy extracts information in
  each
• subspace
• Different combinations of base vectors compose
  the redundant sets of new subspace
• ? expansion strategy
• Minimum function selection
• ? shrinking strategy

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Neural Network Data Classification

• FPGA implementation for fast training process
• Learning results are saved on board
• Testing data sets are generated on board and
  sent
• through the artificial neural network
  generated on
• board to test the successful data
  classification rate
• The results are displayed on board
• Promising application
• Especially useful for feature extraction of
  large data sets
• Catastrophic circuit fault detection

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Information Index Background

• A priori class probabilities are known
• Entropy measure based on conditional
  probabilities

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Information Index Background

• P1 and P2 and a priori class probabilities
• P1w and P2w are conditional probabilities of
  correct
• classification for each class
• P12w and P21w are conditional probabilities of
  misclassification given a test signal
• P1w , P2w, P12w and P21w are calculated using
  Bayesian estimates of their probability density
  functions

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Information Index Background

• probability density functions of P1w , P2w, P12w,
  P21w

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Direct Integration
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Monte Carlo Integration
pdf
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Information Index probability density functions
P2w
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Information Index weighted pdfs
P2w
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Information Index Monte Carlo Integration

• To integrate the probability density function
• generate random points xi with pdf1
• weight generated points according to
• estimate the conditional probability P1w using

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Information Index and Probability of
Misclassification
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Standard Deviation of Information in MC Simulation
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Normalized Standard Deviation of Information
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Information Index Status

• MIIFS was generalized to continuous distributions
• N-dimensional information index was developed
• Efficient N-dimensional integration was used
• Information error analysis was performed
• Information index can be used with non
  Gaussian distributions
• For small training sets and low information index
  information error is larger than information

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Optimum Transformation Background

• Principal Component Analysis (PCA) based on
  Mahalanobis distance suffers from scaling
• PCA assumes Gaussian distributions and estimates
  covariance matrices and mean values
• PCA is sensitive to outliers
• Wavelets provide compact data representation and
  improve recognition
• Improvement shows no statistically significant
  difference in recognition for different wavelets
• Need for a specialized transformation

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Optimum Transformation Haar Wavelet

• Example

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Optimum Transformation Haar Wavelet

• Repeat average and difference log2(n) times

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Optimum Transformation Haar Wavelet

• Waveform interpretation

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Optimum Transformation Haar Wavelet

• Matrix interpretation
• bWa where

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Optimum Transformation Haar Wavelet

• Matrix interpretation for the class of signals
  BWA
• where A is (n x m) input signal matrix
• Selection of n best coefficients performed using
  the information index Bs1S1WA
• where S1 is (n x nlog2(n)) selection matrix

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Optimum Transformation Evolutionary Iterations

• Iterating on the selected result Bs2S2W
  Bs1
• where S2 is a selection matrix or Bs2S2W
  S1W A
• after k iterations Bsk SkW ... S2W
  S1W A
• So, the optimized transformation matrix T
  SkW ... S2W S1W
• can be obtained from the Haar wavelet

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Optimum Transformation Evolutionary Iterations

• Learning with the evolved features

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Optimum Transformation Evolutionary Iterations

• Waveform interpretation of T rows

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Optimum Transformation Evolutionary Iterations

• Mean values and the evolved transformation

Original Signals and the evolved transformation
1.5
1
0.5
Signal Value
0
-0.5
-1
-1.5
0
20
40
60
80
100
120
140
Bin Index
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Two Class Training

• Training on HRR signals 17o depression angle
  profiles of BMP2 and BTR60

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Wavelet-Based Reconfigurable FPGA for
Classification
t
window
8bit
8bit
Sample 1
1
Haar-Wavelet Transform
N.N.
input signal is recognized
Sample m
k
8bit
8bit
Note k ? m
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Block Diagram of The Parallel Architecture
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Simplified Block Diagram of The Serial
Architecture
First the Blue Second the Green
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RAM-Based Wavelet
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The Processing Element
10 2 11 X
9 6 5 X
9 9 5 X
20 8 10 2 11
-8 9 XX
0 0 1 0 1
8 10 2 11
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Results For One Iteration of Haar Wavelet

• For 8 samples
• Parallel arch. 120 CLBs, 128 IOBs, 58ns.
• Serial arch. 98 CLBs, 72 IOBs, 148ns.
• Parallel Arch. wins for larger number of
  samples.
• For 16 samples
• Parallel arch. 320 CLBs, 256 IOBs, 233ns.
• RAM-Based arch. 136 CLBs, 16 IOBs, 1?s.
• RAM-Based Arch. Wins since 1?s is not so slow.
• --------------------------------------------------
  ----------
• These values increase very fast when the of
  samples increases, and the delay becomes
  extremely higher.

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Reconfigurable Haar-Wavelet-Based Architecture
PE
PE
PE
PE
Data
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Test Results

• Testing on HRR signals 15o depression angle
  profiles of BMP2 and BTR60
• With 15 features selected correct classification
  for BMP2 data is 69.3 and for BTR60 is 82.6
• Comparable results in SHARP Confusion Matrix for
  BMP2 data is 56.7 and for BTR60 is 67

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Problem Issues

• BTR60 signals with 17o and 15o depression angles
  do not have compatible statistical distributions

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Problem Issues

• BMP2 and BTR60 signal distributions are not
  Gaussian

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Work Completed

• Information index and its properties
• Multidimensional MC integration
• Information as a measure of learning quality
• Information error
• Wavelets and their effect on pattern recognition
• Haar wavelet as a linear matrix operator
• Evolution of the Haar wavelet
• Statistical support for classification

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Recommendations and Future Work

• Training Data must represent a statistical sample
  of all signals not a hand picked subset
• Probability density functions will be
  approximated using parametric or NN approach
• Information measure will be extended to k-class
  problems
• Training and test will be performed on 12 class
  data
• Dynamic clustering will prepare decision tree
  structure
• Hybrid, evolutionary classifier will be developed