A covariance matrix of a collection of data points x_i R^d can be used to analyz

Question

A covariance matrix of a collection of data points x_i R^d can be used to analyze the variability of each feature and degree of correlation between different features, where d is the number of features in each data point. In the following table, match each covariance matrix with its corresponding analysis. sigma = (9.2 -2.6 -2.6 21.5) sigma = (8.5 -0.7 -0.7 1.3) sigma = 17.2 10.2 10.2 7.6) sigma = (11.8 3.5 4.8 3.5 8.2 1.2 4.8 1.2 8.9) sigma = (10.3 1.1 0.08 1.1 0.8 0.2 0.08 0.2 0.9) sigma = (10.3 8.8 7.6 8.8 8.01 6.4 7.6 6.4 6.6) This data has low redundancy due to low covariance; both features change in the opposite directions due to negative covariance, the second feature has lower variance than the first one. This data has low redundancy due to low covariance, features change in the same directions due to positive covariance. The first feature has relatively higher variance than the other two. This data has low redundancy due to low covariance; features change in the same directions due to positive covariance, the first feature has higher variance than the others. This data has low redundancy due to low covariance; both features change in the opposite directions due to negative covariance, the second feature has relatively higher variance than the first one. The given dataset has high redundancy due to large covariance, in addition features change in the same direction due to positive covariance. The given dataset has high redundancy due to large covariance, in addition both features changes in the same direction due to positive covariance.

Explanation / Answer

Ans:   

Left Right

a 4

b 1

c 6

d 3

e 2

f 5

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