Consequently, both the MpaveMpave and MapaveMapave matrices are dealt with using the singular value decomposition (SVD). The singular value decomposition of a matrix MM is defined by:M=USVTM=USVTwhere MM stands for the MpaveMpave or the MapaveMapave matrix, UU and VV are orthogonal (unitary), and SS (with the same dimensions as MM) is a 210×210210×210 diagonal matrix. The singular values σiσi are the diagonal entries of the SS matrix and are arranged in descending order:σ1?σ2???σ210?0σ1?σ2???σ210?0The σiσis are the singular values of MM and the columns of UU and VV are the left and right singular
Bleomycin Sulfate of MM. In order to reduce the feature dimension, we select the top 21 (10%) σ1,σ2,…,σ10σ1,σ2,…,σ10 by estimating the cumulative contributions AC(σi)AC(σi) for each σiσi:AC(σi)=∑j=1iσj∑j=1210σj×100%According to the 21 selected singular values, we then extract the corresponding 21
vectors Wi(1?i?21)Wi(1?i?21) (210-dimensional vector) from the corresponding columns of the matrix UU. We obtain two sets of WiWi vectors (each set contains 21 vectors), one for parallel and one for antiparallel:W1p,W2p,…,W21pandW1ap,W2ap,…,W21apThis procedure is anticipated to remove the contributions of small dimension values. The two sets of WiWi vectors are the average encoding vectors, which will be used for β-strand pair encoding.
