4. Unsupervised learning

• 4.1. Gaussian mixture models
  • 4.1.1. Expectation-maximization
  • 4.1.2. Variational inference
  • 4.1.3. The Dirichlet Process
    • 4.1.3.1. GMM classifier
    • 4.1.3.2. Variational Gaussian mixtures: VBGMM classifier
    • 4.1.3.3. Infinite Gaussian mixtures: DPGMM classifier
• 4.2. Manifold learning
  • 4.2.1. Introduction
  • 4.2.2. Isomap
    • 4.2.2.1. Complexity
  • 4.2.3. Locally Linear Embedding
    • 4.2.3.1. Complexity
  • 4.2.4. Modified Locally Linear Embedding
    • 4.2.4.1. Complexity
  • 4.2.5. Hessian Eigenmapping
    • 4.2.5.1. Complexity
  • 4.2.6. Local Tangent Space Alignment
    • 4.2.6.1. Complexity
  • 4.2.7. Tips on practical use
• 4.3. Clustering
  • 4.3.1. K-means
    • 4.3.1.1. Mini Batch K-Means
  • 4.3.2. Affinity propagation
  • 4.3.3. Mean Shift
  • 4.3.4. Spectral clustering
  • 4.3.5. Hierarchical clustering
    • 4.3.5.1. Adding connectivity constraints
  • 4.3.6. DBSCAN
  • 4.3.7. Clustering performance evaluation
    • 4.3.7.1. Inertia
      • 4.3.7.1.1. Presentation and usage
      • 4.3.7.1.2. Advantages
      • 4.3.7.1.3. Drawbacks
    • 4.3.7.2. Ajusted Rand index
      • 4.3.7.2.1. Presentation and usage
      • 4.3.7.2.2. Advantages
      • 4.3.7.2.3. Drawbacks
      • 4.3.7.2.4. Mathematical formulation
    • 4.3.7.3. Homogeneity, completeness and V-measure
      • 4.3.7.3.1. Presentation and usage
      • 4.3.7.3.2. Advantages
      • 4.3.7.3.3. Drawbacks
      • 4.3.7.3.4. Mathematical formulation
• 4.4. Decomposing signals in components (matrix factorization problems)
  • 4.4.1. Principal component analysis (PCA)
    • 4.4.1.1. Exact PCA and probabilistic interpretation
    • 4.4.1.2. Approximate PCA
    • 4.4.1.3. Kernel PCA
    • 4.4.1.4. Sparse Principal Components Analysis (SparsePCA and MiniBatchSparsePCA)
  • 4.4.2. Dictionary Learning
    • 4.4.2.1. Generic dictionary learning
    • 4.4.2.2. Mini-batch dictionary learning
  • 4.4.3. Independent component analysis (ICA)
  • 4.4.4. Non-negative matrix factorization (NMF or NNMF)
• 4.5. Covariance estimation
  • 4.5.1. Empirical covariance
  • 4.5.2. Shrunk Covariance
    • 4.5.2.1. Basic shrinkage
    • 4.5.2.2. Ledoit-Wolf shrinkage
    • 4.5.2.3. Oracle Approximating Shrinkage
• 4.6. Hidden Markov Models