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MATH6184Dimensional Reduction:
Principal Component Analysis
Vuong Phan
School of Mathematcal Sciences,
University of Southampton
Office: 54/10005.
Email: t.v.phan@soton.ac.uk
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, Introduction
▶ Dimensional reduction is one of the most important
techniques in ML
▶ The main idea of dimensional reduction is simple
▶ Given a vector of data x ∈ RD , where D is huge. How to
represent x in a smaller dimensional space?
▶ Find a new vector z ∈ RK , where K << D such that the K
most important components are kept.
▶ Two questions
▶ How do we decide the importance of each component?
▶ If the importance of components are similar (or the same),
what components should be deleted?
▶ Principal Component Analysis (PCA) is a simple (but
popular) technique in dimensional reduction relied analysis of
a linear model.
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