主成分分析4，双语.ppt

Chapter 5 ponents Analysis (PCA)
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Presentation Outline
w What is PCA?
w Geometrical approach to PCA
w Analytical approach to PCA
w Properties of PCA
w How to determine the number of PC?
w How to interpret the PC?
w Use of PC scores
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reasons for using ponents analysis
Too Many Variables
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Stone use 1929一1938 data in USA, and receive 17 variables which describe e-pay. He used ponent analysis and got three new variables F1、F2、F3. F1, total e;F2,total e increase ratio;F3,economy increase or decrease. These new variable can use three variables (I、I、t )which can be measured directly.
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F1
F2
F3
i
i
t
F1
1
F2
0
1
F3
0
0
1
i

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i
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l
t
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1
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Solutions
􀂄 Eliminate some redundant variables.
– May lose important information that was uniquely reflected in the eliminated variables.
􀂄 posite scores from variables (sum or average).
– Lost variability among the variables
– Multiple scale scores may still be collinear
􀂄 Create weighted binations of variables while retaining most of the variability in the data.
– Fewer variables; little or no lost variation
– No collinear scales.
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An Easy Choice
To retain most of the information in the data while reducing the number of variables you must deal with, try ponents analysis.
􀂄 Most of the variability in the original data can be retained.
but…
􀂄 Components may not be directly interpretable.
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What is PCA?(什么是主成分分析)
PCA is a technique for forming new variables which are posites of the original variables. The new variables are called ponents(PRIN’s).
The maximum number of PRIN’s that can be formed is equal to the number of original variables. Usually the first few PRIN’s represent most of the information in the original variables and can replace the original variables and hence achieve data reduction, which is the main objective of PCA
The PRIN’s are uncorrelated among themse