## 3 Feature Encoding Methods
### Physicochemical-Based Methods
PseKRAAC incorporates three crucial parameters that describe protein composition, making it a versatile tool for computational proteomics and protein sequence analysis. Amino acids are grouped into clusters on the basis of their physicochemical properties. This reduction simplifies the complexity of protein sequences, making them easier to analyse. Flexible parameterisation:Users can select from various reduced amino acid alphabets and adjust parameters such as the type of analysis (gap or lambda correlation), the number of gaps or lambda values, and the k-mer size. PseKRAAC is freely available as a web server, allowing users to easily generate different modes of PseKRAAC tailored to their specific needs. By incorporating three crucial parameters that describe protein composition, PseKRAAC provides more capability for protein research. This tool is anticipated to become a very useful resource in computational proteomics and protein sequence analysis. **CKSAAGP**  
The composition of k-spaced amino acid group pairs (CKSAAGP) is a sophisticated feature extraction method used in bioinformatics to analyse peptide and protein sequences [122; 123]. This method extends the traditional amino acid composition by considering the spatial relationships between amino acids within a sequence, specifically focusing on pairs of amino acids that are separated by a fixed number of positions (k-spaced). Amino acids are categorised into groups on the basis of their physicochemical properties, such as hydrophobicity, charge, size, and polarity. The method of k-spaced pairs considers pairs of amino acids that are separated by a fixed number of positions (k) within the sequence. For example, if k=2, the method considers pairs of amino acids that are separated by exactly two positions. For a given sequence, all possible k-spaced pairs are identified and grouped on the basis of their physicochemical properties. The frequency or proportion of each group of k-spaced pairs is calculated. This provides a detailed representation of the sequence, capturing both the composition and the spatial relationships between amino acids. CKSAAGP is calculated by identifying and counting all possible k-spaced pairs within the sequence and then grouping them on the basis of their physicochemical properties. The formula for CKSAAGP can be expressed as Equation (4). \[CKSAAGP=\sum_{i=1}^{L-k-1}Group(S_{i},S_{i+k+1}), \tag{4}\]  
where \(L\) is the length of the sequence \(S\), \(S_{i}\) and \(S_{i+k+1}\) are the amino acids at positions \(i\) and \(i+k+1\) in the sequence, and \(Group(S_{i},S_{i+k+1})\) is the group to which the pair \((S_{i},S_{i+k+1})\) belongs. **NMBroto**  
Normalised Moreau-Broto autocorrelation (NMBroto) is a type of autocorrelation descriptor used in bioinformatics to analyse the distribution of amino acid properties along a protein sequence [124]. It captures the correlation between the properties of amino acids at different positions in a sequence, providing insights into the structural and functional characteristics of proteins. The NMBroto descriptor is calculated on the basis of the distribution of specific physicochemical properties of amino acids along the protein sequence. The formula for NMBroto is given by Equation (5). \[NMBroto(d)=\frac{1}{N-d}\sum_{i=1}^{N-d}P_{i}\cdot P_{i+d}, \tag{5}\]  
where \(d\) is the lag parameter, which represents the distance between the amino acids being compared; \(P_{i}\) and \(P_{i+d}\) are the properties of the amino acids at positions \(i\) and \(i+d\), respectively; and \(N\) is the length of the protein sequence. **KST triad**  
The k-spaced conjoint triad (KST triad) is a feature extraction method used in bioinformatics to analyse protein sequences [125; 126]. It extends the concept of the conjoint triad descriptor by considering not only continuous amino acid triplets but also those that are separated by a fixed number of residues (k-spaced). KST triad considers both continuous and k-spaced triads.