Machine Learning Fundamentals

  1. Unsupervised Learning: Dimensionality Reduction
    1. The "Curse of Dimensionality"
      1. Impact on Model Performance
        1. Distance Concentration
          1. Sparsity Issues
            1. Computational Complexity
            2. Visualization Challenges
              1. High-Dimensional Plotting
                1. Interpretation Difficulties
                2. Sample Size Requirements
                  1. Exponential Growth
                    1. Data Sparsity
                  2. Principal Component Analysis (PCA)
                    1. Core Idea: Capturing Maximum Variance
                      1. Variance Maximization
                        1. Orthogonal Components
                          1. Linear Transformation
                          2. Principal Components
                            1. Eigenvectors and Eigenvalues
                              1. Component Ordering
                                1. Component Interpretation
                                2. Explained Variance
                                  1. Variance Ratios
                                    1. Cumulative Variance
                                      1. Scree Plots
                                      2. Steps in PCA
                                        1. Data Standardization
                                          1. Covariance Matrix Computation
                                            1. Eigendecomposition
                                              1. Component Selection
                                                1. Data Transformation
                                                2. Interpreting PCA Results
                                                  1. Loading Vectors
                                                    1. Biplot Analysis
                                                      1. Component Meaning
                                                      2. Limitations of PCA
                                                        1. Linear Assumptions
                                                          1. Interpretability Loss
                                                            1. Outlier Sensitivity
                                                          2. Other Dimensionality Reduction Techniques
                                                            1. t-SNE
                                                              1. Non-Linear Reduction
                                                                1. Neighborhood Preservation
                                                                  1. Visualization Focus
                                                                    1. Perplexity Parameter
                                                                    2. Linear Discriminant Analysis (LDA)
                                                                      1. Supervised Reduction
                                                                        1. Class Separation
                                                                          1. Fisher's Linear Discriminant
                                                                          2. Independent Component Analysis (ICA)
                                                                            1. Statistical Independence
                                                                              1. Signal Separation
                                                                                1. Non-Gaussian Assumptions
                                                                                2. UMAP
                                                                                  1. Uniform Manifold Approximation
                                                                                    1. Topology Preservation
                                                                                      1. Scalability Advantages
                                                                                      2. Autoencoders
                                                                                        1. Neural Network Approach
                                                                                          1. Encoder-Decoder Architecture
                                                                                            1. Non-Linear Mappings

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                                                                                        6. Unsupervised Learning: Clustering

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                                                                                        8. Fundamentals of Model Performance and Improvement