PSSM distance transformation
It has been reported that dipeptides containing two residues separated by a distance along the sequence are important for protein functionality annotation in the work [65]. Additionally, the PSSM score can approximately measure how frequently an amino acid occurs at a position of a sequence. Accordingly, we present here a PSSM distance transformation (PSSM-DT) method to encode the feature vector representation from the PSSM information. PSSM-DT can transform the PSSM information into uniform numeric representation by approximately measuring the occurrence probabilities of any pairs of amino acid separated by a distance along the sequence in a sequence. PSSM-DT results in two kinds of features: PSSM distance transformation of pairs of same amino acids (PSSM-SDT) and PSSM distance transformation of pairs of different amino acids (PSSM-DDT). The PSSM-SDT features approximately measure the occurrence probabilities of pairs of same amino acids separated by a distance of lg along the sequence in a sequence, which can be calculated as below
(3)  PSSM - SDT(  i , l g ) =   ∑  j = 1  L - l g    S  i , j   * S  i , j + l g   / ( L - l g  )
where i is one type of the amino acid, L is the length of the sequence, Si,j is the PSSM score of amino acid j at position i. In such a way, 20*LG is the number of PSSM-SDT features, where LG is the maximum value of lg (lg = 1, 2,...,LG).
The PSSM-DDT features approximately measures the occurrence probabilities of pairs of different amino acids separated by a distance of lg along the sequence, which can be calculated by:
(4)  PSSM - DDT(  i 1 , i 2 , l g ) =   ∑  j = 1  L - l g    S  i 1 , j   * S  i 2 , j + l g   / ( L - l g  )
where i1 and i2 refer to two different types amino acids. Similarly, the total number of PSSM-DDT features can be calculated as 380*LG.
PSSM-DT is the combination of variable PSSM-SDT and PSSM-DDT. Thus a sequence can be transformed into a uniform feature vector with a fixed dimension of 400*LG by using variable PSSM-DT from its PSSM profile.