## 2 Materials and Methods
### Proposed Model
If \(M(X)<1\), then \(P(X_{i}|X_{j})<P(X_{i})\) and \(P(X_{j}|X_{i})<P(X_{j})\), which implies \(X_{i}\) and \(X_{j}\) have an indirect (i.e., decrease in value when conditioned) probabilistic similarity in their dependency to one another. Using M(X) in the logarithmic scale will lead to \(M(X)=0\) (region of no mutuality), \(M(X)>0\) (region of increasing mutuality), and \(M(X)<0\) (region of decreasing mutuality), respectively. These also apply to the dissimilarity measure \(H(X)\). \(M(X)\) can be compared with conventional similarity measures in NLP, such as the cosine similarity and hamming distance measures. However, unlike conventional similarity measures which are separated from the classification model, our proposed similarity measure \(M(X)\) and dissimilarity measure \(H(X)\) form part of our classification model; hence, they can be used to explicitly explain the classification results. One advantage of this proposed model in text classification rests on the fact that it enables the breakdown of a high computational classification problem into smaller less computational classification problems. This may be better in terms of conventional models, whose computational complexity increases with the number of features due to the computation of the marginal distribution. The Markov property can also be applied to reduce such complexity in both the conventional and our proposed models. Also, the use of a heterogeneity function or homogeneity function in the model, rather than a marginal function as in conventional probabilistic models, enables clear visibility of the influence of the relationship between the features to the learning and prediction processes of the model. We shall present a mutuality matrix in Section 3 to capture the probabilistic variation in the homogeneous relationship between the features during learning and show how this variation influences the learning and prediction results of the model. Furthermore, this model can be expressed as an algebraic series as follows:  
\[=H(X)\operatorname*{arg\,max}_{k\in\{1,2,\ldots,m\}}\left(\frac{1 }{P(y_{k})^{n-1}}\prod_{i=0}^{n}P(y_{k}|X_{i})\right) \tag{13}\]3  
where \(a_{0}=P(y|X_{0})\), \(a_{1}=P(y|X_{1})\),..., \(a_{n}=P(y|X_{n})\), \(b_{0}=1\), \(b_{1}=\frac{H(X_{1})}{P(y)}\), \(b_{2}=\frac{H(X_{2})}{P(y)}\),..., \(b_{n}=\frac{H(X_{n})}{P(y)}\), \(H(X_{1})=\frac{P(X_{1})}{P(X_{1}|X_{0})}\), \(H(X_{2})=\frac{P(X_{2})}{P(X_{2}|X_{0},x_{1})}\),..., \(H(X_{n})=\frac{P(X_{n})}{P(X_{n}|\bigcap_The first term \(a_{0}\) is considered as a bias partial class posterior in the model, and \(b\) is a combination of the heterogeneity (or mutuality) and regularization values. In general, \(P(y)\) is considered to act as a regularizer to each heterogeneous (or mutual) relationship \(H(X_{i})\), while \(H(X_{i})\) acts as a normalizer of the partial class posterior \(a_{i}\). In this way, \(H(X)\) acts as a normalizer of the merged (integrated or aggregated) class posterior \(f(y|X)\), while \((P(y))^{1-n}\) acts as a regularizer of \(H(X)\). This representation transforms the model into a network of partial actions, as shown in \[=H(X)\operatorname*{arg\,max}_{k\in\{1,2,\ldots,m\}}\left(\frac{1 }{P(y_{k})^{n-1}}\prod_{i=0}^{n}P(y_{k}|X_{i})\right) \tag{13}\]4 Such a representation is useful for mathematical analysis and the network can be expanded to multiple segmentation and partialization layers; however, this will increase its design and computational complexities. This network is different from conventional Bayesian networks (i.e., belief networks) [18; 19] and Markov networks (i.e., Markov random field) [19], which focus on using the marginal distribution of the input features and ignore the heterogeneity between the input features. To avoid computational overload, the conditional expressions between the features can be reduced to fewer dependent features through the application of the Markov property. Also, each term in the series can be normalized using logarithmic normalization to avoid computational underflow.