Efficient Computation of Recursive Principal Component Analysis

Lecture slides:

• Efficient Computation of Recursive Principal Component Analysis for Structured Input
• Outline
• What are structured domains and why are they important?
• Examples of Structured Data
• Vectorial Data: Principal Component Analysis
• More Complex Objects
• Principal Component Analysis of Sequences and Trees ?
• The Strategy
• Sequences
• Step 1: Sufficient Conditions
• Step 2: Extended State Space
• Step 3: Reduce
• Step 4: Compose
• Recursive PCA for Trees
• Graphs
• The linear system for graphs
• Computational Problems
• Some Basic Observations and Their Exploitation
• Three Techniques
• Minimal State Space
• Minimal DAG
• QR Decomposition
• Datasets for Experiments
• Experiments Results
• Summary
• Impact on a Regression Task: some preliminary results

Author: Alessandro Sperduti, Dipartimento Di Matematica Pura Ed Applicata, Università Degli Studi Di Padova