Machine Learning Fundamentals

  1. Unsupervised Learning: Clustering
    1. Concept of Clustering: Grouping Similar Data Points
      1. Use Cases and Examples
        1. Customer Segmentation
          1. Gene Sequencing
            1. Image Segmentation
              1. Social Network Analysis
            2. K-Means Clustering
              1. The Algorithm
                1. Initialization
                  1. Random Initialization
                    1. K-Means++ Initialization
                      1. Multiple Runs
                      2. Assignment Step
                        1. Distance Calculation
                          1. Cluster Assignment
                          2. Update Step
                            1. Centroid Calculation
                              1. Mean Computation
                              2. Convergence Criteria
                                1. Centroid Stability
                                  1. Maximum Iterations
                                    1. Tolerance Thresholds
                                  2. Choosing the Number of Clusters (k)
                                    1. The Elbow Method
                                      1. Within-Cluster Sum of Squares
                                        1. Elbow Point Detection
                                        2. Silhouette Score
                                          1. Silhouette Coefficient
                                            1. Average Silhouette Width
                                            2. Gap Statistic
                                              1. Information Criteria
                                              2. Limitations of K-Means
                                                1. Spherical Cluster Assumption
                                                  1. Sensitivity to Initialization
                                                    1. Outlier Sensitivity
                                                      1. Fixed Number of Clusters
                                                    2. Hierarchical Clustering
                                                      1. Agglomerative Clustering
                                                        1. Bottom-Up Approach
                                                          1. Single Point Start
                                                            1. Iterative Merging
                                                            2. Linkage Criteria
                                                              1. Single Linkage
                                                                1. Complete Linkage
                                                                  1. Average Linkage
                                                                    1. Ward Linkage
                                                                  2. Divisive Clustering
                                                                    1. Top-Down Approach
                                                                      1. Recursive Splitting
                                                                        1. Computational Complexity
                                                                      2. Dendrograms
                                                                        1. Interpreting Dendrograms
                                                                          1. Tree Structure
                                                                            1. Height Interpretation
                                                                              1. Cluster Identification
                                                                              2. Cutting Dendrograms
                                                                                1. Height-Based Cuts
                                                                                  1. Number-Based Cuts
                                                                              3. Other Clustering Algorithms
                                                                                1. DBSCAN
                                                                                  1. Density-Based Clustering
                                                                                    1. Core Points and Border Points
                                                                                      1. Noise Detection
                                                                                        1. Parameter Selection
                                                                                        2. Mean Shift
                                                                                          1. Mode-Seeking Algorithm
                                                                                            1. Bandwidth Selection
                                                                                              1. Non-Parametric Approach
                                                                                              2. Gaussian Mixture Models
                                                                                                1. Probabilistic Clustering
                                                                                                  1. Expectation-Maximization
                                                                                                    1. Soft Clustering
                                                                                                    2. Spectral Clustering
                                                                                                      1. Graph-Based Approach
                                                                                                        1. Eigenvalue Decomposition
                                                                                                          1. Non-Convex Clusters

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                                                                                                      5. Supervised Learning: Classification

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                                                                                                      7. Unsupervised Learning: Dimensionality Reduction