**B. Kégl
"Principal curves: learning, design, and
applications"
**

Concordia University

**Software
description, ****Java
classes (zip)**, **source
code (zip)**

**Contents (with PDF files of Chapters)**

1.1 Unsupervised Learning

1.1.1 The Formal Model

1.1.2 Areas of Applications

1.1.3 The Simplest Case

1.1.4 A More Realistic Model

1.2 Principal Curves

1.3 Outline of the Thesis

**2 Vector Quantization and Principal Component
Analysis **

2.1 Vector Quantization

2.1.1 Optimal Vector Quantizer

2.1.2 Consistency and Rate of Convergence

2.1.3 Locally Optimal Vector Quantizer

2.1.4 Generalized Lloyd Algorithm

2.2 Principal Component Analysis

2.2.1 One-Dimensional Curves

2.2.2 Principal Component Analysis

2.2.3 Properties of the First Principal Component Line

2.2.4 A Fast PCA Algorithm for Data
Sets

**3 Principal Curves and Related Areas**

3.1 Principal Curves with Self-Consistency Property

3.1.1 The HS Definition

3.1.2 The HS Algorithm for Data Sets

3.1.3 The Bias of the HS Algorithm

3.2 Alternative Definitions and Related Concepts

3.2.1 Alternative Definitions of Principal Curves

3.2.2 The Self-Organizing Map

3.2.3 Nonlinear Principal Component Analysis

**4 Learning Principal Curves with a Length Constraint**

4.1 Principal Curves with a Length Constraint

4.2 Learning Principal Curves

**5 The Polygonal Line Algorithm**

5.1 The Polygonal Line Algorithm

5.1.1 Stopping Condition

5.1.2 The Curvature Penalty

5.1.3 The Penalty Factor

5.1.4 The Projection Step

5.1.5 The Vertex Optimization Step

5.1.6
Convergence of the Inner

5.1.7 Adding a New Vertex

5.1.8 Computational Complexity

5.1.9 Remarks

5.2 Experimental Results

5.2.1 Comparative Experiments

5.2.2 Quantitative Analysis

5.2.3 Failure Modes

**6 Application of Principal Curves to Hand-Written
Character Skeletonization**

6.1 Related Work

6.1.1 Applications and Extensions of the HS Algorithm

6.1.2 Piecewise Linear Approach to Skeletonization

6.2 The Principal Graph Algorithm

6.2.1 Principal Graphs

6.2.2 The Initialization Step

6.2.3 The Restructuring Step

6.3 Experimental Results

6.3.1 Skeletonizing Isolated Digits

6.3.2 Skeletonizing and Compressing Continuous Handwriting

**PDF file “Principal curves:
learning, design, and applications” ~4M**

For more information: http://www.iro.umontreal.ca/~kegl/research/pcurves/