Machine Learning

5.

Unsupervised Learning

5.1.

Clustering Algorithms

5.1.1.

K-Means Clustering

5.1.1.1.

Algorithm Steps

5.1.1.1.1.

5.1.1.1.2.

Assignment Step

5.1.1.1.3.

5.1.1.1.4.

5.1.1.2.

Centroid Initialization Methods

5.1.1.2.1.

Random Initialization

5.1.1.2.2.

5.1.1.2.3.

5.1.1.3.

Determining Optimal k

5.1.1.3.1.

5.1.1.3.2.

Silhouette Analysis

5.1.1.3.3.

5.1.1.3.4.

Information Criteria

5.1.1.4.

Variants of K-Means

5.1.1.4.1.

Mini-Batch K-Means

5.1.1.4.2.

5.1.1.4.3.

5.1.1.5.

Limitations and Assumptions

5.1.1.5.1.

Spherical Clusters

5.1.1.5.2.

Similar Cluster Sizes

5.1.1.5.3.

Sensitivity to Initialization

5.1.2.

Hierarchical Clustering

5.1.2.1.

Agglomerative Clustering

5.1.2.1.1.

Bottom-Up Approach

5.1.2.1.2.

Linkage Criteria

5.1.2.1.2.1.

5.1.2.1.2.2.

Complete Linkage

5.1.2.1.2.3.

Average Linkage

5.1.2.1.2.4.

5.1.2.1.3.

Algorithm Steps

5.1.2.2.

Divisive Clustering

5.1.2.2.1.

Top-Down Approach

5.1.2.2.2.

Splitting Strategies

5.1.2.3.

5.1.2.3.1.

5.1.2.3.2.

5.1.2.3.3.

5.1.2.4.

Distance Metrics

5.1.2.4.1.

Euclidean Distance

5.1.2.4.2.

Manhattan Distance

5.1.2.4.3.

Cosine Similarity

5.1.2.5.

Determining Number of Clusters

5.1.2.5.1.

Dendrogram Analysis

5.1.2.5.2.

Inconsistency Coefficient

5.1.3.

Density-Based Clustering

5.1.3.1.

5.1.3.1.1.

5.1.3.1.2.

5.1.3.1.3.

5.1.3.1.4.

Density Reachability

5.1.3.1.5.

Parameter Selection

5.1.3.1.5.1.

5.1.3.1.5.2.

5.1.3.1.6.

Advantages and Limitations

5.1.3.2.

5.1.3.2.1.

Ordering Points

5.1.3.2.2.

Reachability Distance

5.1.3.2.3.

5.1.3.3.

5.1.3.3.1.

Kernel Density Estimation

5.1.3.3.2.

5.1.4.

Model-Based Clustering

5.1.4.1.

Gaussian Mixture Models

5.1.4.1.1.

Mixture Components

5.1.4.1.2.

5.1.4.1.3.

Model Selection

5.1.4.2.

Expectation-Maximization

5.1.4.2.1.

5.1.4.2.2.

5.1.4.2.3.

5.1.5.

Clustering Evaluation

5.1.5.1.

Internal Measures

5.1.5.1.1.

Silhouette Score

5.1.5.1.2.

Calinski-Harabasz Index

5.1.5.1.3.

Davies-Bouldin Index

5.1.5.2.

External Measures

5.1.5.2.1.

Adjusted Rand Index

5.1.5.2.2.

Normalized Mutual Information

5.1.5.2.3.

Fowlkes-Mallows Index

5.2.

Dimensionality Reduction

5.2.1.

Principal Component Analysis

5.2.1.1.

Covariance Matrix

5.2.1.2.

Eigenvalue Decomposition

5.2.1.3.

Principal Components

5.2.1.3.1.

First Principal Component

5.2.1.3.2.

Subsequent Components

5.2.1.3.3.

5.2.1.4.

Explained Variance

5.2.1.4.1.

5.2.1.4.2.

Cumulative Variance

5.2.1.4.3.

5.2.1.5.

Dimensionality Selection

5.2.1.5.1.

Kaiser Criterion

5.2.1.5.2.

Cumulative Variance Threshold

5.2.1.5.3.

Cross-Validation

5.2.1.6.

PCA Applications

5.2.1.6.1.

Data Compression

5.2.1.6.2.

Noise Reduction

5.2.1.6.3.

5.2.1.7.

5.2.1.7.1.

Linear Assumptions

5.2.1.7.2.

Interpretability

5.2.2.

Factor Analysis

5.2.2.1.

5.2.2.2.

Factor Loadings

5.2.2.3.

5.2.2.4.

5.2.2.5.

Rotation Methods

5.2.2.5.1.

5.2.2.5.2.

5.2.3.

Independent Component Analysis

5.2.3.1.

Statistical Independence

5.2.3.2.

Non-Gaussian Sources

5.2.3.3.

FastICA Algorithm

5.2.3.4.

5.2.3.4.1.

Signal Separation

5.2.3.4.2.

Feature Extraction

5.2.4.

Non-Linear Dimensionality Reduction

5.2.4.1.

5.2.4.1.1.

Stochastic Neighbor Embedding

5.2.4.1.2.

5.2.4.1.3.

Perplexity Parameter

5.2.4.1.4.

Optimization Process

5.2.4.1.5.

Visualization Applications

5.2.4.2.

5.2.4.2.1.

Uniform Manifold Approximation

5.2.4.2.2.

Topological Structure

5.2.4.2.3.

Hyperparameters

5.2.4.3.

Manifold Learning

5.2.4.3.1.

Locally Linear Embedding

5.2.4.3.2.

5.2.4.3.3.

Laplacian Eigenmaps

5.2.5.

Autoencoders for Dimensionality Reduction

5.2.5.1.

Encoder-Decoder Architecture

5.2.5.2.

Bottleneck Layer

5.2.5.3.

Reconstruction Loss

5.2.5.4.

Variational Autoencoders

5.3.

Association Rule Learning

5.3.1.

Market Basket Analysis

5.3.1.1.

Transactions and Items

5.3.1.2.

5.3.1.3.

Association Rules

5.3.2.

Apriori Algorithm

5.3.2.1.

Frequent Itemset Generation

5.3.2.2.

Candidate Generation

5.3.2.3.

Support Counting

5.3.2.4.

Rule Generation

5.3.2.5.

Computational Complexity

5.3.3.

FP-Growth Algorithm

5.3.3.1.

FP-Tree Construction

5.3.3.2.

Conditional Pattern Bases

5.3.3.3.

Efficiency Improvements

5.3.4.

Evaluation Metrics

5.3.4.1.

5.3.4.1.1.

5.3.4.2.

5.3.4.2.1.

5.3.4.3.

5.3.4.3.1.

5.3.4.4.

5.3.4.4.1.

5.3.4.5.

Kulczynski Measure

5.3.4.6.

5.3.5.

5.3.5.1.

Recommendation Systems

5.3.5.2.

5.3.5.3.

Inventory Management

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6. Model Evaluation and Validation