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Pseudo-inverse and projection matrices Pseudo-inverse and projection matrices are also often used in recommendation systems, so I’ll make a note of them. github The file in jupyter notebook format is here . google colaboratory If you want to run it in google colaboratory here Author’s environment The author’s OS is macOS, and the options are different from Linux and Unix commands. !sw_vers ProductName: Mac OS X ProductVersion: 10. …

Singular value decomposition and low-rank approximation I am going to summarize my knowledge of linear algebra, which is mainly needed to understand recommendation systems. The user-item matrices (preference matrices) used in recommendation systems are often discussed under the assumption that low-rank approximations hold. It is based on the implicit assumption that users can often be classified into a finite number of clusters. For example, even if there are one million users of all book e-commerce sites, it is possible to categorize them to some extent, such as users who often buy programming books, users who buy math books, users who buy medical books, and users who buy weekly magazines. …

PageRank and Google matrix I recently had to look up PageRank and Google Matrices, so I’ll try to summarize them for your notes. The textbook is as follows, and the expressions of the formulas are also adapted from this. The Mathematics of Google PageRank - In Search of the Most Powerful Search Engine Ranking Method I actually bought this in 2013 (8 years ago), and it had been lying on …