Understanding about PCA and Scree Plot

1. PRINCIPLE COMPONENT ANALYSIS
ASHUTOSH GAURAV
DEPARTMENT OF STATISTICS
CENTRAL UNIVERSITY OF SOUTH BIHAR

2. CONTENT
• INTRODUCTION
• APPLICATION
• TECHNIQUE
• ADVANTAGES & DISADANTAGES
• REFERENCES

3. INTRODUCTION
• It is introduce by Pearson (1901) and independently by Hotelling
(1933)
• Principle Component analysis (PCA) is a way to reduce data
dimensionality

4. APPLICATION
• Data reduction and Interpretation
• PCA is commonly used in the social sciences, market research and
Industries that use large data set
• Face recognition
• Principle component scores can be used as independent predictors in
regressions
• Outlier detection

5. TECHNIQUE
PCA is based the following assumptions
• The assumption that the dimensionality of data can be efficiently
reduced by linear transformation
• The assumption that most information is contained in those direction
where input data variance is maximum

6. • Idea of the method is to describe the variation of a set of multivariate
data in terms of a set of uncorrelated variables.
• The new variables are derived in decreasing order of importance.
• The first PCA accounts for as much as variation possible of the
variation in the original data.
• The second component is chosen to account for as much as possible in
the remaining variation subject to being with the first component.

7. Data set

8. Methods

9. Variance Covariance Matrix
Eigen values and proportion

10. Score and Scree plot

11. ADVANTAGES & DISADANTAGES
Advantages
• Most widely used method of data reduction (or analysis)
• PCA summarise the data with little information
• Easy to compute
• It is useful for both qualitative and quantitative
• Principle component analysis can help locate outlier in a higher dimensional
space
Disadvantages
• Require much mathematical calculations
• Sometime it is difficult to compute covariance matrix

12. REFERENCES
• Richard, D.W. Wichern (2002). Applied Multivariate Statistical
Analysis, fifth edition (PHI Learning)
• Jackson, J.E (1991). A user’s Guide to Principal Component (Wiley).
• Jolliffe, I.T. (2002). Principal Component Analysis, second edition
(Springer).

13. THANK YOU