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https://archive.ics.uci.edu/ml/datasets/YearPredictionMSD

According to the description given in the above link, the Attribute information specifies "average and covariance over all 'segments', each segment being described by a 12-dimensional timbre vector". So the covariance matrix should have 12*12 = 144 elements. But why is the number of timbre covariance features only 78 ?

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You are right, the covariance matrix should have n^2 elements. However, since cov_{i,j} = cov_{j,i}, there is no need to have a repeated feature cov_{j,i} if cov_{i,j} is already accounted for. Hence there will be only n*(n+1)/2 = 12*13/2 = 78 unique covariances and thus only 78 unique covariance based features (n of those will be variances).

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