Introduction | A synthetic dataset (true rank = 3) | 1. Integrated diagnostics: nmfkc.rank | 2. Cross-validation: nmfkc.ecv and nmfkc.bicv | 3. Clustering stability: nmfkc.consensus | 4. Bayesian ARD: nmfkc.ard | Summary: did they recover the true rank? | How the clustering evolves with rank | Remarks

Introduction | A synthetic network (stochastic block model, 3 communities) | Soft community detection with nmfkc.net | Did it recover the known communities? | Visualising the result | Network diagram (Graphviz DOT): soft vs. hard | How many communities? nmfkc.net.rank | Remarks

Introduction | 1. Data Preparation | 2. Rank Selection (Number of Topics) | 3. Standard NMF | Interpreting Topics (Keywords) | 4. Kernel NMF: Temporal Topic Evolution | Optimizing the Kernel Parameter | Fitting Kernel NMF | Visualization: Standard vs Kernel NMF

Overview | 1. Load and preprocess data | 1.1 Construct exogenous variables | 1.2 Nonnegative normalization | 2. Split into endogenous and exogenous blocks | 3. Baseline NMF model | 3.5 Hyperparameter Tuning for Sparsity (Optional) | 4. NMF-FFB estimation | 5. Diagnostics | 6. Visualization

Introduction | How it works | Example 1: The Iris Dataset (Linear vs. Kernel) | 1. Data Preparation | Step 1: Linear NMF-LAB (Focus on Interpretability) | Step 2: Kernel NMF-LAB (Focus on Performance) | Visualization: Class Prototypes (Basis X) | Example 2: The Palmer Penguins Dataset | 2. Model Fitting | 3. Visualizing "Soft" Classification | 4. Evaluation

Introduction | Example 1: Univariate Autoregression with AirPassengers | 1. Data Preparation | 2. Model Selection (Lag Order) | 3. Model Fitting | 4. Forecasting | Example 2: Vector Autoregression with Canada Dataset | 2. Model Fitting | 3. Latent Structure & Causal Graph

Introduction | Why Mixed Effects? | Key Features | 1. Data: Orthodont (Longitudinal Growth) | 1.1 Prepare the Observation Matrix Y | 1.2 Prepare the Covariate Matrix A | 2. Selecting dfU Cap Rate | Interpreting the Scan | 3. Fitting the NMF-RE Model | 3.1 Model Summary | Understanding the Output | 4. Visualization | Interpreting the Plot | 5. Examining Learned Components | 5.1 Basis Matrix X | 5.2 Coefficient Matrix $\Theta$ | 5.3 Random Effects U | 6. Model Diagnostics | 6.1 Convergence | 6.2 Residual Analysis | 7. Comparison: With and Without Random Effects | Separated Inference with nmfre.inference() | Visualization with nmfkc.DOT() | Summary

Introduction | 1. Basic Usage: Analyzing Movie Ratings | Creating the Data | Running NMF | Interpretation | 1. Basis Matrix X: User Preferences | 2. Coefficient Matrix B: Movie Genres | 2. Visualization | Convergence Plot | Visualizing the Reconstruction | 3. Handling Missing Values (Imputation) | Creating Data with Missing Values | Running NMF with NAs | Predicting the Unknown Rating | Summary