Subspace Clustering

• Introduction
• Notation and problem formulation
  • Problem formulation
• Algorithms
• Matrix Factorization based algorithms
• K-plane clustering
• K-subspace clustering
• Expectation-Maximization for K-subspaces
• Generalized PCA
  • Representing the union of subspaces with a set of homogeneous polynomials
  • Fitting polynomials to data
  • Subspaces by polynomial differentiation
• Sparse Subspace Clustering (SSC)
• SSC by Basis Pursuit
  • Optimization Program Formulations
  • Hands-on SSC-BP with Synthetic Data
• ADMM for Computing Subspace Preserving Representations
  • Linear Subspaces
  • Affine Subspaces
  • Linear Subspaces with Noise
  • Linear Subspaces with Noise and Outliers
  • Affine Subspaces with Noise
  • Affine Subspaces with Noise and Outliers
• SSC by Orthogonal Matching Pursuit
  • Hands-on with SSC-OMP
  • SSC-OMP Implementations
• Motion Segmentation
  • Modeling structure from motion for single object
  • Solving the structure from motion problem
  • Modeling motion for multiple objects
• Synthetic Data Generation
  • Random Subspaces
  • Principal Angles
  • Uniformly Distributed Points in Space
  • Uniformly Distributed Points in Subspaces
• Performance Metrics for Sparse Subspace Clustering
  • Hands-on with Subspace Preservation Metrics
• Sparse Subspace Clustering with MNIST Digits
  • MNIST Dataset
  • SSC-OMP on MNIST Dataset
  • SSC-OMP on MNIST Benchmarks
  • Benchmarks on SSC-MC-OMP
• Yale Faces Dataset
• Sparse Subspace Clustering by Multiple Candidates OMP
  • Algorithm
  • Benchmarks