Vector Search and Embeddings

  1. Similarity Metrics and Distance Functions
    1. Understanding Similarity in Vector Spaces
      1. Geometric Interpretation of Similarity
        1. Relationship Between Distance and Similarity
          1. Choosing Appropriate Metrics
          2. Cosine Similarity
            1. Mathematical Definition
              1. Geometric Interpretation
                1. Normalization Properties
                  1. Use Cases in Text and Image Search
                  2. Euclidean Distance
                    1. L2 Norm Calculation
                      1. Properties and Characteristics
                        1. Sensitivity to Dimensionality
                          1. Applications and Limitations
                          2. Manhattan Distance
                            1. L1 Norm Calculation
                              1. Robustness to Outliers
                                1. Use Cases and Applications
                                2. Dot Product Similarity
                                  1. Relationship to Cosine Similarity
                                    1. Magnitude Sensitivity
                                      1. Computational Efficiency
                                      2. Other Distance Metrics
                                        1. Hamming Distance
                                          1. Jaccard Similarity
                                            1. Minkowski Distance
                                              1. Mahalanobis Distance
                                              2. Metric Selection Considerations
                                                1. Data Characteristics
                                                  1. Application Requirements
                                                    1. Computational Constraints
                                                      1. Interpretability Needs

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                                                    3. Data Representation: Embeddings

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                                                    5. Nearest Neighbor Search Algorithms