SVD for Low-Rank Approximation and Pattern Recognition

A collection of scientific computing experiments (view repo), held as part of the course “Scientific Computing for Data Analysis - 1TD352” at Uppsala University.

In this project, the usage of Singular Value Decomposition is demonstrated, in approximating a matrix representation, e.g. a collection of handwritten images from the MNIST-2D dataset, and conducting further analysis using the U component from the SVD of training data. A pattern recognition problem was tackled, where varying k-rank approximations were done, and using those k columns from the U matrix, a matrix of test examples of digits were tested on the U of training data.

• The behaviour of the classification accuracy while improving the degree of approximation k was investigated, and most of the features could be captured with k=20, with substantial accuracy.
• Interestingly, the handwriting complexity (number of curves, edges, strokes) of the digits is, arguably, also a factor in how well the k number of columns from U suffice in classifying accurately for unseen test images.

The numerical computations were done using the NumPy library, in Python.