Contents

• 1. Introduction
  • 1.1 Motivation
  • 1.2 Outline and contributions
  • 1.3 Why using robot models?
  • 1.4 The sensorimotor approach
    • 1.4.1 Limitations of symbolic representations
    • 1.4.2 Experimental evidence
    • 1.4.3 Perception based on sensorimotor models
  • 1.5 Learning of sensorimotor models
    • 1.5.1 Neural networks
    • 1.5.2 Internal models
    • 1.5.3 Feed-forward networks as internal models
    • 1.5.4 Recurrent neural networks as internal models
    • 1.5.5 Self-organizing maps
    • 1.5.6 Parametrized self-organizing maps
  
  
• 2. Modeling of data distributions
  • 2.1 Principal component analysis (PCA)
    • 2.1.1 Neural networks for PCA
    • 2.1.2 Probabilistic PCA
  • 2.2 Vector quantization
    • 2.2.1 K-means
    • 2.2.2 Soft-clustering
    • 2.2.3 Deterministic annealing
    • 2.2.4 Neural Gas
  • 2.3 Mixture of local PCA
    • 2.3.1 Gaussian mixture models
    • 2.3.2 Mixture of probabilistic PCA
  • 2.4 Kernel PCA
    • 2.4.1 Feature extraction
    • 2.4.2 Centering in feature space
    • 2.4.3 Common kernel functions
  
  
• 3. Mixture of local PCA
  • 3.1 Motivation for local PCA
  • 3.2 Extension of Neural Gas to local PCA
    • 3.2.1 Algorithm
    • 3.2.2 Alternative distance measure
    • 3.2.3 Simulations
  • 3.3 Extension of the mixture of probabilistic PCA
    • 3.3.1 Algorithm
    • 3.3.2 Simulations
  • 3.4 Digit classification
    • 3.4.1 Methods
    • 3.4.2 Results
  • 3.5 Discussion
  
  
• 4. Abstract recurrent neural networks
  • 4.1 Motivation
    • 4.1.1 Why abstract recurrent neural networks?
    • 4.1.2 Potential fields and local minima
  • 4.2 Recall algorithm
  • 4.3 Function approximation on synthetic data
  • 4.4 Image Completion
    • 4.4.1 Windows from natural scenes
    • 4.4.2 Faces
  • 4.5 Kinematic arm model
    • 4.5.1 Methods
    • 4.5.2 Results
  • 4.6 Dependence on the number of input dimensions
  • 4.7 Discussion
  
  
• 5. Kernel PCA for pattern association
  • 5.1 Motivation
  • 5.2 Pattern association algorithm
    • 5.2.1 Spherical potential
    • 5.2.2 Cylindrical potential
    • 5.2.3 Recall
  • 5.3 Experiments
    • 5.3.1 Methods
    • 5.3.2 Results
  • 5.4 Discussion
  
  
• 6. Visuomotor model for a robot arm
  • 6.1 Visual guided grasping
    • 6.1.1 Related work
    • 6.1.2 High-dimensional image data
  • 6.2 Methods
    • 6.2.1 Robot setup
    • 6.2.2 Data collection
    • 6.2.3 Image processing
    • 6.2.4 Tuning curves
    • 6.2.5 Training
    • 6.2.6 Recall
  • 6.3 Results
  • 6.4 Discussion
  
  
• 7. Forward model for a mobile robot
  • 7.1 Introduction
    • 7.1.1 Motivation
    • 7.1.2 Tasks
  • 7.2 Methods
    • 7.2.1 Robot setup
    • 7.2.2 Data collection
    • 7.2.3 Image processing
    • 7.2.4 Forward model: Multi-layer perceptron
    • 7.2.5 Forward model: Abstract recurrent neural network
    • 7.2.6 Performance outside the training domain
    • 7.2.7 Anticipation performance
    • 7.2.8 Goal-directed movements
    • 7.2.9 Mental transformation
  • 7.3 Results
    • 7.3.1 Anticipation with the multi-layer perceptron
    • 7.3.2 Anticipation with the abstract recurrent neural network
    • 7.3.3 Performance outside the training domain
    • 7.3.4 Goal-directed movements
    • 7.3.5 Mental transformation
  • 7.4 Data outside the training domain
  • 7.5 Discussion
  
  
• 8. Conclusions
  • 8.1 Data collection and preprocessing
  • 8.2 Approximation of the data distribution
  • 8.3 Pattern association
  • 8.4 Results compared to other methods
  • 8.5 Perception
  • 8.6 Future direction
  
  
• A. Statistical tools
  • A.1 Bayes' theorem
  • A.2 Maximum likelihood
  • A.3 Iterative mean
  
  
• B. Algorithms
  • B.1 Power method with deflation
  • B.2 Kernel PCA speed-up
  • B.3 Quality measure for a potential field
  
  
• C. Proofs
  • C.1 Probabilistic PCA and error measures
  • C.2 The eigenvalue equation in kernel PCA
  • C.3 Estimate of error accumulation
  • C.4 Contraction of input vectors
  
  
• D. Database of hand-written digits
• E. Notation and Symbols
• Bibliography
• About this document ...