Recommender Systems

Organizes the theoretical correspondence between the vector field operator div·grad = Δ and the Laplacian matrix in graph theory, as a personal reference note.

Explains the theory of low-pass filters in graph signal processing based on eigenvalue decomposition and eigenvectors, with a Python implementation.

Explains the theory of the graph Laplacian and its eigenvalues, introduces the Graph Fourier Transform (GFT), and its Python implementation.

Compiles useful matrix formulas from the Matrix Cookbook covering transpose, trace, determinant, differentiation, and the Woodbury inversion identity.

Explains matrix cofactors and cofactor expansion with worked examples, and implements determinant calculation via cofactors in Python.

Summarizes the basic theory and Python implementation of GNNs (Graph Neural Networks) and GCNs (Graph Convolutional Networks), a specific type of GNN.

Explains five matrix decompositions—Cholesky, LU, QR, spectral, and singular value decomposition—with theory and Python implementation examples.

Explains the mathematical background and algorithms of DeepWalk and Node2Vec, random-walk graph embedding methods, with Python examples.

Explains classical random walks and adjacency matrices, focusing on PageRank and Personalized PageRank, with formulas and Python code examples.