Canonical_Correlation_Analysis_Lecture

Canonical_Correlatio - Canonical Correlation Analysis The objective of CCA is to identify and measure the association between two sets of random

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Canonical Correlation Analysis The objective of CCA is to identify and measure the association between two sets of random variables using a specific matrix function of the variance-covariance matrix of these variables. Σ Σ Σ Σ = 22 21 12 11 2 1 2 1 , ~ µ N X X X Σ Σ Σ Σ 22 21 12 11 2 1 ˆ ˆ ˆ ˆ , ˆ ˆ The pair of a sample canonical variables and maximizes the sample correlation th i ) ˆ , ˆ ( i i w v X a v i i ' ˆ ˆ = X b w i i ' ˆ ˆ = i x x i i x x i i x x i w v b b a a b a r i i ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 2 2 1 1 2 1 ' ' ' , Σ Σ Σ = Hypothesis Test on the Canonical Correlations 22 11 22 11 1 ˆ ˆ ˆ ˆ ˆ ˆ R R R = Σ Σ Σ = Λ Reject if 2 ) 1 )( 1 ( , ) log( + + > Λ r q p r q r a α χ Canonical Correlation Analysis Lecture.doc 1

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options ls=64 ps=450 nodate nonumber; data livestock; input year priceb priceh consumpb consumph ; cards; 1921 8.41 8.73 55.7 65.0 1922 8.68 9.26 59.2 65.9 1923 8.22 6.60 59.8 74.5 1924 8.24 7.23 59.9 74.7 1925 8.64 10.04 60.0 67.3 1926 7.63 9.95 60.7 64.6 1927 9.50 8.32 54.9 68.2 1928 11.41 7.56 49.0 71.3 1929 10.49 7.93 49.8 69.8 1930 9.84 8.51 48.9 67.0 1931 9.20 7.03 48.5 68.3 1932 10.58 6.05 46.7 70.6 1933 8.92 6.48 51.4 69.9 1934 9.52 6.55 55.8 64.2 1935 12.76 11.53 53.5 48.6 1936 9.47 10.62 58.8 55.6 1937 11.37 9.93 55.3 55.9 1938 10.10 8.70 54.5 58.3 1939 9.88 6.66 54.5 64.4 1940 9.91 5.42 55.2 72.5 ;;;;;;;; proc cancorr data=livestock b int out=cscores outstat=canstat vprefix=priscor wprefix=conscor ; var priceb priceh; with consumpb consumph ; title1 'Canonical Correlation Analysis: Prices and Meat Consumption' ; proc print data=cscores; title2 'Canonical Scores'; proc print data=canstat; title2 'Canonical Correlation Statistics'; run; Canonical Correlation Analysis Lecture.doc 2
Univariate Multiple Regression Statistics for Predicting the VAR Variables from the WITH Variables Raw Regression Coefficients priceb priceh consumpb -0.17928782 0.10803736 consumph -0.10514134 -0.18192221 Intercept 26.34996534 14.23155908 Canonical Correlation Analysis: Prices and Meat Consumption The CANCORR Procedure Univariate Multiple Regression Statistics for Predicting the WITH Variables from the VAR Variables Raw Regression Coefficients consumpb consumph priceb -2.2534707 -2.0032757 priceh 1.2251962 -2.7563105 Intercept 66.3336021 107.6162849 Adjusted Approximate Squared Canonical Canonical Standard Canonical Correlation Correlation Error Correlation 1 0.846663 0.821064 0.064962 0.716838 2 0.729116 . 0.107456 0.531610 Eigenvalues of Inv(E)*H = CanRsq/(1-CanRsq) Eigenvalue Difference Proportion Cumulative 1 2.5315 1.3966 0.6904 0.6904 2 1.1350 0.3096 1.0000 Canonical Correlation Analysis Lecture.doc

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This note was uploaded on 12/26/2010 for the course CPSC 499 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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Canonical_Correlatio - Canonical Correlation Analysis The objective of CCA is to identify and measure the association between two sets of random

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