SMAI Homework4-Equation for computing the SVD Solved

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1           Objective Question

Consider the equation for computing the SVD:


SVD decomposition breaks down any invertible transformation into a composition of three geometrical transformations: rotation, scaling, and reflection. True or False?

2           Subjective Question [2 marks]

Consider the tutorial notebook ‘LSI and SVD.ipynb’ and answer the following questions based on your observation.

  1. Briefly explain the plot of the singular values s (or in other words, what can we say about the singular values based on its plot).
  2. Are the U and Vh matrix orthonormal? How will you verify this?

3           Programming Question

Implement a movie recommendation system using SVD. Given the ‘Movielens 100k’ data set, your task is to implement a recommendation system using SVD and compute the root mean squared error of the test set. The excercise notebook ‘Recommender System with SVD.ipynb’ provides you with the starter code.