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PCA : Principal Component 
Analysis 
Author : Nalini Yadav 
Under Guidance of Prof. K. Rajeshwari
PCA 
ï‚› A backbone of modern data analysis. 
ï‚› A black box that is widely used but poorly 
understood. 
ï‚› It is a mathematical tool from applied linear 
algebra. 
ï‚› It is a simple, non-parametric method of 
extracting relevant information from confusing 
data sets. 
ï‚› It provides a roadmap for how to reduce a 
complex data set to a lower dimension
Background knowledge 
Va r i a n c e 
Covariance
Background knowledge 
Cova r i a n c e Matrix 
Eigenvalue
Background knowledge 
 Finding the roots of | A – λ .I| will give the 
eigenvalues and for each of these 
eigenvalues there will be an eigenvector
Background knowledge
Background knowledge 
ï‚› Therefore the first eigenvector is any column 
vector in which the two elements have equal 
magnitude and opposite sign.
Background knowledge
PCA : Example 
ï‚›We collected m parameters about 100 
students 
ï‚›Height 
ï‚›Weight 
ï‚›Hair color 
ï‚›Average grade 
… 
ï‚›We want to find the most important 
parameters that best describe a student.
PCA : Example
PCA : Example 
ï‚› Which parameters can we ignore? 
ï‚› Constant parameter (number of heads) 
1,1,...,1. 
ï‚› Constant parameter with some noise - (thickness of 
hair) 
0.003, 0.005,0.002,....,0.0008 -> low variance 
ï‚› Parameter that is linearly dependent on other 
parameters (head size and height) 
Z= aX + bY
PCA : Example 
ï‚› Change of Basic
PCA : Example
PCA : Example
PCA : Example
PCA : Example
PCA : Example
PCA : Example
PCA : Example
PCA : Example
PCA : Example
PCA : Example
PCA : Example
PCA : Example
PCA : Example
Thank You

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