## 3 Feature Encoding Methods
### Physicochemical-Based Methods
A k-spaced triad is a set of three amino acids where the middle amino acid is separated from the other two by exactly k residues. For example, in a sequence...A...B...C..., if k = 2, then A...B... C forms a k-spaced triad. The method generates a feature vector by counting the occurrences of all possible k-spaced triads in the sequence. This provides a comprehensive representation of the structural and compositional properties of a sequence. The dimensionality of the feature vector depends on the value of k and the number of possible triads. **SOCNumber**  
The sequence-order-coupling number (SOC) is a feature extraction method used in bioinformatics to capture the sequence-order information of protein sequences[127]. This method is particularly useful for predicting protein properties and functions by considering the spatial arrangement of amino acids within a sequence. The SOC number captures sequence-order information by considering the spatial arrangement of amino acids in the protein sequence. This information is crucial for understanding the structural and functional properties of proteins. The coupling number is calculated for each amino acid position in the sequence, considering its interactions with other amino acids within a specified range. This provides a measure of how each amino acid is influenced by its neighbours. The method generates a feature vector that represents the sequence-order information. This vector can be used as input for machine learning models to predict protein properties and functions. The SOC number is used in various bioinformatics applications, including protein structure prediction, protein function prediction, and AMP design. It helps in capturing the local sequence patterns that are crucial for understanding protein behaviour. We choose a range \(d\) within which the interactions between amino acids are considered. This range can be adjusted on the basis of the specific requirements of the analysis. For each amino acid position i in the sequence, the coupling number SOC(i) is calculated via Equation (6). \[SOC(i)=\sum_{j=1}^{d}\frac{1}{j}\cdot\frac{1}{1+|x_{i}-x_{i+j}|}, \tag{6}\]  
where \(x_{i}\) and \(x_{i+j}\) are the physicochemical properties (e.g., hydrophobicity, charge) of the amino acids at positions \(i\) and \(i+j\), and \(j\) is the distance between the amino acids within the specified range d. The feature vector is generated by concatenating the SOC numbers for all amino acid positions in the sequence. **QSOrder**  
QSOrder is a feature extraction algorithm for AMPs [128]. It is based on the concept of pseudo amino acid composition (PseAAC), which incorporates both sequence-order information and the physicochemical properties of amino acids. The algorithm calculates a series of features that reflect the local sequence-order effects and the global physicochemical properties of the peptides. Specifically, it uses a combination of dipeptide compositions, which captures the frequency of adjacent amino acid pairs, and a set of predefined physicochemical properties to generate a feature vector. This feature vector can then be used as input for machine learning models to predict the antimicrobial activity of peptides. The QSOrder algorithm is particularly useful for identifying key features that distinguish antimicrobial peptides from non-antimicrobial peptides, thereby aiding in the design and discovery of new AMPs. **PSSM**  
The position-specific scoring matrix (PSSM) profile is a powerful tool used in bioinformatics to represent the evolutionary conservation and sequence-specific information of a protein or peptide sequence [129]. The first step in generating a PSSM profile is to perform multiple sequence alignment (MSA) of homologous sequences. This involves aligning a set of sequences that are related by evolution, typically obtained through database searches such as BLAST. The alignment captures the conservation and variability of amino acids at each position across the aligned sequences. From the MSA, a frequency matrix is constructed.