Introduction to Linear Algebra by Antonio Campello

In this introductory session on linear algebra, we will explain the main linear algebra concepts and terminology behind some of the core data science algorithms. We will review the concepts of linear combination, vector representation, dot product, matrix decomposition and matrix factorisation. For each concept, we will provide a real-world application including text similarity, image representation, data visualisation and content recommendation.

The objective of the section is twofold: (i) to help the audience with some linear algebra background understand how it applies to data science, and (ii) to help data science practitioners get familiarised with linear algebra concepts so they can better understand core algorithms and their documentation.

• Why do (I think) we need linear algebra in data science?
• Linear algebra for regression
• Vector representations
• The angle between vectors (application to text similarity)
• Matrix representations (application to image representation)
• Matrix decompositions (applications to data visualisation and topic modelling)
• Matrix factorisation (applications to content recommendation)
• When linear is not enough (brief list of non-linear methods).

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